Package 'ergm'

Title: Fit, Simulate and Diagnose Exponential-Family Models for Networks
Description: An integrated set of tools to analyze and simulate networks based on exponential-family random graph models (ERGMs). 'ergm' is a part of the Statnet suite of packages for network analysis. See Hunter, Handcock, Butts, Goodreau, and Morris (2008) <doi:10.18637/jss.v024.i03> and Krivitsky, Hunter, Morris, and Klumb (2023) <doi:10.18637/jss.v105.i06>.
Authors: Mark S. Handcock [aut], David R. Hunter [aut], Carter T. Butts [aut], Steven M. Goodreau [aut], Pavel N. Krivitsky [aut, cre] , Martina Morris [aut], Li Wang [ctb], Kirk Li [ctb], Skye Bender-deMoll [ctb], Chad Klumb [ctb], Michał Bojanowski [ctb] , Ben Bolker [ctb], Christian Schmid [ctb], Joyce Cheng [ctb], Arya Karami [ctb], Adrien Le Guillou [ctb]
Maintainer: Pavel N. Krivitsky <[email protected]>
License: GPL-3 + file LICENSE
Version: 4.7.5
Built: 2024-11-07 13:42:49 UTC
Source: CRAN

Help Index

A meta-constraint indicating handling of arbitrary dyadic constraints

Description

This is a flag in the proposal table indicating that the proposal can enforce arbitrary combinations of dyadic constraints. It cannot be invoked directly by the user.

See Also

ergmConstraint for index of constraints and hints currently visible to the package.

Keywords

None

Absolute difference in nodal attribute

Description

This term adds one network statistic to the model equaling the sum of abs(attr[i]-attr[j])^pow for all edges ⁠(i,j)⁠ in the network.

Usage

# binary: absdiff(attr,
#                 pow=1)

# valued: absdiff(attr,
#                 pow=1,
#                 form="sum")

Arguments

attr

a vertex attribute specification (see Specifying Vertex attributes and Levels (?nodal_attributes) for details.)
pow

power to which to take the absolute difference
form

character how to aggregate tie values in a valued ERGM

Note

ergm versions 3.9.4 and earlier used different arguments for this term. See ergm-options for how to invoke the old behaviour.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

directed, dyad-independent, quantitative nodal attribute, undirected, binary, valued

Categorical absolute difference in nodal attribute

Description

This term adds one statistic for every possible nonzero distinct value of abs(attr[i]-attr[j]) in the network. The value of each such statistic is the number of edges in the network with the corresponding absolute difference.

Usage

# binary: absdiffcat(attr,
#                 base=NULL,
#                 levels=NULL)

# valued: absdiffcat(attr,
#                 base=NULL,
#                 levels=NULL,
#                 form="sum")

Arguments

attr

a vertex attribute specification (see Specifying Vertex attributes and Levels (?nodal_attributes) for details.)
base

deprecated
levels

specifies which nonzero difference to include in or exclude from the model. (See Specifying Vertex attributes and Levels (?nodal_attributes) for details.)
form

character how to aggregate tie values in a valued ERGM

Note

ergm versions 3.9.4 and earlier used different arguments for this term. See ergm-options for how to invoke the old behaviour.

The argument base is retained for backwards compatibility and may be removed in a future version. When both base and levels are passed, levels overrides base.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

categorical nodal attribute, directed, dyad-independent, undirected, binary, valued

Alternating kk-star

Description

Add one network statistic to the model equal to a weighted alternating sequence of kk-star statistics with weight parameter lambda.

Usage

# binary: altkstar(lambda,
#                 fixed=FALSE)

Arguments

lambda

weight parameter to model
fixed

indicates whether the decay parameter is fixed at the given value, or is to be fit as a curved exponential family model (see Hunter and Handcock, 2006). The default is FALSE, which means the scale parameter is not fixed and thus the model is a CEF model.

Details

This is the version given in Snijders et al. (2006). The gwdegree and altkstar produce mathematically equivalent models, as long as they are used together with the edges (or kstar(1)) term, yet the interpretation of the gwdegree parameters is slightly more straightforward than the interpretation of the altkstar parameters. For this reason, we recommend the use of the gwdegree instead of altkstar. See Section 3 and especially equation (13) of Hunter (2007) for details.

Note

This term can only be used with undirected networks.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

categorical nodal attribute, curved, undirected, binary

ANOVA for ERGM Fits

Description

Compute an analysis of variance table for one or more ERGM fits.

Usage

## S3 method for class 'ergm'
anova(object, ..., eval.loglik = FALSE)

## S3 method for class 'ergmlist'
anova(object, ..., eval.loglik = FALSE)

Arguments

object, ...

objects of ergm, usually, a result of a call to ergm().
eval.loglik

a logical specifying whether the log-likelihood will be evaluated if missing.

Details

Specifying a single object gives a sequential analysis of variance table for that fit. That is, the reductions in the residual sum of squares as each term of the formula is added in turn are given in the rows of a table, plus the residual sum of squares.

The table will contain F statistics (and P values) comparing the mean square for the row to the residual mean square.

If more than one object is specified, the table has a row for the residual degrees of freedom and sum of squares for each model. For all but the first model, the change in degrees of freedom and sum of squares is also given. (This only make statistical sense if the models are nested.) It is conventional to list the models from smallest to largest, but this is up to the user.

If any of the objects do not have estimated log-likelihoods, produces an error, unless eval.loglik=TRUE.

Value

An object of class "anova" inheriting from class "data.frame".

Warning

The comparison between two or more models will only be valid if they are fitted to the same dataset. This may be a problem if there are missing values and 's default of na.action = na.omit is used, and anova.ergmlist() will detect this with an error.

See Also

The model fitting function ergm(), anova(), logLik.ergm() for adding the log-likelihood to an existing ergm object.

Examples

data(molecule)
molecule %v% "atomic type" <- c(1,1,1,1,1,1,2,2,2,2,2,2,2,3,3,3,3,3,3,3)
fit0 <- ergm(molecule ~ edges)
anova(fit0)
fit1 <- ergm(molecule ~ edges + nodefactor("atomic type"))
anova(fit1)

fit2 <- ergm(molecule ~ edges + nodefactor("atomic type") +  gwesp(0.5,
  fixed=TRUE), eval.loglik=TRUE) # Note the eval.loglik argument.
anova(fit0, fit1)
anova(fit0, fit1, fit2)

Approximate Hotelling T^2-Test for One or Two Population Means

Description

A multivariate hypothesis test for a single population mean or a difference between them. This version attempts to adjust for multivariate autocorrelation in the samples.

Usage

approx.hotelling.diff.test(
  x,
  y = NULL,
  mu0 = 0,
  assume.indep = FALSE,
  var.equal = FALSE,
  ...
)

Arguments

x

a numeric matrix of data values with cases in rows and variables in columns.
y

an optinal matrix of data values with cases in rows and variables in columns for a 2-sample test.
mu0

an optional numeric vector: for a 1-sample test, the poulation mean under the null hypothesis; and for a 2-sample test, the difference between population means under the null hypothesis; defaults to a vector of 0s.
assume.indep

if TRUE, performs an ordinary Hotelling's test without attempting to account for autocorrelation.
var.equal

for a 2-sample test, perform the pooled test: assume population variance-covariance matrices of the two variables are equal.
...

additional arguments, passed on to spectrum0.mvar(), etc.; in particular, ⁠order.max=⁠ can be used to limit the order of the AR model used to estimate the effective sample size.

Value

An object of class htest with the following information:

statistic

The T2T^2 statistic.
parameter

Degrees of freedom.
p.value

P-value.
method

Method specifics.
null.value

Null hypothesis mean or mean difference.
alternative

Always "two.sided".
estimate

Sample difference.
covariance

Estimated variance-covariance matrix of the estimate of the difference.
covariance.x

Estimated variance-covariance matrix of the estimate of the mean of x.
covariance.y

Estimated variance-covariance matrix of the estimate of the mean of y.

It has a print method print.htest().

Note

For mcmc.list input, the variance for this test is estimated with unpooled means. This is not strictly correct.

References

Hotelling, H. (1947). Multivariate Quality Control. In C. Eisenhart, M. W. Hastay, and W. A. Wallis, eds. Techniques of Statistical Analysis. New York: McGraw-Hill.

See Also

t.test()

Create a Simple Random network of a Given Size

Description

as.network.numeric() creates a random Bernoulli network of the given size as an object of class network.

Usage

## S3 method for class 'numeric'
as.network(
  x,
  directed = TRUE,
  hyper = FALSE,
  loops = FALSE,
  multiple = FALSE,
  bipartite = FALSE,
  ignore.eval = TRUE,
  names.eval = NULL,
  edge.check = FALSE,
  density = NULL,
  init = NULL,
  numedges = NULL,
  ...
)

Arguments

x

count; the number of nodes in the network
directed

logical; should edges be interpreted as directed?
hyper

logical; are hyperedges allowed? Currently ignored.
loops

logical; should loops be allowed? Currently ignored.
multiple

logical; are multiplex edges allowed? Currently ignored.
bipartite

count; should the network be interpreted as bipartite? If present (i.e., non-NULL) it is the count of the number of actors in the bipartite network. In this case, the number of nodes is equal to the number of actors plus the number of events (with all actors preceding all events). The edges are then interpreted as nondirected.
ignore.eval

logical; ignore edge values? Currently ignored.
names.eval

optionally, the name of the attribute in which edge values should be stored. Currently ignored.
edge.check

logical; perform consistency checks on new edges?
density

numeric; the probability of a tie for Bernoulli networks. If neither density nor init is given, it defaults to the number of nodes divided by the number of dyads (so the expected number of ties is the same as the number of nodes.)
init

numeric; the log-odds of a tie for Bernoulli networks. It is only used if density is not specified.
numedges

count; if present, sample the Bernoulli network conditional on this number of edges (rather than independently with the specified probability).
...

additional arguments

Details

The network will not have vertex, edge or network attributes. These can be added with operators such as %v%, %n%, %e%.

Value

An object of class network

References

Butts, C.T. 2002. “Memory Structures for Relational Data in R: Classes and Interfaces” Working Paper.

See Also

network

Examples

# Draw a random directed network with 25 nodes
g <- network(25)

# Draw a random undirected network with density 0.1
g <- network(25, directed=FALSE, density=0.1)

# Draw a random bipartite network with 4 actors and 6 events and density 0.1
g <- network(10, bipartite=4, directed=FALSE, density=0.1)

# Draw a random directed network with 25 nodes and 50 edges
g <- network(25, numedges=50)

Asymmetric dyads

Description

This term adds one network statistic to the model equal to the number of pairs of actors for which exactly one of (i→j)(i{\rightarrow}j) or (j→i)(j{\rightarrow}i) exists.

Usage

# binary: asymmetric(attr=NULL, diff=FALSE, keep=NULL, levels=NULL)

Arguments

attr

quantitative attribute (see Specifying Vertex attributes and Levels (?nodal_attributes) for details.) If specified, only symmetric pairs that match on the vertex attribute are counted.
diff

Used in the same way as for the nodematch term. (See nodematch (ergmTerm?nodematch) for details.)
keep

deprecated
level

Used in the same way as for the nodematch term. (See nodematch (ergmTerm?nodematch) for details.)

Note

This term can only be used with directed networks.

The argument keep is retained for backwards compatibility and may be removed in a future version. When both keep and levels are passed, levels overrides keep.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

directed, dyad-independent, triad-related, binary

Number of dyads with values greater than or equal to a threshold

Description

Adds the number of statistics equal to the length of threshold equaling to the number of dyads whose values equal or exceed the corresponding element of threshold .

Usage

# valued: atleast(threshold=0)

Arguments

threshold

vector of numerical values

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

directed, dyad-independent, undirected, valued

Number of dyads with values less than or equal to a threshold

Description

Adds the number of statistics equal to the length of threshold equaling to the number of dyads whose values equal or are exceeded by the corresponding element of threshold .

Usage

# valued: atmost(threshold=0)

Arguments

threshold

a vector of numerical values

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

directed, dyad-independent, undirected, valued

Edge covariate by attribute pairing

Description

This term adds one statistic to the model, equal to the sum of the covariate values for each edge appearing in the network, where the covariate value for a given edge is determined by its mixing type on attr. Undirected networks are regarded as having undirected mixing, and it is assumed that mat is symmetric in that case.

This term can be useful for simulating large networks with many mixing types, where nodemix would be slow due to the large number of statistics, and edgecov cannot be used because an adjacency matrix would be too big.

Usage

# binary: attrcov(attr, mat)

Arguments

attr

a vertex attribute specification (see Specifying Vertex attributes and Levels (?nodal_attributes) for details.)
mat

a matrix of covariates with the same dimensions as a mixing matrix for attr

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

directed, dyad-independent, undirected, binary

Wrap binary terms for use in valued models

Description

Wraps binary ergm terms for use in valued models, with formula specifying which terms are to be wrapped and form specifying how they are to be used and how the binary network they are evaluated on is to be constructed.

Usage

# valued: B(formula, form)

Arguments

formula

a one-sided ergm()-style formula whose RHS contains the binary ergm terms to be evaluated. Which terms may be used depends on the argument form
form

One of three values:

  • "sum": see section "Generalizations of binary terms" in ergmTerm help; all terms in formula must be dyad-independent.

  • "nonzero": section "Generalizations of binary terms" in ergmTerm help; any binary ergm terms may be used in formula .

  • a one-sided formula value-dependent network. form must contain one "valued" ergm term, with the following properties:

    • dyadic independence;

    • dyadwise contribution of either 0 or 1; and

    • dyadwise contribution of 0 for a 0-valued dyad.

    Formally, this means that it is expressable as

    g(y)=∑i,jfi,j(yi,j),g(y) = \sum_{i,j} f_{i,j}(y_{i,j}),

    where for all ii, jj, and yy, fi,j(yi,j)f_{i,j}(y_{i,j}) is either 0 or 1 and, in particular, fi,j(0)=0f_{i,j}(0)=0.

    Examples of such terms include nonzero , ininterval() , atleast() , atmost() , greaterthan() , lessthen() , and equalto() .

    Then, the value of the statistic will be the value of the statistics in formula evaluated on a binary network that is defined to have an edge if and only if the corresponding dyad of the valued network adds 1 to the valued term in form .

Details

For example, B(~nodecov("a"), form="sum") is equivalent to nodecov("a", form="sum") and similarly with form="nonzero" .

When a valued implementation is available, it should be preferred, as it is likely to be faster.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

operator, valued

Concurrent node count for the first mode in a bipartite network

Description

This term adds one network statistic to the model, equal to the number of nodes in the first mode of the network with degree 2 or higher. The first mode of a bipartite network object is sometimes known as the "actor" mode. This term can only be used with undirected bipartite networks.

Usage

# binary: b1concurrent(by=NULL, levels=NULL)

Arguments

by

optional argument specifying a vertex attribute (see Specifying Vertex attributes and Levels (?nodal_attributes) for details). It functions just like the by argument of the b1degree term. Without the optional argument, this statistic is equivalent to b1mindegree(2) .
levels

TODO (See Specifying Vertex attributes and Levels (?nodal_attributes) for details.)

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

bipartite, categorical nodal attribute, undirected, binary

Main effect of a covariate for the first mode in a bipartite network

Description

This term adds a single network statistic for each quantitative attribute or matrix column to the model equaling the total value of attr(i) for all edges (i,j)(i,j) in the network. This term may only be used with bipartite networks. For categorical attributes, see b1factor .

Usage

# binary: b1cov(attr)

# valued: b1cov(attr, form="sum")

Arguments

attr

a vertex attribute specification (see Specifying Vertex attributes and Levels (?nodal_attributes) for details.)
form

character how to aggregate tie values in a valued ERGM

Note

ergm versions 3.9.4 and earlier used different arguments for this term. See ergm-options for how to invoke the old behaviour.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

bipartite, dyad-independent, frequently-used, quantitative nodal attribute, undirected, binary, valued

Degree range for the first mode in a bipartite network

Description

This term adds one network statistic to the model for each element of from (or to ); the iith such statistic equals the number of nodes of the first mode ("actors") in the network of degree greater than or equal to from[i] but strictly less than to[i] , i.e. with edge count in semiopen interval ⁠[from,to)⁠ .

This term can only be used with bipartite networks; for directed networks see idegrange and odegrange . For undirected networks, see degrange , and see b2degrange for degrees of the second mode ("events").

Usage

# binary: b1degrange(from, to=`+Inf`, by=NULL, homophily=FALSE, levels=NULL)

Arguments

from, to

vectors of distinct integers. If one of the vectors have length 1, it is recycled to the length of the other. Otherwise, it must have the same length.
by, levels, homophily

the optional argument by specifies a vertex attribute (see Specifying Vertex attributes and Levels (?nodal_attributes) for details). If this is specified and homophily is TRUE , then degrees are calculated using the subnetwork consisting of only edges whose endpoints have the same value of the by attribute. If by is specified and homophily is FALSE (the default), then separate degree range statistics are calculated for nodes having each separate value of the attribute. levels selects which levels of by' to include.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

bipartite, undirected, binary

Degree for the first mode in a bipartite network

Description

This term adds one network statistic to the model for each element in d ; the iith such statistic equals the number of nodes of degree d[i] in the first mode of a bipartite network, i.e. with exactly d[i] edges. The first mode of a bipartite network object is sometimes known as the "actor" mode.

Usage

# binary: b1degree(d, by=NULL, levels=NULL)

Arguments

d

a vector of distinct integers.
by, levels, homophily

the optional argument by specifies a vertex attribute (see Specifying Vertex attributes and Levels (?nodal_attributes) for details). If this is specified and homophily is TRUE , then degrees are calculated using the subnetwork consisting of only edges whose endpoints have the same value of the by attribute. If by is specified and homophily is FALSE (the default), then separate degree range statistics are calculated for nodes having each separate value of the attribute. levels selects which levels of by' to include.

Note

This term can only be used with undirected bipartite networks.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

bipartite, categorical nodal attribute, frequently-used, undirected, binary

Preserve the actor degree for bipartite networks

Description

For bipartite networks, preserve the degree for the first mode of each vertex of the given network, while allowing the degree for the second mode to vary.

Usage

# b1degrees

See Also

ergmConstraint for index of constraints and hints currently visible to the package.

Keywords

bipartite

Dyadwise shared partners for dyads in the first bipartition

Description

This term adds one network statistic to the model for each element in d ; the iith such statistic equals the number of dyads in the first bipartition with exactly d[i] shared partners. (Those shared partners, of course, must be members of the second bipartition.) This term can only be used with bipartite networks.

Usage

# binary: b1dsp(d)

Arguments

d

a vector of distinct integers.

Note

This term takes an additional term option (see options?ergm), cache.sp, controlling whether the implementation will cache the number of shared partners for each dyad in the network; this is usually enabled by default.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

bipartite, undirected, binary

Factor attribute effect for the first mode in a bipartite network

Description

This term adds multiple network statistics to the model, one for each of (a subset of) the unique values of the attr attribute. Each of these statistics gives the number of times a node with that attribute in the first mode of the network appears in an edge. The first mode of a bipartite network object is sometimes known as the "actor" mode.

Usage

# binary: b1factor(attr, base=1, levels=-1)

# valued: b1factor(attr, base=1, levels=-1, form="sum")

Arguments

attr

a vertex attribute specification (see Specifying Vertex attributes and Levels (?nodal_attributes) for details.)
base

deprecated
levels

this optional argument controls which levels of the attribute attributes and Levels (?nodal_attributes) for details.)
form

character how to aggregate tie values in a valued ERGM

Note

To include all attribute values is usually not a good idea, because the sum of all such statistics equals the number of edges and hence a linear dependency would arise in any model also including edges. The default, levels=-1, is therefore to omit the first (in lexicographic order) attribute level. To include all levels, pass either levels=TRUE (i.e., keep all levels) or levels=NULL (i.e., do not filter levels).

The argument base is retained for backwards compatibility and may be removed in a future version. When both base and levels are passed, levels overrides base.

This term can only be used with undirected bipartite networks.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

bipartite, categorical nodal attribute, dyad-independent, frequently-used, undirected, binary, valued

Minimum degree for the first mode in a bipartite network

Description

This term adds one network statistic to the model for each element in d ; the ii th such statistic equals the number of nodes in the first mode of a bipartite network with at least degree d[i] . The first mode of a bipartite network object is sometimes known as the "actor" mode.

Usage

# binary: b1mindegree(d)

Arguments

d

a vector of distinct integers.

Note

This term can only be used with undirected bipartite networks.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

bipartite, undirected, binary

Nodal attribute-based homophily effect for the first mode in a bipartite network

Description

This term is introduced in Bomiriya et al (2014). With the default alpha and beta values, this term will simply be a homophily based two-star statistic. This term adds one statistic to the model unless diff is set to TRUE , in which case the term adds multiple network statistics to the model, one for each of (a subset of) the unique values of the attr attribute.

Usage

# binary: b1nodematch(attr, diff=FALSE, keep=NULL, alpha=1, beta=1, byb2attr=NULL,
#                     levels=NULL)

Arguments

attr

a vertex attribute specification (see Specifying Vertex attributes and Levels (?nodal_attributes) for details.)
diff

by default, one statistic will be added to the model. If diff is set to TRUE, one statistic will be added for each unique value of the attr attribute
keep

deprecated
alpha, beta

optional discount parameters both of which take values from ⁠[0, 1]⁠, only one should be set at one time
byb2attr

specifies a second mode categorical attribute. Setting this argument will separate the orginal statistics based on the values of the set second mode attribute— i.e. for example, if diff is FALSE , then the sum of all the statistics for each level of this second-mode attribute will be equal to the original b1nodematch statistic where byb2attr set to NULL .
levels

select a subset of attr values to include. (See Specifying Vertex attributes and Levels (?nodal_attributes) for details.)

Details

If an alpha discount parameter is used, each of these statistics gives the sum of the number of common second-mode nodes raised to the power alpha for each pair of first-mode nodes with that attribute. If a beta discount parameter is used, each of these statistics gives half the sum of the number of two-paths with two first-mode nodes with that attribute as the two ends of the two path raised to the power beta for each edge in the network.

Note

This term can only be used with undirected bipartite networks.

The argument keep is retained for backwards compatibility and may be removed in a future version. When both keep and levels are passed, levels overrides keep.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

bipartite, categorical nodal attribute, dyad-independent, frequently-used, undirected, binary

Degree

Description

This term adds one network statistic for each node in the first bipartition, equal to the number of ties of that node. This term can only be used with bipartite networks. For directed networks, see sender and receiver. For unipartite networks, see sociality.

Usage

# binary: b1sociality(nodes=-1)

# valued: b1sociality(nodes=-1, form="sum")

Arguments

nodes

By default, nodes=-1 means that the statistic for the first node (in the second bipartition) will be omitted, but this argument may be changed to control which statistics are included. The nodes argument is interpreted using the new UI for level specification (see Specifying Vertex Attributes and Levels (?nodal_attributes) for details), where both the attribute and the sorted unique values are the vector of vertex indices (nb1 + 1):n , where nb1 is the size of the first bipartition and n is the total number of nodes in the network. Thus nodes=120 will include only the statistic for the 120th node in the second biparition, while nodes=I(120) will include only the statistic for the 120th node in the entire network.
form

character how to aggregate tie values in a valued ERGM

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

bipartite, dyad-independent, undirected, binary, valued

kk-stars for the first mode in a bipartite network

Description

This term adds one network statistic to the model for each element in k . The ii th such statistic counts the number of distinct k[i] -stars whose center node is in the first mode of the network. The first mode of a bipartite network object is sometimes known as the "actor" mode. A kk -star is defined to be a center node NN and a set of kk different nodes {O1,…,Ok}\{O_1, \dots, O_k\} such that the ties {N,Oi}\{N, O_i\} exist for i=1,…,ki=1, \dots, k. This term can only be used for undirected bipartite networks.

Usage

# binary: b1star(k, attr=NULL, levels=NULL)

Arguments

k

a vector of distinct integers
attr, levels

a vertex attribute specification; if attr is specified, then the count is over the instances where all nodes involved have the same value of the attribute. levels specified which values of attr are included in the count. (See Specifying Vertex attributes and Levels (?nodal_attributes) for details.)

Note

b1star(1) is equal to b2star(1) and to edges .

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

bipartite, categorical nodal attribute, undirected, binary

Mixing matrix for kk-stars centered on the first mode of a bipartite network

Description

This term counts all kk-stars in which the b2 nodes (called events in some contexts) are homophilous in the sense that they all share the same value of attr . However, the b1 node (in some contexts, the actor) at the center of the kk-star does NOT have to have the same value as the b2 nodes; indeed, the values taken by the b1 nodes may be completely distinct from those of the b2 nodes, which allows for the use of this term in cases where there are two separate nodal attributes, one for the b1 nodes and another for the b2 nodes (in this case, however, these two attributes should be combined to form a single nodal attribute, attr). A different statistic is created for each value of attr seen in a b1 node, even if no kk-stars are observed with this value.

Usage

# binary: b1starmix(k, attr, base=NULL, diff=TRUE)

Arguments

k

only a single value of kk is allowed
attr

a vertex attribute specification (see Specifying Vertex attributes and Levels (?nodal_attributes) for details.)
base

deprecated
diff

whether a different statistic is created for each value seen in a b2 node. When diff=TRUE, the default, a different statistic is created for each value and thus the behavior of this term is reminiscent of the nodemix term, from which it takes its name; when diff=FALSE , all homophilous kk-stars are counted together, though these kk-stars are still categorized according to the value of the central b1 node.

Note

The argument base is retained for backwards compatibility and may be removed in a future version. When both base and levels are passed, levels overrides base.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

bipartite, categorical nodal attribute, undirected, binary

Two-star census for central nodes centered on the first mode of a bipartite network

Description

This term takes two nodal attributes. Assuming that there are n1n_1 values of b1attr among the b1 nodes and n2n_2 values of b2attr among the b2 nodes, then the total number of distinct categories of two stars according to these two attributes is n1(n2)(n2+1)/2n_1(n_2)(n_2+1)/2. By default, this model term creates a distinct statistic counting each of these categories.

Usage

# binary: b1twostar(b1attr, b2attr, base=NULL, b1levels=NULL, b2levels=NULL, levels2=NULL)

Arguments

b1attr

b1 nodes (actors in some contexts) (see Specifying Vertex attributes and Levels (?nodal_attributes) for details)
b2attr

b2 nodes (events in some contexts). If b2attr is not passed, it is assumed to be the same as b1attr .
b1levels, b2levels, base, levels2

used to leave some of the categories out (see Specifying Vertex attributes and Levels (?nodal_attributes) for details)

Note

The argument base is retained for backwards compatibility and may be removed in a future version. When both base and levels are passed, levels overrides base.

The argument base is retained for backwards compatibility and may be removed in a future version. When both base and levels2 are passed, levels2 overrides base.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

bipartite, categorical nodal attribute, undirected, binary

Concurrent node count for the second mode in a bipartite network

Description

This term adds one network statistic to the model, equal to the number of nodes in the second mode of the network with degree 2 or higher. The second mode of a bipartite network object is sometimes known as the "event" mode. Without the optional argument, this statistic is equivalent to b2mindegree(2).

Usage

# binary: b2concurrent(by=NULL)

Arguments

by

This optional argument specifie a vertex attribute (see Specifying Vertex attributes and Levels (?nodal_attributes) for details); it functions just like the by argument of the b2degree term.

Note

This term can only be used with undirected bipartite networks.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

bipartite, frequently-used, undirected, binary

Main effect of a covariate for the second mode in a bipartite network

Description

This term adds a single network statistic for each quantitative attribute or matrix column to the model equaling the total value of attr(j) for all edges (i,j)(i,j) in the network. This term may only be used with bipartite networks. For categorical attributes, see b2factor.

Usage

# binary: b2cov(attr)

# valued: b2cov(attr, form="sum")

Arguments

attr

a vertex attribute specification (see Specifying Vertex attributes and Levels (?nodal_attributes) for details.)
form

character how to aggregate tie values in a valued ERGM

Note

ergm versions 3.9.4 and earlier used different arguments for this term. See ergm-options for how to invoke the old behaviour.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

bipartite, dyad-independent, frequently-used, quantitative nodal attribute, undirected, binary, valued

Degree range for the second mode in a bipartite network

Description

This term adds one network statistic to the model for each element of from (or to ); the ii th such statistic equals the number of nodes of the second mode ("events") in the network of degree greater than or equal to from[i] but strictly less than to[i] , i.e. with edge count in semiopen interval ⁠[from,to)⁠ .

This term can only be used with bipartite networks; for directed networks see idegrange and odegrange . For undirected networks, see degrange , and see b1degrange for degrees of the first mode ("actors").

Usage

# binary: b2degrange(from, to=+Inf, by=NULL, homophily=FALSE, levels=NULL)

Arguments

from, to

vectors of distinct integers. If one of the vectors have length 1, it is recycled to the length of the other. Otherwise, it must have the same length.
by, levels, homophily

the optional argument by specifies a vertex attribute (see Specifying Vertex attributes and Levels (?nodal_attributes) for details). If this is specified and homophily is TRUE , then degrees are calculated using the subnetwork consisting of only edges whose endpoints have the same value of the by attribute. If by is specified and homophily is FALSE (the default), then separate degree range statistics are calculated for nodes having each separate value of the attribute. levels selects which levels of by' to include.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

bipartite, undirected, binary

Degree for the second mode in a bipartite network

Description

This term adds one network statistic to the model for each element in d ; the ii th such statistic equals the number of nodes of degree d[i] in the second mode of a bipartite network, i.e. with exactly d[i] edges. The second mode of a bipartite network object is sometimes known as the "event" mode.

Usage

# binary: b2degree(d, by=NULL)

Arguments

d

a vector of distinct integers
by

this optional term specifies a vertex attribute (see Specifying Vertex attributes and Levels (?nodal_attributes) for details). If this is specified then each node's degree is tabulated only with other nodes having the same value of the by attribute.

Note

This term can only be used with undirected bipartite networks.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

bipartite, categorical nodal attribute, frequently-used, undirected, binary

Preserve the receiver degree for bipartite networks

Description

For bipartite networks, preserve the degree for the second mode of each vertex of the given network, while allowing the degree for the first mode to vary.

Usage

# b2degrees

See Also

ergmConstraint for index of constraints and hints currently visible to the package.

Keywords

bipartite

Dyadwise shared partners for dyads in the second bipartition

Description

This term adds one network statistic to the model for each element in d ; the ii th such statistic equals the number of dyads in the second bipartition with exactly d[i] shared partners. (Those shared partners, of course, must be members of the first bipartition.) This term can only be used with bipartite networks.

Usage

# binary: b2dsp(d)

Arguments

d

a vector of distinct integers

Note

This term takes an additional term option (see options?ergm), cache.sp, controlling whether the implementation will cache the number of shared partners for each dyad in the network; this is usually enabled by default.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

bipartite, undirected, binary

Factor attribute effect for the second mode in a bipartite network

Description

This term adds multiple network statistics to the model, one for each of (a subset of) the unique values of the attr attribute. Each of these statistics gives the number of times a node with that attribute in the second mode of the network appears in an edge. The second mode of a bipartite network object is sometimes known as the "event" mode.

Usage

# binary: b2factor(attr, base=1, levels=-1)

# valued: b2factor(attr, base=1, levels=-1, form="sum")

Arguments

attr

a vertex attribute specification (see Specifying Vertex attributes and Levels (?nodal_attributes) for details.)
base

deprecated
levels

this optional argument controls which levels of the attribute attributes and Levels (?nodal_attributes) for details.)
form

character how to aggregate tie values in a valued ERGM

Note

To include all attribute values is usually not a good idea, because the sum of all such statistics equals the number of edges and hence a linear dependency would arise in any model also including edges. The default, levels=-1, is therefore to omit the first (in lexicographic order) attribute level. To include all levels, pass either levels=TRUE (i.e., keep all levels) or levels=NULL (i.e., do not filter levels).

The argument base is retained for backwards compatibility and may be removed in a future version. When both base and levels are passed, levels overrides base.

This term can only be used with undirected bipartite networks.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

bipartite, categorical nodal attribute, dyad-independent, frequently-used, undirected, binary, valued

Minimum degree for the second mode in a bipartite network

Description

This term adds one network statistic to the model for each element in d ; the ii th such statistic equals the number of nodes in the second mode of a bipartite network with at least degree d[i] . The second mode of a bipartite network object is sometimes known as the "event" mode.

Usage

# binary: b2mindegree(d)

Arguments

d

a vector of distinct integers

Note

This term can only be used with undirected bipartite networks.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

bipartite, undirected, binary

Nodal attribute-based homophily effect for the second mode in a bipartite network

Description

This term is introduced in Bomiriya et al (2014). With the default alpha and beta values, this term will simply be a homophily based two-star statistic. This term adds one statistic to the model unless diff is set to TRUE , in which case the term adds multiple network statistics to the model, one for each of (a subset of) the unique values of the attr attribute.

Usage

# binary: b2nodematch(attr, diff=FALSE, keep=NULL, alpha=1, beta=1, byb1attr=NULL,
#                     levels=NULL)

Arguments

diff

by default, one statistic will be added to the model. If diff is set to TRUE, one statistic will be added for each unique value of the attr attribute
keep

deprecated
alpha, beta

optional discount parameters both of which take values from ⁠[0, 1]⁠, only one should be set at one time
byb2attr

specifies a second mode categorical attribute. Setting this argument will separate the orginal statistics based on the values of the set second mode attribute— i.e. for example, if diff is FALSE , then the sum of all the statistics for each level of this second-mode attribute will be equal to the original b1nodematch statistic where byb2attr set to NULL .
levels

select a subset of attr values to include. (See Specifying Vertex attributes and Levels (?nodal_attributes) for details.)
attr

a vertex attribute specification (see Specifying Vertex attributes and Levels (?nodal_attributes) for details.)

Details

If an alpha discount parameter is used, each of these statistics gives the sum of the number of common first-mode nodes raised to the power alpha for each pair of second-mode nodes with that attribute. If a beta discount parameter is used, each of these statistics gives half the sum of the number of two-paths with two second-mode nodes with that attribute as the two ends of the two path raised to the power beta for each edge in the network.

Note

This term can only be used with undirected bipartite networks.

The argument keep is retained for backwards compatibility and may be removed in a future version. When both keep and levels are passed, levels overrides keep.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

bipartite, categorical nodal attribute, dyad-independent, frequently-used, undirected, binary

Degree

Description

This term adds one network statistic for each node in the second bipartition, equal to the number of ties of that node. For directed networks, see sender and receiver . For unipartite networks, see sociality .

Usage

# binary: b2sociality(nodes=-1)

# valued: b2sociality(nodes=-1, form="sum")

Arguments

nodes

By default, nodes=-1 means that the statistic for the first node (in the second bipartition) will be omitted, but this argument may be changed to control which statistics are included. The nodes argument is interpreted using the new UI for level specification (see Specifying Vertex Attributes and Levels (?nodal_attributes) for details), where both the attribute and the sorted unique values are the vector of vertex indices (nb1 + 1):n , where nb1 is the size of the first bipartition and n is the total number of nodes in the network. Thus nodes=120 will include only the statistic for the 120th node in the second biparition, while nodes=I(120) will include only the statistic for the 120th node in the entire network.
form

character how to aggregate tie values in a valued ERGM

Note

This term can only be used with undirected bipartite networks.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

bipartite, dyad-independent, undirected, binary, valued

kk-stars for the second mode in a bipartite network

Description

This term adds one network statistic to the model for each element in k . The ii th such statistic counts the number of distinct k[i] -stars whose center node is in the second mode of the network. The second mode of a bipartite network object is sometimes known as the "event" mode. A kk -star is defined to be a center node NN and a set of kk different nodes {O1,…,Ok}\{O_1, \dots, O_k\} such that the ties {N,Oi}\{N, O_i\} exist for i=1,…,ki=1, \dots, k . This term can only be used for undirected bipartite networks.

Usage

# binary: b2star(k, attr=NULL, levels=NULL)

Arguments

k

a vector of distinct integers
attr, levels

a vertex attribute specification; if attr is specified, then the count is over the instances where all nodes involved have the same value of the attribute. levels specified which values of attr are included in the count. (See Specifying Vertex attributes and Levels (?nodal_attributes) for details.)

Note

b2star(1) is equal to b1star(1) and to edges .

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

bipartite, categorical nodal attribute, undirected, binary

Mixing matrix for kk-stars centered on the second mode of a bipartite network

Description

This term is exactly the same as b1starmix except that the roles of b1 and b2 are reversed.

Usage

# binary: b2starmix(k, attr, base=NULL, diff=TRUE)

Arguments

k

only a single value of kk is allowed
attr

a vertex attribute specification (see Specifying Vertex attributes and Levels (?nodal_attributes) for details.)
base

deprecated
diff

whether a different statistic is created for each value seen in a b1 node. When diff=TRUE, the default, a different statistic is created for each value and thus the behavior of this term is reminiscent of the nodemix term, from which it takes its name; when diff=FALSE , all homophilous kk-stars are counted together, though these kk-stars are still categorized according to the value of the central b1 node.

Note

The argument base is retained for backwards compatibility and may be removed in a future version. When both base and levels are passed, levels overrides base.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

bipartite, categorical nodal attribute, undirected, binary

Two-star census for central nodes centered on the second mode of a bipartite network

Description

This term is exactly the same as b1twostar except that the roles of b1 and b2 are reversed.

Usage

# binary: b2twostar(b1attr, b2attr, base=NULL, b1levels=NULL, b2levels=NULL, levels2=NULL)

Arguments

b1attr

b1 nodes (actors in some contexts) (see Specifying Vertex attributes and Levels (?nodal_attributes) for details)
b2attr

b2 nodes (events in some contexts). If b1attr is not passed, it is assumed to be the same as b2attr .
b1levels, b2levels, base, levels2

used to leave some of the categories out (see Specifying Vertex attributes and Levels (?nodal_attributes) for details)

Note

The argument base is retained for backwards compatibility and may be removed in a future version. When both base and levels are passed, levels overrides base.

The argument base is retained for backwards compatibility and may be removed in a future version. When both base and levels2 are passed, levels2 overrides base.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

bipartite, categorical nodal attribute, undirected, binary

Balanced triads

Description

This term adds one network statistic to the model equal to the number of triads in the network that are balanced. The balanced triads are those of type 102 or 300 in the categorization of Davis and Leinhardt (1972). For details on the 16 possible triad types, see ?triad.classify in the {sna} package. For an undirected network, the balanced triads are those with an odd number of ties (i.e., 1 and 3).

Usage

# binary: balance

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

directed, triad-related, undirected, binary

Constrain maximum and minimum vertex degree

Description

Condition on the number of inedge or outedges posessed by a node. See Placing Bounds on Degrees section for more information. (?ergmConstraint)

Usage

# bd(attribs, maxout, maxin, minout, minin)

Arguments

attribs

a matrix of logicals with dimension ⁠(n_nodes, attrcount)⁠ for the attributes on which we are conditioning, where attrcount is the number of distinct attributes values to condition on.
maxout, maxin, minout, minin

matrices of alter attributes with the same dimension as attribs when used in conjunction with attribs. Otherwise, vectors of integers specifying the relevant limits. If the vector is of length 1, the limit is applied to all nodes. If an individual entry is NA, then there is no restriction of that kind is applied. For undirected networks (bipartite and not) use minout and maxout.

See Also

ergmConstraint for index of constraints and hints currently visible to the package.

Keywords

directed, undirected

Bernoulli reference

Description

Specifies each dyad's baseline distribution to be Bernoulli with probability of the tie being 0.50.5 . This is the only reference measure used in binary mode.

Usage

# Bernoulli

See Also

ergmReference for index of reference distributions currently visible to the package.

Keywords

binary, discrete, finite, nonnegative

Block-diagonal structure constraint

Description

Force a block-diagonal structure (and its bipartite analogue) on the network. Only dyads (i,j)(i,j) for which attr(i)==attr(j) can have edges.

Note that the current implementation requires that blocks be contiguous for unipartite graphs, and for bipartite graphs, they must be contiguous within a partition and must have the same ordering in both partitions. (They do not, however, require that all blocks be represented in both partitions, but those that overlap must have the same order.)

If multiple block-diagonal constraints are given, or if attr is a vector with multiple attribute names, blocks will be constructed on all attributes matching.

Usage

# blockdiag(attr)

Arguments

attr

a vertex attribute specification (see Specifying Vertex attributes and Levels (?nodal_attributes) for details.)

See Also

ergmConstraint for index of constraints and hints currently visible to the package.

Keywords

directed, dyad-independent, undirected

Constrain blocks of dyads defined by mixing type on a vertex attribute.

Description

Any dyad whose toggle would produce a nonzero change statistic for a nodemix term with the same arguments will be fixed. Note that the levels2 argument has a different default value for blocks than it does for nodemix.

Usage

# blocks(attr=NULL, levels=NULL, levels2=FALSE, b1levels=NULL, b2levels=NULL)

Arguments

attr

a vertex attribute specification (see Specifying Vertex attributes and Levels (?nodal_attributes) for details.)
b1levels, b2levels, levels, level2

control what mixing types are fixed. levels2 applies to all networks; levels applies to unipartite networks; b1levels and b2levels apply to bipartite networks (see Specifying Vertex attributes and Levels (?nodal_attributes) for details)

See Also

ergmConstraint for index of constraints and hints currently visible to the package.

Keywords

directed, dyad-independent, undirected

Ensures an Ergm Term and its Arguments Meet Appropriate Conditions

Description

Helper functions for implementing ergm() terms, to check whether the term can be used with the specified network. For information on ergm terms, see ergmTerm. ergm.checkargs, ergm.checkbipartite, and ergm.checkderected are helper functions for an old API and are deprecated. Use check.ErgmTerm.

Usage

check.ErgmTerm(
  nw,
  arglist,
  directed = NULL,
  bipartite = NULL,
  nonnegative = FALSE,
  varnames = NULL,
  vartypes = NULL,
  defaultvalues = list(),
  required = NULL,
  dep.inform = rep(FALSE, length(required)),
  dep.warn = rep(FALSE, length(required)),
  argexpr = NULL
)

Arguments

nw

the network that term X is being checked against
arglist

the list of arguments for term X
directed

logical, whether term X requires a directed network; default=NULL
bipartite

whether term X requires a bipartite network (T or F); default=NULL
nonnegative

whether term X requires a network with only nonnegative weights; default=FALSE
varnames

the vector of names of the possible arguments for term X; default=NULL
vartypes

the vector of types of the possible arguments for term X, separated by commas; an empty string ("") or NA disables the check for that argument, and also see Details; default=NULL
defaultvalues

the list of default values for the possible arguments of term X; default=list()
required

the logical vector of whether each possible argument is required; default=NULL
dep.inform, dep.warn

a list of length equal to the number of arguments the term can take; if the corresponding element of the list is not FALSE, a message() or a warning() respectively will be issued if the user tries to pass it; if the element is a character string, it will be used as a suggestion for replacement.
argexpr

optional call typically obtained by calling substitute(arglist).

Details

The check.ErgmTerm function ensures for the InitErgmTerm.X function that the term X:

  • is applicable given the 'directed' and 'bipartite' attributes of the given network

  • is not applied to a directed bipartite network

  • has an appropiate number of arguments

  • has correct argument types if arguments where provided

  • has default values assigned if defaults are available

by halting execution if any of the first 3 criteria are not met.

As a convenience, if an argument is optional and its default is NULL, then NULL is assumed to be an acceptable argument type as well.

Value

A list of the values for each possible argument of term X; user provided values are used when given, default values otherwise. The list also has an attr(,"missing") attribute containing a named logical vector indicating whether a particular argument had been set to its default. If ⁠argexpr=⁠ argument is provided, attr(,"exprs") attribute is also returned, containing expressions.

Target statistics and model fit to a hypothetical 50,000-node network population with 50,000 nodes based on egocent

Description

This dataset consists of three objects, each based on data from King County, Washington, USA (where Seattle is located) derived from the National Survey of Family Growth (NSFG) (https://www.cdc.gov/nchs/nsfg/index.htm). The full dataset cannot be released publicly, so some aspects of these objects are simulated based on the real data. These objects may be used to illustrate that network modeling may be performed using data that are collected on egos only, i.e., without directly observing information about alters in a network except for information reported from egos. The hypothetical population reepresented by this dataset consists of only a subset of individuals, as categorized by their age, race / ethnicity / immigration status, and gender and sexual identity.

Usage

data(cohab)

Details

The three objects are

cohab_MixMat

Mixing matrix on 'race'. Based on ego reports of the race / ethnicity / immigration status of their cohabiting partners, this matrix gives counts of ego-alter ties by the race of each individual for a hypothetical population. These counts are based on the NSFG mixing matrix. Only five categories of the 'race' variable are included here: Black, Black immigrant, Hispanic, Hispanic immigrant, and White.

cohab_PopWts

Data frame of demographic characteristics together with relative counts (weights) in a hypothetical population. Individuals are classified according to five variables: age in years, race (same five categories of race / ethnicity / immigration status as above), sex (Male or Female), sexual identity (Female, Male who has sex with Females, or Male who has sex with Males or Females), and number of model-predicted persistent partnerships with non-cohabiting partners (0 or 1, where 1 means any nonzero value; the number is capped at 3), and number of partners (0 or 1).

cohab_TargetStats

Vector of target (expected) statistics for a 15-term ERGM applied to a network of 50,000 nodes in which a tie represents a cohabitation relationship between two nodes. It is assumed for the purposes of these statistics that only male-female cohabitation relationships are allowed and that no individual may have such a relationship with more than one person. That is, each node must have degree zero or one. The ergm formula is: ~ edges + nodefactor("sex.ident", levels = 3) + nodecov("age") + nodecov("agesq") + nodefactor("race", levels = -5) + nodefactor("othr.net.deg", levels = -1) + nodematch("race", diff = TRUE) + absdiff("sqrt.age.adj")

References

Krivitsky, P.N., Hunter, D.R., Morris, M., and Klumb, C. (2021). ergm 4.0: New Features and Improvements. arXiv

National Center for Health Statistics (NCHS). (2020). 2006-2015 National Survey of Family Growth Public-Use Data and Documentation. Hyattsville, MD: CDC National Center for Health Statistics. Retrieved from https://www.cdc.gov/nchs/nsfg/index.htm

See Also

ergm

Coincident node count for the second mode in a bipartite (aka two-mode) network

Description

By default this term adds one network statistic to the model for each pair of nodes of mode two. It is equal to the number of (first mode) mutual partners of that pair. The first mode of a bipartite network object is sometimes known as the "actor" mode and the seconds as the "event" mode. So this is the number of actors going to both events in the pair. This term can only be used with undirected bipartite networks.

Usage

# binary: coincidence(levels=NULL,active=0)

Arguments

levels

specifies which pairs of nodes in mode two to include. (See Specifying Vertex attributes and Levels (?nodal_attributes) for details.)
active

selects pairs for which the observed count is at least active . Ignored if levels is specified. (Thus, indices passed as levels should correspond to indices when levels = NULL and active = 0.)

Note

ergm versions 3.9.4 and earlier used different arguments for this term. See ergm-options for how to invoke the old behaviour.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

bipartite, undirected, binary

Concurrent node count

Description

This term adds one network statistic to the model, equal to the number of nodes in the network with degree 2 or higher. This term can only be used with undirected networks.

Usage

# binary: concurrent(by=NULL, levels=NULL)

Arguments

by

this optional argument specifies a vertex attribute (see Specifying Vertex attributes and Levels (?nodal_attributes) for details.) It functions just like the by argument of the degree term.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

categorical nodal attribute, undirected, binary

Concurrent tie count

Description

This term adds one network statistic to the model, equal to the number of ties incident on each actor beyond the first. This term can only be used with undirected networks.

Usage

# binary: concurrentties(by=NULL, levels=NULL)

Arguments

by

a vertex attribute (see Specifying Vertex attributes and Levels (?nodal_attributes) for details.); it functions just like the by argument of the degree term
levels

TODO (See Specifying Vertex attributes and Levels (?nodal_attributes) for details.)

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

categorical nodal attribute, undirected, binary

Auxiliary function for fine-tuning ERGM fitting.

Description

This function is only used within a call to the ergm() function. See the Usage section in ergm() for details. Also see the Details section about some of the interactions between its arguments.

Usage

control.ergm(
  drop = TRUE,
  init = NULL,
  init.method = NULL,
  main.method = c("MCMLE", "Stochastic-Approximation"),
  force.main = FALSE,
  main.hessian = TRUE,
  checkpoint = NULL,
  resume = NULL,
  MPLE.samplesize = .Machine$integer.max,
  init.MPLE.samplesize = function(d, e) max(sqrt(d), e, 40) * 8,
  MPLE.type = c("glm", "penalized", "logitreg"),
  MPLE.maxit = 10000,
  MPLE.nonvar = c("warning", "message", "error"),
  MPLE.nonident = c("warning", "message", "error"),
  MPLE.nonident.tol = 1e-10,
  MPLE.covariance.samplesize = 500,
  MPLE.covariance.method = "invHess",
  MPLE.covariance.sim.burnin = 1024,
  MPLE.covariance.sim.interval = 1024,
  MPLE.check = TRUE,
  MPLE.constraints.ignore = FALSE,
  MCMC.prop = trim_env(~sparse + .triadic),
  MCMC.prop.weights = "default",
  MCMC.prop.args = list(),
  MCMC.interval = NULL,
  MCMC.burnin = EVL(MCMC.interval * 16),
  MCMC.samplesize = NULL,
  MCMC.effectiveSize = NULL,
  MCMC.effectiveSize.damp = 10,
  MCMC.effectiveSize.maxruns = 16,
  MCMC.effectiveSize.burnin.pval = 0.2,
  MCMC.effectiveSize.burnin.min = 0.05,
  MCMC.effectiveSize.burnin.max = 0.5,
  MCMC.effectiveSize.burnin.nmin = 16,
  MCMC.effectiveSize.burnin.nmax = 128,
  MCMC.effectiveSize.burnin.PC = FALSE,
  MCMC.effectiveSize.burnin.scl = 32,
  MCMC.effectiveSize.order.max = NULL,
  MCMC.return.stats = 2^12,
  MCMC.runtime.traceplot = FALSE,
  MCMC.maxedges = Inf,
  MCMC.addto.se = TRUE,
  MCMC.packagenames = c(),
  SAN.maxit = 4,
  SAN.nsteps.times = 8,
  SAN = control.san(term.options = term.options, SAN.maxit = SAN.maxit, SAN.prop =
    MCMC.prop, SAN.prop.weights = MCMC.prop.weights, SAN.prop.args = MCMC.prop.args,
    SAN.nsteps = EVL(MCMC.burnin, 16384) * SAN.nsteps.times, SAN.samplesize =
    EVL(MCMC.samplesize, 1024), SAN.packagenames = MCMC.packagenames, parallel =
    parallel, parallel.type = parallel.type, parallel.version.check =
    parallel.version.check),
  MCMLE.termination = c("confidence", "Hummel", "Hotelling", "precision", "none"),
  MCMLE.maxit = 60,
  MCMLE.conv.min.pval = 0.5,
  MCMLE.confidence = 0.99,
  MCMLE.confidence.boost = 2,
  MCMLE.confidence.boost.threshold = 1,
  MCMLE.confidence.boost.lag = 4,
  MCMLE.NR.maxit = 100,
  MCMLE.NR.reltol = sqrt(.Machine$double.eps),
  obs.MCMC.mul = 1/4,
  obs.MCMC.samplesize.mul = sqrt(obs.MCMC.mul),
  obs.MCMC.samplesize = EVL(round(MCMC.samplesize * obs.MCMC.samplesize.mul)),
  obs.MCMC.effectiveSize = NVL3(MCMC.effectiveSize, . * obs.MCMC.mul),
  obs.MCMC.interval.mul = sqrt(obs.MCMC.mul),
  obs.MCMC.interval = EVL(round(MCMC.interval * obs.MCMC.interval.mul)),
  obs.MCMC.burnin.mul = sqrt(obs.MCMC.mul),
  obs.MCMC.burnin = EVL(round(MCMC.burnin * obs.MCMC.burnin.mul)),
  obs.MCMC.prop = MCMC.prop,
  obs.MCMC.prop.weights = MCMC.prop.weights,
  obs.MCMC.prop.args = MCMC.prop.args,
  obs.MCMC.impute.min_informative = function(nw) network.size(nw)/4,
  obs.MCMC.impute.default_density = function(nw) 2/network.size(nw),
  MCMLE.min.depfac = 2,
  MCMLE.sampsize.boost.pow = 0.5,
  MCMLE.MCMC.precision = if (startsWith("confidence", MCMLE.termination[1])) 0.1 else
    0.005,
  MCMLE.MCMC.max.ESS.frac = 0.1,
  MCMLE.metric = c("lognormal", "logtaylor", "Median.Likelihood", "EF.Likelihood",
    "naive"),
  MCMLE.method = c("BFGS", "Nelder-Mead"),
  MCMLE.dampening = FALSE,
  MCMLE.dampening.min.ess = 20,
  MCMLE.dampening.level = 0.1,
  MCMLE.steplength.margin = 0.05,
  MCMLE.steplength = NVL2(MCMLE.steplength.margin, 1, 0.5),
  MCMLE.steplength.parallel = c("observational", "never"),
  MCMLE.sequential = TRUE,
  MCMLE.density.guard.min = 10000,
  MCMLE.density.guard = exp(3),
  MCMLE.effectiveSize = 64,
  obs.MCMLE.effectiveSize = NULL,
  MCMLE.interval = 1024,
  MCMLE.burnin = MCMLE.interval * 16,
  MCMLE.samplesize.per_theta = 32,
  MCMLE.samplesize.min = 256,
  MCMLE.samplesize = NULL,
  obs.MCMLE.samplesize.per_theta = round(MCMLE.samplesize.per_theta *
    obs.MCMC.samplesize.mul),
  obs.MCMLE.samplesize.min = 256,
  obs.MCMLE.samplesize = NULL,
  obs.MCMLE.interval = round(MCMLE.interval * obs.MCMC.interval.mul),
  obs.MCMLE.burnin = round(MCMLE.burnin * obs.MCMC.burnin.mul),
  MCMLE.steplength.solver = c("glpk", "lpsolve"),
  MCMLE.last.boost = 4,
  MCMLE.steplength.esteq = TRUE,
  MCMLE.steplength.miss.sample = function(x1) c(max(ncol(rbind(x1)) * 2, 30), 10),
  MCMLE.steplength.min = 1e-04,
  MCMLE.effectiveSize.interval_drop = 2,
  MCMLE.save_intermediates = NULL,
  MCMLE.nonvar = c("message", "warning", "error"),
  MCMLE.nonident = c("warning", "message", "error"),
  MCMLE.nonident.tol = 1e-10,
  SA.phase1_n = function(q, ...) max(200, 7 + 3 * q),
  SA.initial_gain = 0.1,
  SA.nsubphases = 4,
  SA.min_iterations = function(q, ...) (7 + q),
  SA.max_iterations = function(q, ...) (207 + q),
  SA.phase3_n = 1000,
  SA.interval = 1024,
  SA.burnin = SA.interval * 16,
  SA.samplesize = 1024,
  CD.samplesize.per_theta = 128,
  obs.CD.samplesize.per_theta = 128,
  CD.nsteps = 8,
  CD.multiplicity = 1,
  CD.nsteps.obs = 128,
  CD.multiplicity.obs = 1,
  CD.maxit = 60,
  CD.conv.min.pval = 0.5,
  CD.NR.maxit = 100,
  CD.NR.reltol = sqrt(.Machine$double.eps),
  CD.metric = c("naive", "lognormal", "logtaylor", "Median.Likelihood", "EF.Likelihood"),
  CD.method = c("BFGS", "Nelder-Mead"),
  CD.dampening = FALSE,
  CD.dampening.min.ess = 20,
  CD.dampening.level = 0.1,
  CD.steplength.margin = 0.5,
  CD.steplength = 1,
  CD.adaptive.epsilon = 0.01,
  CD.steplength.esteq = TRUE,
  CD.steplength.miss.sample = function(x1) ceiling(sqrt(ncol(rbind(x1)))),
  CD.steplength.min = 1e-04,
  CD.steplength.parallel = c("observational", "always", "never"),
  CD.steplength.solver = c("glpk", "lpsolve"),
  loglik = control.logLik.ergm(),
  term.options = NULL,
  seed = NULL,
  parallel = 0,
  parallel.type = NULL,
  parallel.version.check = TRUE,
  parallel.inherit.MT = FALSE,
  ...
)

Arguments

drop

Logical: If TRUE, terms whose observed statistic values are at the extremes of their possible ranges are dropped from the fit and their corresponding parameter estimates are set to plus or minus infinity, as appropriate. This is done because maximum likelihood estimates cannot exist when the vector of observed statistic lies on the boundary of the convex hull of possible statistic values.
init

numeric or NA vector equal in length to the number of parameters in the model or NULL (the default); the initial values for the estimation and coefficient offset terms. If NULL is passed, all of the initial values are computed using the method specified by control$init.method. If a numeric vector is given, the elements of the vector are interpreted as follows:

  • Elements corresponding to terms enclosed in offset() are used as the fixed offset coefficients. Note that offset coefficients alone can be more conveniently specified using ergm() argument offset.coef. If both offset.coef and init arguments are given, values in offset.coef will take precedence.

  • Elements that do not correspond to offset terms and are not NA are used as starting values in the estimation.

  • Initial values for the elements that are NA are fit using the method specified by control$init.method.

Passing control.ergm(init=coef(prev.fit)) can be used to “resume” an uncoverged ergm() run, though checkpoint and 'resume' would be better under most circumstances.
init.method

A chatacter vector or NULL. The default method depends on the reference measure used. For the binary ("Bernoulli") ERGMs, with dyad-independent constraints, it's maximum pseudo-likelihood estimation (MPLE). Other valid values include "zeros" for a 0 vector of appropriate length and "CD" for contrastive divergence. If passed explicitly, this setting overrides the reference's limitations.

Valid initial methods for a given reference are set by the ⁠InitErgmReference.*⁠ function.
main.method

One of "MCMLE" (default) or "Stochastic-Approximation". Chooses the estimation method used to find the MLE. MCMLE attempts to maximize an approximation to the log-likelihood function. Stochastic-Approximation are both stochastic approximation algorithms that try to solve the method of moments equation that yields the MLE in the case of an exponential family model. The direct use of the likelihood function has many theoretical advantages over stochastic approximation, but the choice will depend on the model and data being fit. See Handcock (2000) and Hunter and Handcock (2006) for details.
force.main

Logical: If TRUE, then force MCMC-based estimation method, even if the exact MLE can be computed via maximum pseudolikelihood estimation.
main.hessian

Logical: If TRUE, then an approximate Hessian matrix is used in the MCMC-based estimation method.
checkpoint

At the start of every iteration, save the state of the optimizer in a way that will allow it to be resumed. The name is passed through sprintf() with iteration number as the second argument. (For example, checkpoint="step_%03d.RData" will save to step_001.RData, step_002.RData, etc.)
resume

If given a file name of an RData file produced by checkpoint, the optimizer will attempt to resume after restoring the state. Control parameters from the saved state will be reused, except for those whose value passed via control.ergm() had change from the saved run. Note that if the network, the model, or some critical settings differ between runs, the results may be undefined.
MPLE.samplesize, init.MPLE.samplesize

These parameters control the maximum number of dyads (potential ties) that will be used by the MPLE to construct the predictor matrix for its logistic regression. In general, the algorithm visits dyads in a systematic sample that, if it does not hit one of these limits, will visit every informative dyad. If a limit is exceeded, case-control approximation to the likelihood, comprising all edges and those non-edges that have been visited by the algorithm before the limit was exceeded will be used.

MPLE.samplesize limits the number of dyads visited, unless the MPLE is being computed for the purpose of being the initial value for MCMC-based estimation, in which case init.MPLE.samplesize is used instead, All of these can be specified either as numbers or as ⁠function(d,e)⁠ taking the number of informative dyads and informative edges. Specifying or returning a larger number than the number of informative dyads is safe.
MPLE.type

One of "glm", "penalized", or "logitreg". Chooses method of calculating MPLE. "glm" is the usual formal logistic regression called via glm(), whereas "penalized" uses the bias-reduced method of Firth (1993) as originally implemented by Meinhard Ploner, Daniela Dunkler, Harry Southworth, and Georg Heinze in the "logistf" package. "logitreg" is an "in-house" implementation that is slower and probably less stable but supports nonlinear logistic regression. It is invoked automatically when the model has curved terms.
MPLE.maxit

Maximum number of iterations for "logitreg" implementation of MPLE.
MPLE.nonident, MPLE.nonident.tol, MPLE.nonvar, MCMLE.nonident, MCMLE.nonident.tol, MCMLE.nonvar

A rudimentary nonidentifiability/multicollinearity diagnostic. If MPLE.nonident.tol > 0, test the MPLE covariate matrix or the CD statistics matrix has linearly dependent columns via QR decomposition with tolerance MPLE.nonident.tol. This is often (not always) indicative of a non-identifiable (multicollinear) model. If nonidentifiable, depending on MPLE.nonident issue a warning, an error, or a message specifying the potentially redundant statistics. Before the diagnostic is performed, covariates that do not vary (i.e., all-zero columns) are dropped, with their handling controlled by MPLE.nonvar. The corresponding ⁠MCMLE.*⁠ arguments provide a similar diagnostic for the unconstrained MCMC sample's estimating functions.
MPLE.covariance.method, MPLE.covariance.samplesize, MPLE.covariance.sim.burnin, MPLE.covariance.sim.interval

Controls for estimating the MPLE covariance matrix. ⁠MPLE.covariance method⁠ determines the method, with invHess (the default) returning the covariance estimate obtained from the glm(). Godambe estimates the covariance matrix using the Godambe-matrix (Schmid and Hunter 2023). This method is recommended for dyad-dependent models. Alternatively, bootstrap estimates standard deviations using a parametric bootstrapping approach (see Schmid and Desmarais 2017). The other parameters control, respectively, the number of networks to simulate, the MCMC burn-in, and the MCMC interval for Godambe and bootstrap methods.
MPLE.check

If TRUE (the default), perform the MPLE existence check described by Schmid and Hunter (2023).
MPLE.constraints.ignore

If TRUE, MPLE will ignore all dyad-independent constraints except for those due to attributes missingness. This can be used to avert evaluating and storing the rlebdms for very large networks except where absolutely necessary. Note that this can be very dangerous unless you know what you are doing.
MCMC.prop

Specifies the proposal (directly) and/or a series of "hints" about the structure of the model being sampled. The specification is in the form of a one-sided formula with hints separated by + operations. If the LHS exists and is a string, the proposal to be used is selected directly.

A common and default "hint" is ~sparse, indicating that the network is sparse and that the sample should put roughly equal weight on selecting a dyad with or without a tie as a candidate for toggling.
MCMC.prop.weights

Specifies the proposal distribution used in the MCMC Metropolis-Hastings algorithm. Possible choices depending on selected reference and constraints arguments of the ergm() function, but often include "TNT" and "random", and the "default" is to use the one with the highest priority available.
MCMC.prop.args

An alternative, direct way of specifying additional arguments to proposal.
MCMC.interval

Number of proposals between sampled statistics. Increasing interval will reduces the autocorrelation in the sample, and may increase the precision in estimates by reducing MCMC error, at the expense of time. Set the interval higher for larger networks.
MCMC.burnin

Number of proposals before any MCMC sampling is done. It typically is set to a fairly large number.
MCMC.samplesize

Number of network statistics, randomly drawn from a given distribution on the set of all networks, returned by the Metropolis-Hastings algorithm. Increasing sample size may increase the precision in the estimates by reducing MCMC error, at the expense of time. Set it higher for larger networks, or when using parallel functionality.
MCMC.effectiveSize, MCMC.effectiveSize.damp, MCMC.effectiveSize.maxruns, MCMC.effectiveSize.burnin.pval, MCMC.effectiveSize.burnin.min, MCMC.effectiveSize.burnin.max, MCMC.effectiveSize.burnin.nmin, MCMC.effectiveSize.burnin.nmax, MCMC.effectiveSize.burnin.PC, MCMC.effectiveSize.burnin.scl, MCMC.effectiveSize.order.max

Set MCMC.effectiveSize to a non-NULL value to adaptively determine the burn-in and the MCMC length needed to get the specified effective size; 50 is a reasonable value. In the adaptive MCMC mode, MCMC is run forward repeatedly (MCMC.samplesize*MCMC.interval steps, up to MCMC.effectiveSize.maxruns times) until the target effective sample size is reached or exceeded.

After each run, the returned statistics are mapped to the estimating function scale, then an exponential decay model is fit to the scaled statistics to find that burn-in which would reduce the difference between the initial values of statistics and their equilibrium values by a factor of MCMC.effectiveSize.burnin.scl of what it initially was, bounded by MCMC.effectiveSize.min and MCMC.effectiveSize.max as proportions of sample size. If the best-fitting decay exceeds MCMC.effectiveSize.max, the exponential model is considered to be unsuitable and MCMC.effectiveSize.min is used.

A Geweke diagnostic is then run, after thinning the sample to MCMC.effectiveSize.burnin.nmax. If this Geweke diagnostic produces a pp-value higher than MCMC.effectiveSize.burnin.pval, it is accepted.

If MCMC.effectiveSize.burnin.PC>0, instead of using the full sample for burn-in estimation, at most this many principal components are used instead.

The effective size of the post-burn-in sample is computed via Vats et al. (2019), and compared to the target effective size. If it is not matched, the MCMC run is resumed, with the additional draws needed linearly extrapolated but weighted in favor of the baseline MCMC.samplesize by the weighting factor MCMC.effectiveSize.damp (higher = less damping). Lastly, if after an MCMC run, the number of samples equals or exceeds 2*MCMC.samplesize, the chain will be thinned by 2 until it falls below that, while doubling MCMC.interval. MCMC.effectiveSize.order.max can be used to set the order of the AR model used to estimate the effective sample size and the variance for the Geweke diagnostic.

Lastly, if MCMC.effectiveSize is a matrix, say, WW, it will be treated as a target precision (inverse-variance) matrix. If VV is the sample covariance matrix, the target effective size neffn_{\text{eff}} will be set such that V/neffV/n_{\text{eff}} is close to WW in magnitude, specifically that tr⁡((V/neff)W)/p≈1\operatorname{tr}((V/n_{\text{eff}})W)/p\approx 1.
MCMC.return.stats

Numeric: If positive, include an mcmc.list (two, if observational process was involved) of MCMC network statistics from the last iteration of network of the estimation. They will be thinned to have length of at most MCMC.return.stats. They are used for MCMC diagnostics.
MCMC.runtime.traceplot

Logical: If TRUE, plot traceplots of the MCMC sample after every MCMC MLE iteration.
MCMC.maxedges

The maximum number of edges that may occur during the MCMC sampling. If this number is exceeded at any time, sampling is stopped immediately.
MCMC.addto.se

Whether to add the standard errors induced by the MCMC algorithm to the estimates' standard errors.
MCMC.packagenames

Names of packages in which to look for change statistic functions in addition to those autodetected. This argument should not be needed outside of very strange setups.
SAN.maxit

When target.stats argument is passed to ergm(), the maximum number of attempts to use san() to obtain a network with statistics close to those specified.
SAN.nsteps.times

Multiplier for SAN.nsteps relative to MCMC.burnin. This lets one control the amount of SAN burn-in (arguably, the most important of SAN parameters) without overriding the other SAN defaults.
SAN

Control arguments to san(). See control.san() for details.
MCMLE.termination

The criterion used for terminating MCMLE estimation:

  • "Hummel" Terminate when the Hummel step length is 1 for two consecutive iterations. For the last iteration, the sample size is boosted by a factor of MCMLE.last.boost. See Hummel et. al. (2012).

Note that this criterion is incompatible with MCMLE.steplength ≠\ne 1 or MCMLE.steplength.margin == NULL.

  • "Hotelling" After every MCMC sample, an autocorrelation-adjusted Hotelling's T^2 test for equality of MCMC-simulated network statistics to observed is conducted, and if its P-value exceeds MCMLE.conv.min.pval, the estimation is considered to have converged and finishes. This was the default option in ergm version 3.1.

  • "precision" Terminate when the estimated loss in estimating precision due to using MCMC standard errors is below the precision bound specified by MCMLE.MCMC.precision, and the Hummel step length is 1 for two consecutive iterations. See MCMLE.MCMC.precision for details. This feature is in experimental status until we verify the coverage of the standard errors.

Note that this criterion is incompatible with MCMLE.steplength≠1\code{MCMLE.steplength}\ne 1 or MCMLE.steplength.margin=NULL\code{MCMLE.steplength.margin}=\code{NULL}.

  • "confidence": Performs an equivalence test to prove with level of confidence MCMLE.confidence that the true value of the deviation of the simulated mean value parameter from the observed is within an ellipsoid defined by the inverse-variance-covariance of the sufficient statistics multiplied by a scaling factor control$MCMLE.MCMC.precision (which has a different default).

  • "none" Stop after MCMLE.maxit iterations.

MCMLE.maxit

Maximum number of times the parameter for the MCMC should be updated by maximizing the MCMC likelihood. At each step the parameter is changed to the values that maximizes the MCMC likelihood based on the current sample.
MCMLE.conv.min.pval

The P-value used in the Hotelling test for early termination.
MCMLE.confidence

The confidence level for declaring convergence for "confidence" methods.
MCMLE.confidence.boost

The maximum increase factor in sample size (or target effective size, if enabled) when the "confidence" termination criterion is either not approaching the tolerance region or is unable to prove convergence.
MCMLE.confidence.boost.threshold, MCMLE.confidence.boost.lag

Sample size or target effective size will be increaed if the distance from the tolerance region fails to decrease more than MCMLE.confidence.boost.threshold in this many successive iterations.
MCMLE.NR.maxit, MCMLE.NR.reltol

The method, maximum number of iterations and relative tolerance to use within the optim rountine in the MLE optimization. Note that by default, ergm uses trust, and falls back to optim only when trust fails.
obs.MCMC.prop, obs.MCMC.prop.weights, obs.MCMC.prop.args, obs.MCMLE.effectiveSize, obs.MCMC.samplesize, obs.MCMC.burnin, obs.MCMC.interval, obs.MCMC.mul, obs.MCMC.samplesize.mul, obs.MCMC.burnin.mul, obs.MCMC.interval.mul, obs.MCMC.effectiveSize, obs.MCMLE.burnin, obs.MCMLE.interval, obs.MCMLE.samplesize, obs.MCMLE.samplesize.per_theta, obs.MCMLE.samplesize.min

Corresponding MCMC parameters and settings used for the constrained sample when unobserved data are present in the estimation routine. By default, they are controlled by the ⁠*.mul⁠ parameters, as fractions of the corresponding settings for the unconstrained (standard) MCMC.

These can, in turn, be controlled by obs.MCMC.mul, which can be used to set the overal multiplier for the number of MCMC steps in the constrained sample; one half of its effect applies to the burn-in and interval and the other half to the total sample size. For example, for obs.MCMC.mul=1/4 (the default), obs.MCMC.samplesize is set to 1/4=1/2\sqrt{1/4}=1/2 that of obs.MCMC.samplesize, and obs.MCMC.burnin and obs.MCMC.interval are set to 1/4=1/2\sqrt{1/4}=1/2 of their respective unconstrained sampling parameters. When MCMC.effectiveSize or MCMLE.effectiveSize are given, their corresponding obs parameters are set to them multiplied by obs.MCMC.mul.

Lastly, if MCMLE.effectiveSize is not NULL but obs.MCMLE.effectiveSize is, the constrained sample's target effective size is set adaptively to achieve a similar precision for the estimating functions as that achieved for the unconstrained.
obs.MCMC.impute.min_informative, obs.MCMC.impute.default_density

Controls for imputation of missing dyads for initializing MCMC sampling. If numeric, obs.MCMC.impute.min_informative specifies the minimum number dyads that need to be non-missing before sample network density is used as the imputation density. It can also be specified as a function that returns this value. obs.MCMC.impute.default_density similarly controls the imputation density when number of non-missing dyads is too low.
MCMLE.min.depfac, MCMLE.sampsize.boost.pow

When using adaptive MCMC effective size, and methods that increase the MCMC sample size, use MCMLE.sampsize.boost.pow as the power of the boost amount (relative to the boost of the target effective size), but ensure that sample size is no less than MCMLE.min.depfac times the target effective size.
MCMLE.MCMC.precision, MCMLE.MCMC.max.ESS.frac

MCMLE.MCMC.precision is a vector of upper bounds on the standard errors induced by the MCMC algorithm, expressed as a percentage of the total standard error. The MCMLE algorithm will terminate when the MCMC standard errors are below the precision bound, and the Hummel step length is 1 for two consecutive iterations. This is an experimental feature.

If effective sample size is used (see MCMC.effectiveSize), then ergm may increase the target ESS to reduce the MCMC standard error.
MCMLE.metric

Method to calculate the loglikelihood approximation. See Hummel et al (2010) for an explanation of "lognormal" and "naive".
MCMLE.method

Deprecated. By default, ergm uses trust, and falls back to optim with Nelder-Mead method when trust fails.
MCMLE.dampening

(logical) Should likelihood dampening be used?
MCMLE.dampening.min.ess

The effective sample size below which dampening is used.
MCMLE.dampening.level

The proportional distance from boundary of the convex hull move.
MCMLE.steplength.margin

The extra margin required for a Hummel step to count as being inside the convex hull of the sample. Set this to 0 if the step length gets stuck at the same value over several iteraions. Set it to NULL to use fixed step length. Note that this parameter is required to be non-NULL for MCMLE termination using Hummel or precision criteria.
MCMLE.steplength

Multiplier for step length (on the mean-value parameter scale), which may (for values less than one) make fitting more stable at the cost of computational efficiency.

If MCMLE.steplength.margin is not NULL, the step length will be set using the algorithm of Hummel et al. (2010). In that case, it will serve as the maximum step length considered. However, setting it to anything other than 1 will preclude using Hummel or precision as termination criteria.
MCMLE.steplength.parallel

Whether parallel multisection search (as opposed to a bisection search) for the Hummel step length should be used if running in multiple threads. Possible values (partially matched) are "never", and (default) "observational" (i.e., when missing data MLE is used).
MCMLE.sequential

Logical: If TRUE, the next iteration of the fit uses the last network sampled as the starting network. If FALSE, always use the initially passed network. The results should be similar (stochastically), but the TRUE option may help if the target.stats in the ergm() function are far from the initial network.
MCMLE.density.guard.min, MCMLE.density.guard

A simple heuristic to stop optimization if it finds itself in an overly dense region, which usually indicates ERGM degeneracy: if the sampler encounters a network configuration that has more than MCMLE.density.guard.min edges and whose number of edges is exceeds the observed network by more than MCMLE.density.guard, the optimization process will be stopped with an error.
MCMLE.effectiveSize, MCMLE.effectiveSize.interval_drop, MCMLE.burnin, MCMLE.interval, MCMLE.samplesize, MCMLE.samplesize.per_theta, MCMLE.samplesize.min

Sets the corresponding ⁠MCMC.*⁠ parameters when main.method="MCMLE" (the default). Used because defaults may be different for different methods. MCMLE.samplesize.per_theta controls the MCMC sample size (not target effective size) as a function of the number of (curved) parameters in the model, and MCMLE.samplesize.min sets the minimum sample size regardless of their number.
MCMLE.steplength.solver

The linear program solver to use for MCMLE step length calculation. Can be either "glpk" to use Rglpk or "lpsolve" to use lpSolveAPI. Rglpk can be orders of magnitude faster, particularly for models with many parameters and with large sample sizes, so it is used where available; but it requires an external library to install under some operating systems, so fallback to lpSolveAPI provided.
MCMLE.last.boost

For the Hummel termination criterion, increase the MCMC sample size of the last iteration by this factor.
MCMLE.steplength.esteq

For curved ERGMs, should the estimating function values be used to compute the Hummel step length? This allows the Hummel stepping algorithm converge when some sufficient statistics are at 0.
MCMLE.steplength.miss.sample

In fitting the missing data MLE, the rules for step length become more complicated. In short, it is necessary for all points in the constrained sample to be in the convex hull of the unconstrained (though they may be on the border); and it is necessary for their centroid to be in its interior. This requires checking a large number of points against whether they are in the convex hull, so to speed up the procedure, a sample is taken of the points most likely to be outside it. This parameter specifies the sample size or a function of the unconstrained sample matrix to determine the sample size. If the parameter or the return value of the function has a length of 2, the first element is used as the sample size, and the second element is used in an early-termination heuristic, only continuing the tests until this many test points in a row did not yield a change in the step length.
MCMLE.steplength.min

Stops MCMLE estimation when the step length gets stuck below this minimum value.
MCMLE.save_intermediates

Every iteration, after MCMC sampling, save the MCMC sample and some miscellaneous information to a file with this name. This is mainly useful for diagnostics and debugging. The name is passed through sprintf() with iteration number as the second argument. (For example, MCMLE.save_intermediates="step_%03d.RData" will save to step_001.RData, step_002.RData, etc.)
SA.phase1_n

A constant or a function of number of free parameters q, number of free canonical statistic p, and network size n, giving the number of MCMC samples to draw in Phase 1 of the stochastic approximation algorithm. Defaults to max⁡(200,7+3p)\max(200, 7+3p). See Snijders (2002) for details.
SA.initial_gain

Initial gain to Phase 2 of the stochastic approximation algorithm. Defaults to 0.1. See Snijders (2002) for details.
SA.nsubphases

Number of sub-phases in Phase 2 of the stochastic approximation algorithm. Defaults to MCMLE.maxit. See Snijders (2002) for details.
SA.min_iterations, SA.max_iterations

A constant or a function of number of free parameters q, number of free canonical statistic p, and network size n, giving the baseline numbers of iterations within each subphase of Phase 2 of the stochastic approximation algorithm. Default to 7+p7+p and 207+p207+p, respectively. See Snijders (2002) for details.
SA.phase3_n

Sample size for the MCMC sample in Phase 3 of the stochastic approximation algorithm. See Snijders (2002) for details.
SA.burnin, SA.interval, SA.samplesize

Sets the corresponding ⁠MCMC.*⁠ parameters when main.method="Stochastic-Approximation".
CD.samplesize.per_theta, obs.CD.samplesize.per_theta, CD.maxit, CD.conv.min.pval, CD.NR.maxit, CD.NR.reltol, CD.metric, CD.method, CD.dampening, CD.dampening.min.ess, CD.dampening.level, CD.steplength.margin, CD.steplength, CD.steplength.parallel, CD.adaptive.epsilon, CD.steplength.esteq, CD.steplength.miss.sample, CD.steplength.min, CD.steplength.solver

Miscellaneous tuning parameters of the CD sampler and optimizer. These have the same meaning as their ⁠MCMLE.*⁠ and ⁠MCMC.*⁠ counterparts.

Note that only the Hotelling's stopping criterion is implemented for CD.
CD.nsteps, CD.multiplicity

Main settings for contrastive divergence to obtain initial values for the estimation: respectively, the number of Metropolis–Hastings steps to take before reverting to the starting value and the number of tentative proposals per step. Computational experiments indicate that increasing CD.multiplicity improves the estimate faster than increasing CD.nsteps — up to a point — but it also samples from the wrong distribution, in the sense that while as CD.nsteps→∞\rightarrow\infty, the CD estimate approaches the MLE, this is not the case for CD.multiplicity.

In practice, MPLE, when available, usually outperforms CD for even a very high CD.nsteps (which is, in turn, not very stable), so CD is useful primarily when MPLE is not available. This feature is to be considered experimental and in flux.

The default values have been set experimentally, providing a reasonably stable, if not great, starting values.
CD.nsteps.obs, CD.multiplicity.obs

When there are missing dyads, CD.nsteps and CD.multiplicity must be set to a relatively high value, as the network passed is not necessarily a good start for CD. Therefore, these settings are in effect if there are missing dyads in the observed network, using a higher default number of steps.
loglik

See control.ergm.bridge()
term.options

A list of additional arguments to be passed to term initializers. See ? term.options.
seed

Seed value (integer) for the random number generator. See set.seed().
parallel

Number of threads in which to run the sampling. Defaults to 0 (no parallelism). See ergm-parallel for details and troubleshooting.
parallel.type

API to use for parallel processing. Defaults to using the parallel package with PSOCK clusters. See ergm-parallel.
parallel.version.check

Logical: If TRUE, check that the version of ergm running on the slave nodes is the same as that running on the master node.
parallel.inherit.MT

Logical: If TRUE, slave nodes and processes inherit the set.MT_terms() setting.
...

A dummy argument to catch deprecated or mistyped control parameters.

Details

Different estimation methods or components of estimation have different efficient tuning parameters; and we generally want to use the estimation controls to inform the simulation controls in control.simulate.ergm(). To accomplish this, control.ergm() uses method-specific controls, with the method identified by the prefix:

CD

Contrastive Divergence estimation (Krivitsky 2017)

MPLE

Maximum Pseudo-Likelihood Estimation (Strauss and Ikeda 1990)

MCMLE

Monte-Carlo MLE (Hunter and Handcock 2006; Hummel et al. 2012)

SA

Stochastic Approximation via Robbins–Monro (Robbins and Monro 1951; Snijders 2002)

SAN

Simulated Annealing used when target.stats are specified for ergm()

obs

Missing data MLE (Handcock and Gile 2010)

init

Affecting how initial parameter guesses are obtained

parallel

Affecting parallel processing

MCMC

Low-level MCMC simulation controls

Corresponding MCMC controls will usually be overwritten by the method-specific ones. After the estimation finishes, they will contain the last MCMC parameters used.

Value

A list with arguments as components.

References

Handcock MS, Gile KJ (2010). “Modeling Social Networks from Sampled Data.” Annals of Applied Statistics, 4(1), 5–25. ISSN 1932-6157, doi:10.1214/08-AOAS221.

Hummel RM, Hunter DR, Handcock MS (2012). “Improving Simulation-based Algorithms for Fitting ERGMs.” Journal of Computational and Graphical Statistics, 21(4), 920–939. doi:10.1080/10618600.2012.679224.

Hunter DR, Handcock MS (2006). “Inference in Curved Exponential Family Models for Networks.” Journal of Computational and Graphical Statistics, 15(3), 565–583. ISSN 1061-8600, doi:10.1198/106186006X133069.

Krivitsky PN (2017). “Using Contrastive Divergence to Seed Monte Carlo MLE for Exponential-family Random Graph Models.” Computational Statistics & Data Analysis, 107, 149–161. doi:10.1016/j.csda.2016.10.015.

Robbins H, Monro S (1951). “A Stochastic Approximation Method.” The Annals of Mathematical Statistics, 22(3), 400–407. ISSN 00034851.

Schmid CS, Desmarais BA (2017). “Exponential random graph models with big networks: Maximum pseudolikelihood estimation and the parametric bootstrap.” In 2017 IEEE International Conference on Big Data (Big Data), 116–121. doi:10.1109/bigdata.2017.8257919.

Schmid CS, Hunter DR (2023). “Computing Pseudolikelihood Estimators for Exponential-Family Random Graph Models.” Journal of Data Science, 21(2), 295–309. doi:10.6339/23-JDS1094.

Snijders TAB (2002). “Markov chain Monte Carlo Estimation of Exponential Random Graph Models.” Journal of Social Structure, 3(2).

Strauss D, Ikeda M (1990). “Pseudolikelihood Estimation for Social Networks.” Journal of the American Statistical Association, 85(409), 204–212. ISSN 0162-1459, doi:10.1080/01621459.1990.10475327.

Vats D, Flegal JM, Jones GL (2019). “Multivariate output analysis for Markov chain Monte Carlo.” Biometrika, 106(2), 321-337. doi:10.1093/biomet/asz002.

See Also

ergm(). The control.simulate() function performs a similar function for simulate.ergm(); control.gof() performs a similar function for gof().

Auxiliaries for Controlling ergm.bridge.llr() and logLik.ergm()

Description

Auxiliary functions as user interfaces for fine-tuning the ergm.bridge.llr() algorithm, which approximates log likelihood ratios using bridge sampling.

By default, the bridge sampler inherits its control parameters from the ergm() fit; control.logLik.ergm() allows the user to selectively override them.

Usage

control.ergm.bridge(
  bridge.nsteps = 16,
  bridge.target.se = NULL,
  bridge.bidirectional = TRUE,
  drop = TRUE,
  MCMC.burnin = MCMC.interval * 128,
  MCMC.burnin.between = max(ceiling(MCMC.burnin/sqrt(bridge.nsteps)), MCMC.interval * 16),
  MCMC.interval = 128,
  MCMC.samplesize = 16384,
  obs.MCMC.burnin = obs.MCMC.interval * 128,
  obs.MCMC.burnin.between = max(ceiling(obs.MCMC.burnin/sqrt(bridge.nsteps)),
    obs.MCMC.interval * 16),
  obs.MCMC.interval = MCMC.interval,
  obs.MCMC.samplesize = MCMC.samplesize,
  MCMC.prop = trim_env(~sparse + .triadic),
  MCMC.prop.weights = "default",
  MCMC.prop.args = list(),
  obs.MCMC.prop = MCMC.prop,
  obs.MCMC.prop.weights = MCMC.prop.weights,
  obs.MCMC.prop.args = MCMC.prop.args,
  MCMC.maxedges = Inf,
  MCMC.packagenames = c(),
  term.options = list(),
  seed = NULL,
  parallel = 0,
  parallel.type = NULL,
  parallel.version.check = TRUE,
  parallel.inherit.MT = FALSE,
  ...
)

control.logLik.ergm(
  bridge.nsteps = 16,
  bridge.target.se = NULL,
  bridge.bidirectional = TRUE,
  drop = NULL,
  MCMC.burnin = NULL,
  MCMC.interval = NULL,
  MCMC.samplesize = NULL,
  obs.MCMC.samplesize = MCMC.samplesize,
  obs.MCMC.interval = MCMC.interval,
  obs.MCMC.burnin = MCMC.burnin,
  MCMC.prop = NULL,
  MCMC.prop.weights = NULL,
  MCMC.prop.args = NULL,
  obs.MCMC.prop = MCMC.prop,
  obs.MCMC.prop.weights = MCMC.prop.weights,
  obs.MCMC.prop.args = MCMC.prop.args,
  MCMC.maxedges = Inf,
  MCMC.packagenames = NULL,
  term.options = NULL,
  seed = NULL,
  parallel = NULL,
  parallel.type = NULL,
  parallel.version.check = TRUE,
  parallel.inherit.MT = FALSE,
  ...
)

Arguments

bridge.nsteps

Number of geometric bridges to use.
bridge.target.se

If not NULL, if the estimated MCMC standard error of the likelihood estimate exceeds this, repeat the bridge sampling, accumulating samples.
bridge.bidirectional

Whether the bridge sampler first bridges from from to to, then from to to from (skipping the first burn-in), etc. if multiple attempts are required.
drop

See control.ergm().
MCMC.burnin

Number of proposals before any MCMC sampling is done. It typically is set to a fairly large number.
MCMC.burnin.between

Number of proposals between the bridges; typically, less and less is needed as the number of steps decreases.
MCMC.interval

Number of proposals between sampled statistics.
MCMC.samplesize

Number of network statistics, randomly drawn from a given distribution on the set of all networks, returned by the Metropolis-Hastings algorithm.
obs.MCMC.burnin, obs.MCMC.burnin.between, obs.MCMC.interval, obs.MCMC.samplesize

The obs versions of these arguments are for the unobserved data simulation algorithm.
MCMC.prop

Specifies the proposal (directly) and/or a series of "hints" about the structure of the model being sampled. The specification is in the form of a one-sided formula with hints separated by + operations. If the LHS exists and is a string, the proposal to be used is selected directly.

A common and default "hint" is ~sparse, indicating that the network is sparse and that the sample should put roughly equal weight on selecting a dyad with or without a tie as a candidate for toggling.
MCMC.prop.weights

Specifies the proposal distribution used in the MCMC Metropolis-Hastings algorithm. Possible choices depending on selected reference and constraints arguments of the ergm() function, but often include "TNT" and "random", and the "default" is to use the one with the highest priority available.
MCMC.prop.args

An alternative, direct way of specifying additional arguments to proposal.
obs.MCMC.prop, obs.MCMC.prop.weights, obs.MCMC.prop.args

The obs versions of these arguments are for the unobserved data simulation algorithm.
MCMC.maxedges

The maximum number of edges that may occur during the MCMC sampling. If this number is exceeded at any time, sampling is stopped immediately.
MCMC.packagenames

Names of packages in which to look for change statistic functions in addition to those autodetected. This argument should not be needed outside of very strange setups.
term.options

A list of additional arguments to be passed to term initializers. See ? term.options.
seed

Seed value (integer) for the random number generator. See set.seed().
parallel

Number of threads in which to run the sampling. Defaults to 0 (no parallelism). See ergm-parallel for details and troubleshooting.
parallel.type

API to use for parallel processing. Defaults to using the parallel package with PSOCK clusters. See ergm-parallel.
parallel.version.check

Logical: If TRUE, check that the version of ergm running on the slave nodes is the same as that running on the master node.
parallel.inherit.MT

Logical: If TRUE, slave nodes and processes inherit the set.MT_terms() setting.
...

A dummy argument to catch deprecated or mistyped control parameters.

Details

control.ergm.bridge() is only used within a call to the ergm.bridge.llr(), ergm.bridge.dindstart.llk(), or ergm.bridge.0.llk() functions.

control.logLik.ergm() is only used within a call to the logLik.ergm().

Value

A list with arguments as components.

See Also

ergm.bridge.llr()

logLik.ergm()

Auxiliary for Controlling ERGM Goodness-of-Fit Evaluation

Description

Auxiliary function as user interface for fine-tuning ERGM Goodness-of-Fit Evaluation.

The control.gof.ergm version is intended to be used with gof.ergm() specifically and will "inherit" as many control parameters from ergm fit as possible().

Usage

control.gof.formula(
  nsim = 100,
  MCMC.burnin = 10000,
  MCMC.interval = 1000,
  MCMC.batch = 0,
  MCMC.prop = trim_env(~sparse + .triadic),
  MCMC.prop.weights = "default",
  MCMC.prop.args = list(),
  MCMC.maxedges = Inf,
  MCMC.packagenames = c(),
  MCMC.runtime.traceplot = FALSE,
  network.output = "network",
  seed = NULL,
  parallel = 0,
  parallel.type = NULL,
  parallel.version.check = TRUE,
  parallel.inherit.MT = FALSE
)

control.gof.ergm(
  nsim = 100,
  MCMC.burnin = NULL,
  MCMC.interval = NULL,
  MCMC.batch = NULL,
  MCMC.prop = NULL,
  MCMC.prop.weights = NULL,
  MCMC.prop.args = NULL,
  MCMC.maxedges = NULL,
  MCMC.packagenames = NULL,
  MCMC.runtime.traceplot = FALSE,
  network.output = "network",
  seed = NULL,
  parallel = 0,
  parallel.type = NULL,
  parallel.version.check = TRUE,
  parallel.inherit.MT = FALSE
)

Arguments

nsim

Number of networks to be randomly drawn using Markov chain Monte Carlo. This sample of networks provides the basis for comparing the model to the observed network.
MCMC.burnin

Number of proposals before any MCMC sampling is done. It typically is set to a fairly large number.
MCMC.interval

Number of proposals between sampled statistics.
MCMC.batch

if not 0 or NULL, sample about this many networks per call to the lower-level code; this can be useful if ⁠output=⁠ is a function, where it can be used to limit the number of networks held in memory at any given time.
MCMC.prop

Specifies the proposal (directly) and/or a series of "hints" about the structure of the model being sampled. The specification is in the form of a one-sided formula with hints separated by + operations. If the LHS exists and is a string, the proposal to be used is selected directly.

A common and default "hint" is ~sparse, indicating that the network is sparse and that the sample should put roughly equal weight on selecting a dyad with or without a tie as a candidate for toggling.
MCMC.prop.weights

Specifies the proposal distribution used in the MCMC Metropolis-Hastings algorithm. Possible choices depending on selected reference and constraints arguments of the ergm() function, but often include "TNT" and "random", and the "default" is to use the one with the highest priority available.
MCMC.prop.args

An alternative, direct way of specifying additional arguments to proposal.
MCMC.maxedges

The maximum number of edges that may occur during the MCMC sampling. If this number is exceeded at any time, sampling is stopped immediately.
MCMC.packagenames

Names of packages in which to look for change statistic functions in addition to those autodetected. This argument should not be needed outside of very strange setups.
MCMC.runtime.traceplot

Logical: If TRUE, plot traceplots of the MCMC sample.
network.output

R class with which to output networks. The options are "network" (default) and "edgelist.compressed" (which saves space but only supports networks without vertex attributes)
seed

Seed value (integer) for the random number generator. See set.seed().
parallel

Number of threads in which to run the sampling. Defaults to 0 (no parallelism). See ergm-parallel for details and troubleshooting.
parallel.type

API to use for parallel processing. Defaults to using the parallel package with PSOCK clusters. See ergm-parallel.
parallel.version.check

Logical: If TRUE, check that the version of ergm running on the slave nodes is the same as that running on the master node.
parallel.inherit.MT

Logical: If TRUE, slave nodes and processes inherit the set.MT_terms() setting.

Details

This function is only used within a call to the gof() function. See the Usage section in gof() for details.

Value

A list with arguments as components.

See Also

gof(). The control.simulate() function performs a similar function for simulate.ergm(); control.ergm() performs a similar function for ergm().

Auxiliary for Controlling SAN

Description

Auxiliary function as user interface for fine-tuning simulated annealing algorithm.

Usage

control.san(
  SAN.maxit = 4,
  SAN.tau = 1,
  SAN.invcov = NULL,
  SAN.invcov.diag = FALSE,
  SAN.nsteps.alloc = function(nsim) 2^seq_len(nsim),
  SAN.nsteps = 2^19,
  SAN.samplesize = 2^12,
  SAN.prop = trim_env(~sparse + .triadic),
  SAN.prop.weights = "default",
  SAN.prop.args = list(),
  SAN.packagenames = c(),
  SAN.ignore.finite.offsets = TRUE,
  term.options = list(),
  seed = NULL,
  parallel = 0,
  parallel.type = NULL,
  parallel.version.check = TRUE,
  parallel.inherit.MT = FALSE
)

Arguments

SAN.maxit

Number of temperature levels to use.
SAN.tau

Tuning parameter, specifying the temperature of the process during the penultimate iteration. (During the last iteration, the temperature is set to 0, resulting in a greedy search, and during the previous iterations, the temperature is set to ⁠SAN.tau*(iterations left after this one)⁠.
SAN.invcov

Initial inverse covariance matrix used to calculate Mahalanobis distance in determining how far a proposed MCMC move is from the target.stats vector. If NULL, initially set to the identity matrix. In either case, during subsequent runs, it is estimated empirically.
SAN.invcov.diag

Whether to only use the diagonal of the covariance matrix. It seems to work better in practice.
SAN.nsteps.alloc

Either a numeric vector or a function of the number of runs giving a sequence of relative lengths of simulated annealing runs.
SAN.nsteps

Number of MCMC proposals for all the annealing runs combined.
SAN.samplesize

Number of realisations' statistics to obtain for tuning purposes.
SAN.prop

Specifies the proposal (directly) and/or a series of "hints" about the structure of the model being sampled. The specification is in the form of a one-sided formula with hints separated by + operations. If the LHS exists and is a string, the proposal to be used is selected directly.

A common and default "hint" is ~sparse, indicating that the network is sparse and that the sample should put roughly equal weight on selecting a dyad with or without a tie as a candidate for toggling.
SAN.prop.weights

Specifies the proposal distribution used in the SAN Metropolis-Hastings algorithm. Possible choices depending on selected reference and constraints arguments of the ergm() function, but often include "TNT" and "random", and the "default" is to use the one with the highest priority available.
SAN.prop.args

An alternative, direct way of specifying additional arguments to proposal.
SAN.packagenames

Names of packages in which to look for change statistic functions in addition to those autodetected. This argument should not be needed outside of very strange setups.
SAN.ignore.finite.offsets

Whether SAN should ignore (treat as 0) finite offsets.
term.options

A list of additional arguments to be passed to term initializers. See ? term.options.
seed

Seed value (integer) for the random number generator. See set.seed().
parallel

Number of threads in which to run the sampling. Defaults to 0 (no parallelism). See ergm-parallel for details and troubleshooting.
parallel.type

API to use for parallel processing. Defaults to using the parallel package with PSOCK clusters. See ergm-parallel.
parallel.version.check

Logical: If TRUE, check that the version of ergm running on the slave nodes is the same as that running on the master node.
parallel.inherit.MT

Logical: If TRUE, slave nodes and processes inherit the set.MT_terms() setting.

Details

This function is only used within a call to the san() function. See the Usage section in san() for details.

Value

A list with arguments as components.

See Also

san()

Auxiliary for Controlling ERGM Simulation

Description

Auxiliary function as user interface for fine-tuning ERGM simulation. control.simulate, control.simulate.formula, and control.simulate.formula.ergm are all aliases for the same function.

While the others supply a full set of simulation settings, control.simulate.ergm when passed as a control parameter to simulate.ergm() allows some settings to be inherited from the ERGM stimation while overriding others.

Usage

control.simulate.formula.ergm(
  MCMC.burnin = MCMC.interval * 16,
  MCMC.interval = 1024,
  MCMC.prop = trim_env(~sparse + .triadic),
  MCMC.prop.weights = "default",
  MCMC.prop.args = list(),
  MCMC.batch = NULL,
  MCMC.effectiveSize = NULL,
  MCMC.effectiveSize.damp = 10,
  MCMC.effectiveSize.maxruns = 1000,
  MCMC.effectiveSize.burnin.pval = 0.2,
  MCMC.effectiveSize.burnin.min = 0.05,
  MCMC.effectiveSize.burnin.max = 0.5,
  MCMC.effectiveSize.burnin.nmin = 16,
  MCMC.effectiveSize.burnin.nmax = 128,
  MCMC.effectiveSize.burnin.PC = FALSE,
  MCMC.effectiveSize.burnin.scl = 1024,
  MCMC.effectiveSize.order.max = NULL,
  MCMC.maxedges = Inf,
  MCMC.packagenames = c(),
  MCMC.runtime.traceplot = FALSE,
  network.output = "network",
  term.options = NULL,
  parallel = 0,
  parallel.type = NULL,
  parallel.version.check = TRUE,
  parallel.inherit.MT = FALSE,
  ...
)

control.simulate(
  MCMC.burnin = MCMC.interval * 16,
  MCMC.interval = 1024,
  MCMC.prop = trim_env(~sparse + .triadic),
  MCMC.prop.weights = "default",
  MCMC.prop.args = list(),
  MCMC.batch = NULL,
  MCMC.effectiveSize = NULL,
  MCMC.effectiveSize.damp = 10,
  MCMC.effectiveSize.maxruns = 1000,
  MCMC.effectiveSize.burnin.pval = 0.2,
  MCMC.effectiveSize.burnin.min = 0.05,
  MCMC.effectiveSize.burnin.max = 0.5,
  MCMC.effectiveSize.burnin.nmin = 16,
  MCMC.effectiveSize.burnin.nmax = 128,
  MCMC.effectiveSize.burnin.PC = FALSE,
  MCMC.effectiveSize.burnin.scl = 1024,
  MCMC.effectiveSize.order.max = NULL,
  MCMC.maxedges = Inf,
  MCMC.packagenames = c(),
  MCMC.runtime.traceplot = FALSE,
  network.output = "network",
  term.options = NULL,
  parallel = 0,
  parallel.type = NULL,
  parallel.version.check = TRUE,
  parallel.inherit.MT = FALSE,
  ...
)

control.simulate.formula(
  MCMC.burnin = MCMC.interval * 16,
  MCMC.interval = 1024,
  MCMC.prop = trim_env(~sparse + .triadic),
  MCMC.prop.weights = "default",
  MCMC.prop.args = list(),
  MCMC.batch = NULL,
  MCMC.effectiveSize = NULL,
  MCMC.effectiveSize.damp = 10,
  MCMC.effectiveSize.maxruns = 1000,
  MCMC.effectiveSize.burnin.pval = 0.2,
  MCMC.effectiveSize.burnin.min = 0.05,
  MCMC.effectiveSize.burnin.max = 0.5,
  MCMC.effectiveSize.burnin.nmin = 16,
  MCMC.effectiveSize.burnin.nmax = 128,
  MCMC.effectiveSize.burnin.PC = FALSE,
  MCMC.effectiveSize.burnin.scl = 1024,
  MCMC.effectiveSize.order.max = NULL,
  MCMC.maxedges = Inf,
  MCMC.packagenames = c(),
  MCMC.runtime.traceplot = FALSE,
  network.output = "network",
  term.options = NULL,
  parallel = 0,
  parallel.type = NULL,
  parallel.version.check = TRUE,
  parallel.inherit.MT = FALSE,
  ...
)

control.simulate.ergm(
  MCMC.burnin = NULL,
  MCMC.interval = NULL,
  MCMC.scale = 1,
  MCMC.prop = NULL,
  MCMC.prop.weights = NULL,
  MCMC.prop.args = NULL,
  MCMC.batch = NULL,
  MCMC.effectiveSize = NULL,
  MCMC.effectiveSize.damp = 10,
  MCMC.effectiveSize.maxruns = 1000,
  MCMC.effectiveSize.burnin.pval = 0.2,
  MCMC.effectiveSize.burnin.min = 0.05,
  MCMC.effectiveSize.burnin.max = 0.5,
  MCMC.effectiveSize.burnin.nmin = 16,
  MCMC.effectiveSize.burnin.nmax = 128,
  MCMC.effectiveSize.burnin.PC = FALSE,
  MCMC.effectiveSize.burnin.scl = 1024,
  MCMC.effectiveSize.order.max = NULL,
  MCMC.maxedges = Inf,
  MCMC.packagenames = NULL,
  MCMC.runtime.traceplot = FALSE,
  network.output = "network",
  term.options = NULL,
  parallel = 0,
  parallel.type = NULL,
  parallel.version.check = TRUE,
  parallel.inherit.MT = FALSE,
  ...
)

Arguments

MCMC.burnin

Number of proposals before any MCMC sampling is done. It typically is set to a fairly large number.
MCMC.interval

Number of proposals between sampled statistics.
MCMC.prop

Specifies the proposal (directly) and/or a series of "hints" about the structure of the model being sampled. The specification is in the form of a one-sided formula with hints separated by + operations. If the LHS exists and is a string, the proposal to be used is selected directly.

A common and default "hint" is ~sparse, indicating that the network is sparse and that the sample should put roughly equal weight on selecting a dyad with or without a tie as a candidate for toggling.
MCMC.prop.weights

Specifies the proposal distribution used in the MCMC Metropolis-Hastings algorithm. Possible choices depending on selected reference and constraints arguments of the ergm() function, but often include "TNT" and "random", and the "default" is to use the one with the highest priority available.
MCMC.prop.args

An alternative, direct way of specifying additional arguments to proposal.
MCMC.batch

if not 0 or NULL, sample about this many networks per call to the lower-level code; this can be useful if ⁠output=⁠ is a function, where it can be used to limit the number of networks held in memory at any given time.
MCMC.effectiveSize, MCMC.effectiveSize.damp, MCMC.effectiveSize.maxruns, MCMC.effectiveSize.burnin.pval, MCMC.effectiveSize.burnin.min, MCMC.effectiveSize.burnin.max, MCMC.effectiveSize.burnin.nmin, MCMC.effectiveSize.burnin.nmax, MCMC.effectiveSize.burnin.PC, MCMC.effectiveSize.burnin.scl, MCMC.effectiveSize.order.max

Set MCMC.effectiveSize to a non-NULL value to adaptively determine the burn-in and the MCMC length needed to get the specified effective size; 50 is a reasonable value. In the adaptive MCMC mode, MCMC is run forward repeatedly (MCMC.samplesize*MCMC.interval steps, up to MCMC.effectiveSize.maxruns times) until the target effective sample size is reached or exceeded.

After each run, the returned statistics are mapped to the estimating function scale, then an exponential decay model is fit to the scaled statistics to find that burn-in which would reduce the difference between the initial values of statistics and their equilibrium values by a factor of MCMC.effectiveSize.burnin.scl of what it initially was, bounded by MCMC.effectiveSize.min and MCMC.effectiveSize.max as proportions of sample size. If the best-fitting decay exceeds MCMC.effectiveSize.max, the exponential model is considered to be unsuitable and MCMC.effectiveSize.min is used.

A Geweke diagnostic is then run, after thinning the sample to MCMC.effectiveSize.burnin.nmax. If this Geweke diagnostic produces a pp-value higher than MCMC.effectiveSize.burnin.pval, it is accepted.

If MCMC.effectiveSize.burnin.PC>0, instead of using the full sample for burn-in estimation, at most this many principal components are used instead.

The effective size of the post-burn-in sample is computed via Vats et al. (2019), and compared to the target effective size. If it is not matched, the MCMC run is resumed, with the additional draws needed linearly extrapolated but weighted in favor of the baseline MCMC.samplesize by the weighting factor MCMC.effectiveSize.damp (higher = less damping). Lastly, if after an MCMC run, the number of samples equals or exceeds 2*MCMC.samplesize, the chain will be thinned by 2 until it falls below that, while doubling MCMC.interval. MCMC.effectiveSize.order.max can be used to set the order of the AR model used to estimate the effective sample size and the variance for the Geweke diagnostic.

Lastly, if MCMC.effectiveSize is a matrix, say, WW, it will be treated as a target precision (inverse-variance) matrix. If VV is the sample covariance matrix, the target effective size neffn_{\text{eff}} will be set such that V/neffV/n_{\text{eff}} is close to WW in magnitude, specifically that tr⁡((V/neff)W)/p≈1\operatorname{tr}((V/n_{\text{eff}})W)/p\approx 1.
MCMC.maxedges

The maximum number of edges that may occur during the MCMC sampling. If this number is exceeded at any time, sampling is stopped immediately.
MCMC.packagenames

Names of packages in which to look for change statistic functions in addition to those autodetected. This argument should not be needed outside of very strange setups.
MCMC.runtime.traceplot

Logical: If TRUE, plot traceplots of the MCMC sample.
network.output

R class with which to output networks. The options are "network" (default) and "edgelist.compressed" (which saves space but only supports networks without vertex attributes)
term.options

A list of additional arguments to be passed to term initializers. See ? term.options.
parallel

Number of threads in which to run the sampling. Defaults to 0 (no parallelism). See ergm-parallel for details and troubleshooting.
parallel.type

API to use for parallel processing. Defaults to using the parallel package with PSOCK clusters. See ergm-parallel.
parallel.version.check

Logical: If TRUE, check that the version of ergm running on the slave nodes is the same as that running on the master node.
parallel.inherit.MT

Logical: If TRUE, slave nodes and processes inherit the set.MT_terms() setting.
...

A dummy argument to catch deprecated or mistyped control parameters.
MCMC.scale

For control.simulate.ergm() inheriting MCMC.burnin and MCMC.interval from the ergm fit, the multiplier for the inherited values. This can be useful because MCMC parameters used in the fit are tuned to generate a specific effective sample size for the sufficient statistic in a large MCMC sample, so the inherited values might not generate independent realisations.

Details

This function is only used within a call to the ERGM simulate() function. See the Usage section in simulate.ergm() for details.

Value

A list with arguments as components.

See Also

simulate.ergm(), simulate.formula(). control.ergm() performs a similar function for ergm(); control.gof() performs a similar function for gof().

Cyclic triples

Description

By default, this term adds one statistic to the model, equal to the number of cyclic triples in the network, defined as a set of edges of the form {(i→j),(j→k),(k→i)}\{(i{\rightarrow}j), (j{\rightarrow}k), (k{\rightarrow}i)\} .

Usage

# binary: ctriple(attr=NULL, diff=FALSE, levels=NULL)

# binary: ctriad

Arguments

attr, diff

quantitative attribute (see Specifying Vertex attributes and Levels (?nodal_attributes) for details.) If attr is specified and diff is FALSE , then the statistic is the number of cyclic triples where all three nodes have the same value of the attribute. If attr is specified and diff is TRUE , then one statistic is added to the model for each value of attr, equal to the number of cyclic triples where all three nodes have that value of the attribute.
levels

specifies the value of attr to consider if attr is passed and diff=TRUE. (See Specifying Vertex attributes and Levels (?nodal_attributes) for details.)

Note

This term can only be used with directed networks.

for all directed networks, triangle is equal to ttriple+ctriple , so at most two of these three terms can be in a model.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

categorical nodal attribute, directed, triad-related, binary

Impose a curved structure on term parameters

Description

Arguments may have the same forms as in the API, but for convenience, alternative forms are accepted.

If the model in formula is curved, then the outputs of this operator term's map argument will be used as inputs to the curved terms of the formula model.

Curve is an obsolete alias and may be deprecated and removed in a future release.

Usage

# binary: Curve(formula, params, map, gradient=NULL, minpar=-Inf, maxpar=+Inf, cov=NULL)

# binary: Parametrise(formula, params, map, gradient=NULL, minpar=-Inf, maxpar=+Inf,
#           cov=NULL)

# binary: Parametrize(formula, params, map, gradient=NULL, minpar=-Inf, maxpar=+Inf,
#           cov=NULL)

# valued: Curve(formula, params, map, gradient=NULL, minpar=-Inf, maxpar=+Inf, cov=NULL)

# valued: Parametrise(formula, params, map, gradient=NULL, minpar=-Inf, maxpar=+Inf,
#           cov=NULL)

# valued: Parametrize(formula, params, map, gradient=NULL, minpar=-Inf, maxpar=+Inf,
#           cov=NULL)

Arguments

formula

a one-sided ergm()-style formula with the terms to be evaluated
params

a named list whose names are the curved parameter names, may also be a character vector with names.
map

the mapping from curved to canonical. May have the following forms:

  • a ⁠function(x, n, ...)⁠ treated as in the API: called with x set to the curved parameter vector, n to the length of output expected, and cov , if present, passed in ... . The function must return a numeric vector of length n .

  • a numeric vector to fix the output coefficients, like in an offset.

  • a character string to select (partially-matched) one of predefined forms. Currently, the defined forms include:

    • "rep" recycle the input vector to the length of the output vector as a rep function would.

gradient

its gradient function. It is optional if map is constant or one of the predefined forms; otherwise it must have one of the following forms:

  • a ⁠function(x, n, ...)⁠ treated as in the API: called with x set to the curved parameter vector, n to the length of output expected, and cov , if present, passed in ... . The function must return a numeric matrix with length(params) rows and n columns.

  • a numeric matrix to fix the gradient; this is useful when map is linear.

  • a character string to select (partially-matched) one of predefined forms. Currently, the defined forms include:

    • "linear" calculate the (constant) gradient matrix using finite differences. Note that this will be done only once at the initialization stage, so use only if you are certain map is, in fact, linear.

minpar, maxpar

the minimum and maximum allowed curved parameter values. The parameters will be recycled to the appropriate length.
cov

optional

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

operator, binary, valued

k-Cycle Census

Description

This term adds one network statistic to the model for each value of k , corresponding to the number of k -cycles (or, alternately, semicycles) in the graph.

This term can be used with either directed or undirected networks.

Usage

# binary: cycle(k, semi=FALSE)

Arguments

k

a vector of integers giving the cycle lengths to count. Directed cycle lengths may range from 2 to N (the network size); undirected cycle lengths and semicycle lengths may range from 3 to N ; length 2 semicycles are not currently supported.
semi

an optional logical indicating whether semicycles (rather than directed cycles) should be counted; this is ignored in the undirected case.
directed

2-cycles are equivalent to mutual dyads.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

directed, undirected, binary

Cyclical ties

Description

This term adds one statistic, equal to the number of ties i→ji\rightarrow j such that there exists a two-path from jj to ii . (Related to the ttriple term.)

Usage

# binary: cyclicalties(attr=NULL, levels=NULL)

# valued: cyclicalties(threshold=0)

Arguments

attr

quantitative attribute (see Specifying Vertex attributes and Levels (?nodal_attributes) for details.) If set, all three nodes involved ( ii , jj , and the node on the two-path) must match on this attribute in order for i→ji\rightarrow j to be counted.
levels

TODO (See Specifying Vertex attributes and Levels (?nodal_attributes) for details.)

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

directed, undirected, binary, valued

Cyclical weights

Description

This statistic implements the cyclical weights statistic, like that defined by Krivitsky (2012), Equation 13, but with the focus dyad being yj,iy_{j,i} rather than yi,jy_{i,j} . For each option, the first (and the default) is more stable but also more conservative, while the second is more sensitive but more likely to induce a multimodal distribution of networks.

Usage

# valued: cyclicalweights(twopath="min", combine="max", affect="min")

Arguments

twopath

the minimum of the constituent dyads ( "min" ) or their geometric mean ( "geomean" )
combine

the maximum of the 2-path strengths ( "max" ) or their sum ( "sum" )
affected

the minimum of the focus dyad and the combined strength of the two paths ( "min" ) or their geometric mean ( "geomean" )

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

directed, nonnegative, undirected, valued

Degree Correlation

Description

This term adds one network statistic equal to the correlation of the degrees of all pairs of nodes in the network which are tied. Only coded for undirected networks.

Usage

# binary: degcor

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

undirected, binary

Degree Cross-Product

Description

This term adds one network statistic equal to the mean of the cross-products of the degrees of all pairs of nodes in the network which are tied. Only coded for undirected networks.

Usage

# binary: degcrossprod

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

undirected, binary

Degree range

Description

This term adds one network statistic to the model for each element of from (or to ); the ii th such statistic equals the number of nodes in the network of degree greater than or equal to from[i] but strictly less than to[i] , i.e. with edges in semiopen interval ⁠[from,to)⁠ .

Usage

# binary: degrange(from, to=+Inf, by=NULL, homophily=FALSE, levels=NULL)

Arguments

from, to

vectors of distinct integers. If one of the vectors have length 1, it is recycled to the length of the other. Otherwise, it must have the same length.
by, levels, homophily

the optional argument by specifies a vertex attribute (see Specifying Vertex attributes and Levels (?nodal_attributes) for details). If this is specified and homophily is TRUE , then degrees are calculated using the subnetwork consisting of only edges whose endpoints have the same value of the by attribute. If by is specified and homophily is FALSE (the default), then separate degree range statistics are calculated for nodes having each separate value of the attribute. levels selects which levels of by' to include.

Details

This term can only be used with undirected networks; for directed networks see idegrange and odegrange . This term can be used with bipartite networks, and will count nodes of both first and second mode in the specified degree range. To count only nodes of the first mode ("actors"), use b1degrange and to count only those fo the second mode ("events"), use b2degrange .

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

categorical nodal attribute, undirected, binary

Degree

Description

This term adds one network statistic to the model for each element in d ; the ii th such statistic equals the number of nodes in the network of degree d[i] , i.e. with exactly d[i] edges. This term can only be used with undirected networks; for directed networks see idegree and odegree .

Usage

# binary: degree(d, by=NULL, homophily=FALSE, levels=NULL)

Arguments

d

vector of distinct integers
by, levels, homophily

the optional argument by specifies a vertex attribute (see Specifying Vertex attributes and Levels (?nodal_attributes) for details). If this is specified and homophily is TRUE , then degrees are calculated using the subnetwork consisting of only edges whose endpoints have the same value of the by attribute. If by is specified and homophily is FALSE (the default), then separate degree range statistics are calculated for nodes having each separate value of the attribute. levels selects which levels of by' to include.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

categorical nodal attribute, frequently-used, undirected, binary

Degree to the 3/2 power

Description

This term adds one network statistic to the model equaling the sum over the actors of each actor's degree taken to the 3/2 power (or, equivalently, multiplied by its square root). This term is an undirected analog to the terms of Snijders et al. (2010), equations (11) and (12). This term can only be used with undirected networks.

Usage

# binary: degree1.5

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

undirected, binary

Computes and Returns the Degree Distribution Information for a Given Network

Description

The degreedist generic computes and returns the degree distribution (number of vertices in the network with each degree value) for a given network. This help page documents the function. For help about the ERGM sample space constraint with that name, try help("degreedist-constraint").

Usage

degreedist(object, ...)

## S3 method for class 'network'
degreedist(object, print = TRUE, ...)

Arguments

object

a network object or some other object for which degree distribution is meaningful.
...

Additional arguments to functions.
print

logical, whether to print the degree distribution.

Value

If directed, a matrix of the distributions of in and out degrees; this is row bound and only contains degrees for which one of the in or out distributions has a positive count. If bipartite, a list containing the degree distributions of b1 and b2. Otherwise, a vector of the positive values in the degree distribution

Methods (by class)

  • degreedist(network): Method for network objects.

Examples

data(faux.mesa.high)
degreedist(faux.mesa.high)

Preserve the degree distribution of the given network

Description

Only networks whose degree distributions are the same as those in the network passed in the model formula have non-zero probability.

Usage

# degreedist

See Also

ergmConstraint for index of constraints and hints currently visible to the package.

Keywords

directed, undirected

Preserve the degree of each vertex of the given network

Description

Only networks whose vertex degrees are the same as those in the network passed in the model formula have non-zero probability. If the network is directed, both indegree and outdegree are preserved.

Usage

# degrees

# nodedegrees

See Also

ergmConstraint for index of constraints and hints currently visible to the package.

Keywords

directed, undirected

Density

Description

This term adds one network statistic equal to the density of the network. For undirected networks, density equals kstar(1) or edges divided by n(n−1)/2n(n-1)/2 ; for directed networks, density equals edges or istar(1) or ostar(1) divided by n(n−1)n(n-1) .

Usage

# binary: density

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

directed, dyad-independent, undirected, binary

Difference

Description

For values of pow other than 0 , this term adds one network statistic to the model, equaling the sum, over directed edges (i,j)(i,j) , of sign.action(attr[i]-attr[j])^pow if dir is "t-h" and of sign.action(attr[j]-attr[i])^pow if "h-t" . That is, the argument dir determines which vertex's attribute is subtracted from which, with tail being the origin of a directed edge and head being its destination, and bipartite networks' edges being treated as going from the first part (b1) to the second (b2).

If pow==0 , the exponentiation is replaced by the signum function: +1 if the difference is positive, 0 if there is no difference, and -1 if the difference is negative. Note that this function is applied after the sign.action . The comparison is exact, so when using calculated values of attr , ensure that values that you want to be considered equal are, in fact, equal.

Usage

# binary: diff(attr, pow=1, dir="t-h", sign.action="identity")

# valued: diff(attr, pow=1, dir="t-h", sign.action="identity", form ="sum")

Arguments

attr

a vertex attribute specification (see Specifying Vertex attributes and Levels (?nodal_attributes) for details.)
pow

exponent for the node difference
dir

determines which vertix's attribute is subtracted from which. Accepts: "t-h" (the default), "tail-head" , "b1-b2", "h-t" , "head-tail" , and "b2-b1" .
sign.action

one of "identity", "abs", "posonly", "negonly". The following sign.actions are possible:

  • "identity" (the default) no transformation of the difference regardless of sign

  • "abs" absolute value of the difference: equivalent to the absdiff term

  • "posonly" positive differences are kept, negative differences are replaced by 0

  • "negonly" negative differences are kept, positive differences are replaced by 0

form

character how to aggregate tie values in a valued ERGM

Note

this term may not be meaningful for unipartite undirected networks unless sign.action=="abs" . When used on such a network, it behaves as if all edges were directed, going from the lower-indexed vertex to the higher-indexed vertex.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

bipartite, directed, dyad-independent, frequently-used, quantitative nodal attribute, undirected, binary, valued

Discrete Uniform reference

Description

Specifies each dyad's baseline distribution to be discrete uniform between a and b (both inclusive): h(y)=1h(y)=1 , with the support being a, a+1, ..., b-1, b.

Usage

# DiscUnif(a,b)

Arguments

a, b

minimum and maximum to the baseline discrete uniform distribution, both inclusive. Both values must be finite.

See Also

ergmReference for index of reference distributions currently visible to the package.

Keywords

discrete, finite

Directed dyadwise shared partners

Description

This term adds one network statistic to the model for each element in d where the ii th such statistic equals the number of dyads in the network with exactly d[i] shared partners.

Usage

# binary: ddsp(d, type="OTP")

# binary: dsp(d, type="OTP")

Arguments

d

a vector of distinct integers
type

A string indicating the type of shared partner or path to be considered for directed networks: "OTP" (default for directed), "ITP", "RTP", "OSP", and "ISP"; has no effect for undirected. See the section below on Shared partner types for details.

Shared partner types

While there is only one shared partner configuration in the undirected case, nine distinct configurations are possible for directed graphs, selected using the type argument. Currently, terms may be defined with respect to five of these configurations; they are defined here as follows (using terminology from Butts (2008) and the relevent package):

  • Outgoing Two-path ("OTP"): vertex kk is an OTP shared partner of ordered pair (i,j)(i,j) iff i→k→ji \to k \to j. Also known as "transitive shared partner".

  • Incoming Two-path ("ITP"): vertex kk is an ITP shared partner of ordered pair (i,j)(i,j) iff j→k→ij \to k \to i. Also known as "cyclical shared partner"

  • Reciprocated Two-path ("RTP"): vertex kk is an RTP shared partner of ordered pair (i,j)(i,j) iff i↔k↔ji \leftrightarrow k \leftrightarrow j.

  • Outgoing Shared Partner ("OSP"): vertex kk is an OSP shared partner of ordered pair (i,j)(i,j) iff i→k,j→ki \to k, j \to k.

  • Incoming Shared Partner ("ISP"): vertex kk is an ISP shared partner of ordered pair (i,j)(i,j) iff k→i,k→jk \to i, k \to j.

By default, outgoing two-paths ("OTP") are calculated. Note that Robins et al. (2009) define closely related statistics to several of the above, using slightly different terminology.

Note

This term takes an additional term option (see options?ergm), cache.sp, controlling whether the implementation will cache the number of shared partners for each dyad in the network; this is usually enabled by default.

This term can only be used with directed networks.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

directed, binary

Dyadic covariate

Description

This term adds three statistics to the model, each equal to the sum of the covariate values for all dyads occupying one of the three possible non-empty dyad states (mutual, upper-triangular asymmetric, and lower-triangular asymmetric dyads, respectively), with the empty or null state serving as a reference category. If the network is undirected, x is either a matrix of edgewise covariates, or a network; if the latter, optional argument attrname provides the name of the edge attribute to use for edge values. This term adds one statistic to the model, equal to the sum of the covariate values for each edge appearing in the network. The edgecov and dyadcov terms are equivalent for undirected networks.

Usage

# binary: dyadcov(x, attrname=NULL)

Arguments

x, attrname

a specification for the dyadic covariate: either one of the following, or the name of a network attribute containing one of the following:

a covariate matrix

with dimensions n×nn \times n for unipartite networks and b×(n−b)b \times (n-b) for bipartite networks; attrname, if given, is used to construct the term name.

a network object

with the same size and bipartitedness as LHS; attrname, if given, provides the name of the quantitative edge attribute to use for covariate values (in this case, missing edges in x are assigned a covariate value of zero).

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

directed, dyad-independent, quantitative dyadic attribute, undirected, binary

A soft constraint to adjust the sampled distribution for dyad-level noise with known perturbation probabilities

Description

It is assumed that the observed LHS network is a noisy observation of some unobserved true network, with p01 giving the dyadwise probability of erroneously observing a tie where the true network had a non-tie and p10 giving the dyadwise probability of erroneously observing a nontie where the true network had a tie.

Usage

# dyadnoise(p01, p10)

Arguments

p01, p10

can both be scalars or both be adjacency matrices of the same dimension as that of the LHS network giving these probabilities.

Note

See Karwa et al. (2016) for an application.

See Also

ergmConstraint for index of constraints and hints currently visible to the package.

Keywords

directed, dyad-independent, soft, undirected

Constrain fixed or varying dyad-independent terms

Description

This is an "operator" constraint that takes one or two ergmTerm dyad-independent formulas. For the terms in the ⁠vary=⁠ formula, only those that change at least one of the terms will be allowed to vary, and all others will be fixed. If both formulas are given, the dyads that vary either for one or for the other will be allowed to vary. Note that a formula passed to Dyads without an argument name will default to ⁠fix=⁠ .

Usage

# Dyads(fix=NULL, vary=NULL)

Arguments

fix, vary

formula with only dyad-independent terms

See Also

ergmConstraint for index of constraints and hints currently visible to the package.

Keywords

directed, dyad-independent, operator, undirected

Two versions of an E. Coli network dataset

Description

This network data set comprises two versions of a biological network in which the nodes are operons in Escherichia Coli and a directed edge from one node to another indicates that the first encodes the transcription factor that regulates the second.

Usage

data(ecoli)

Details

The network object ecoli1 is directed, with 423 nodes and 519 arcs. The object ecoli2 is an undirected version of the same network, in which all arcs are treated as edges and the five isolated nodes (which exhibit only self-regulation in ecoli1) are removed, leaving 418 nodes.

Licenses and Citation

When publishing results obtained using this data set, the original authors (Salgado et al, 2001; Shen-Orr et al, 2002) should be cited, along with this R package.

Source

The data set is based on the RegulonDB network (Salgado et al, 2001) and was modified by Shen-Orr et al (2002).

References

Salgado et al (2001), Regulondb (version 3.2): Transcriptional Regulation and Operon Organization in Escherichia Coli K-12, Nucleic Acids Research, 29(1): 72-74.

Shen-Orr et al (2002), Network Motifs in the Transcriptional Regulation Network of Escerichia Coli, Nature Genetics, 31(1): 64-68.

%Saul and Filkov (2007)

%Hummel et al (2010)

Edge covariate

Description

This term adds one statistic to the model, equal to the sum of the covariate values for each edge appearing in the network. The edgecov term applies to both directed and undirected networks. For undirected networks the covariates are also assumed to be undirected. The edgecov and dyadcov terms are equivalent for undirected networks.

Usage

# binary: edgecov(x, attrname=NULL)

# valued: edgecov(x, attrname=NULL, form="sum")

Arguments

x, attrname

a specification for the dyadic covariate: either one of the following, or the name of a network attribute containing one of the following:

a covariate matrix

with dimensions n×nn \times n for unipartite networks and b×(n−b)b \times (n-b) for bipartite networks; attrname, if given, is used to construct the term name.

a network object

with the same size and bipartitedness as LHS; attrname, if given, provides the name of the quantitative edge attribute to use for covariate values (in this case, missing edges in x are assigned a covariate value of zero).
form

character how to aggregate tie values in a valued ERGM

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

directed, dyad-independent, frequently-used, quantitative dyadic attribute, undirected, binary, valued

Preserve the edge count of the given network

Description

Only networks having the same number of edges as the network passed in the model formula have non-zero probability.

Usage

# edges

See Also

ergmConstraint for index of constraints and hints currently visible to the package.

Keywords

None

Number of edges in the network

Description

This term adds one network statistic equal to the number of edges (i.e. nonzero values) in the network. For undirected networks, edges is equal to kstar(1); for directed networks, edges is equal to both ostar(1) and istar(1).

Usage

# binary: edges

# valued: nonzero

# valued: edges

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

directed, dyad-independent, undirected, binary, valued

Preserve values of dyads incident on vertices with given attribute

Description

Preserve values of dyads incident on vertices with attribute attr being TRUE or if attrname is NULL , the vertex attribute "na" being FALSE.

Usage

# egocentric(attr=NULL, direction="both")

Arguments

attr

a vertex attribute specification (see Specifying Vertex attributes and Levels (?nodal_attributes) for details.)
direction

one of "both", "out" and "in", only applies to directed networks. "out" only preserves the out-dyads of those actors and "in" preserves their in-dyads.

See Also

ergmConstraint for index of constraints and hints currently visible to the package.

Keywords

directed, dyad-independent, undirected

Convert a curved ERGM into a form suitable as initial values for the same ergm. Deprecated in 4.0.0.

Description

The generic enformulate.curved converts an ergm object or formula of a model with curved terms to the variant in which the curved parameters embedded into the formula and are removed from the parameter vector. This is the form that used to be required by ergm() calls.

Usage

enformulate.curved(object, ...)

## S3 method for class 'ergm'
enformulate.curved(object, ...)

## S3 method for class 'formula'
enformulate.curved(object, theta, ...)

Arguments

object

An ergm object or an ERGM formula. The curved terms of the given formula (or the formula used in the fit) must have all of their arguments passed by name.
...

Unused at this time.
theta

Curved model parameter configuration.

Details

Because of a current kludge in ergm(), output from one run cannot be directly passed as initial values (control.ergm(init=)) for the next run if any of the terms are curved. One workaround is to embed the curved parameters into the formula (while keeping fixed=FALSE) and remove them from control.ergm(init=).

This function automates this process for curved ERGM terms included with the ergm package. It does not work with curved terms not included in ergm.

Value

A list with the following components:

formula

The formula with curved parameter estimates incorporated.
theta

The coefficient vector with curved parameter estimates removed.

See Also

ergm(), simulate.ergm()

Number of dyads with values equal to a specific value (within tolerance)

Description

Adds one statistic equal to the number of dyads whose values are within tolerance of value , i.e., between value-tolerance and value+tolerance , inclusive.

Usage

# valued: equalto(value=0, tolerance=0)

Arguments

value

numerical threshold
tolerance

numerical threshold

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

directed, dyad-independent, undirected, valued

Exponential-Family Random Graph Models

Description

ergm() is used to fit exponential-family random graph models (ERGMs), in which the probability of a given network, yy, on a set of nodes is h(y)exp⁡{η(θ)⋅g(y)}/c(θ)h(y) \exp\{\eta(\theta) \cdot g(y)\}/c(\theta), where h(y)h(y) is the reference measure (usually h(y)=1h(y)=1), g(y)g(y) is a vector of network statistics for yy, η(θ)\eta(\theta) is a natural parameter vector of the same length (with η(θ)=θ\eta(\theta)=\theta for most terms), and c(θ)c(\theta) is the normalizing constant for the distribution. ergm() can return a maximum pseudo-likelihood estimate, an approximate maximum likelihood estimate based on a Monte Carlo scheme, or an approximate contrastive divergence estimate based on a similar scheme. (For an overview of the package (Hunter et al. 2008; Krivitsky et al. 2023), see ergm.)

Usage

ergm(
  formula,
  response = NULL,
  reference = ~Bernoulli,
  constraints = ~.,
  obs.constraints = ~. - observed,
  offset.coef = NULL,
  target.stats = NULL,
  eval.loglik = getOption("ergm.eval.loglik"),
  estimate = c("MLE", "MPLE", "CD"),
  control = control.ergm(),
  verbose = FALSE,
  ...,
  basis = ergm.getnetwork(formula),
  newnetwork = c("one", "all", "none")
)

is.ergm(object)

## S3 method for class 'ergm'
is.na(x)

## S3 method for class 'ergm'
anyNA(x, ...)

## S3 method for class 'ergm'
nobs(object, ...)

## S3 method for class 'ergm'
print(x, digits = max(3, getOption("digits") - 3), ...)

## S3 method for class 'ergm'
vcov(object, sources = c("all", "model", "estimation"), ...)

Arguments

formula

An R formula, of the form y ~ <model terms>, where y is a network object or a matrix that can be coerced to a network object. For the details on the possible <model terms>, see ergmTerm and Morris, Handcock and Hunter (2008) for binary ERGM terms and Krivitsky (2012) for valued ERGM terms (terms for weighted edges). To create a network object in R, use the network() function, then add nodal attributes to it using the %v% operator if necessary. Enclosing a model term in offset() fixes its value to one specified in offset.coef. (A second argument—a logical or numeric index vector—can be used to select which of the parameters within the term are offsets.)
response

Either a character string, a formula, or NULL (the default), to specify the response attributes and whether the ERGM is binary or valued. Interpreted as follows:

NULL

Model simple presence or absence, via a binary ERGM.

character string

The name of the edge attribute whose value is to be modeled. Type of ERGM will be determined by whether the attribute is logical (TRUE/FALSE) for binary or numeric for valued.

a formula

must be of the form NAME~EXPR|TYPE (with | being literal). EXPR is evaluated in the formula's environment with the network's edge attributes accessible as variables. The optional NAME specifies the name of the edge attribute into which the results should be stored, with the default being a concise version of EXPR. Normally, the type of ERGM is determined by whether the result of evaluating EXPR is logical or numeric, but the optional TYPE can be used to override by specifying a scalar of the type involved (e.g., TRUE for binary and 1 for valued).
reference

A one-sided formula specifying the reference measure (h(y)h(y)) to be used. See help for ERGM reference measures implemented in the ergm package.
constraints

A formula specifying one or more constraints on the support of the distribution of the networks being modeled. Multiple constraints may be given, separated by “+” and “-” operators. See ergmConstraint for the detailed explanation of their semantics and also for an indexed list of the constraints visible to the ergm package.

The default is to have no constraints except those provided through the ergmlhs API.

Together with the model terms in the formula and the reference measure, the constraints define the distribution of networks being modeled.

It is also possible to specify a proposal function directly either by passing a string with the function's name (in which case, arguments to the proposal should be specified through the MCMC.prop.args argument to the relevant control function, or by giving it on the LHS of the hints formula to MCMC.prop argument to the control function. This will override the one chosen automatically.

Note that not all possible combinations of constraints and reference measures are supported. However, for relatively simple constraints (i.e., those that simply permit or forbid specific dyads or sets of dyads from changing), arbitrary combinations should be possible.
obs.constraints

A one-sided formula specifying one or more constraints or other modification in addition to those specified by constraints, following the same syntax as the constraints argument.

This allows the domain of the integral in the numerator of the partially obseved network face-value likelihoods of Handcock and Gile (2010) and Karwa et al. (2017) to be specified explicitly.

The default is to constrain the integral to only integrate over the missing dyads (if present), after incorporating constraints provided through the ergmlhs API.

It is also possible to specify a proposal function directly by passing a string with the function's name of the obs.MCMC.prop argument to the relevant control function. In that case, arguments to the proposal should be specified through the obs.prop.args argument to the relevant control function.
offset.coef

A vector of coefficients for the offset terms.
target.stats

vector of "observed network statistics," if these statistics are for some reason different than the actual statistics of the network on the left-hand side of formula. Equivalently, this vector is the mean-value parameter values for the model. If this is given, the algorithm finds the natural parameter values corresponding to these mean-value parameters. If NULL, the mean-value parameters used are the observed statistics of the network in the formula.

eval.loglik

Logical: For dyad-dependent models, if TRUE, use bridge sampling to evaluate the log-likelihoood associated with the fit. Has no effect for dyad-independent models. Since bridge sampling takes additional time, setting to FALSE may speed performance if likelihood values (and likelihood-based values like AIC and BIC) are not needed. Can be set globally via option(ergm.eval.loglik=...), which is set to TRUE when the package is loaded. (See options?ergm.)

estimate

If "MPLE," then the maximum pseudolikelihood estimator is returned. If "MLE" (the default), then an approximate maximum likelihood estimator is returned. For certain models, the MPLE and MLE are equivalent, in which case this argument is ignored. (To force MCMC-based approximate likelihood calculation even when the MLE and MPLE are the same, see the force.main argument of control.ergm(). If "CD" (EXPERIMENTAL), the Monte-Carlo contrastive divergence estimate is returned. )

control

A list of control parameters for algorithm tuning, typically constructed with control.ergm(). Its documentation gives the the list of recognized control parameters and their meaning. The more generic utility snctrl() (StatNet ConTRoL) also provides argument completion for the available control functions and limited argument name checking.
verbose

A logical or an integer to control the amount of progress and diagnostic information to be printed. FALSE/0 produces minimal output, with higher values producing more detail. Note that very high values (5+) may significantly slow down processing.
...

Additional arguments, to be passed to lower-level functions.
basis

a value (usually a network) to override the LHS of the formula.
newnetwork

One of "one" (the default), "all", or "none" (or, equivalently, FALSE), specifying whether the network(s) from the last iteration of the MCMC sampling should be returned as a part of the fit as a elements newnetwork and newnetworks. (See their entries in section Value below for details.) Partial matching is supported.
object

an ergm object.
x, digits

See print().
sources

For the vcov method, specify whether to return the covariance matrix from the ERGM model, the estimation process, or both combined.

Value

ergm() returns an object of ergm that is a list consisting of the following elements:

coef

The Monte Carlo maximum likelihood estimate of θ\theta, the vector of coefficients for the model parameters.
sample

The n×pn\times p matrix of network statistics, where nn is the sample size and pp is the number of network statistics specified in the model, generated by the last iteration of the MCMC-based likelihood maximization routine. These statistics are centered with respect to the observed statistics or target.stats, unless missing data MLE is used.
sample.obs

As sample, but for the constrained sample.
iterations

The number of Newton-Raphson iterations required before convergence.
MCMCtheta

The value of θ\theta used to produce the Markov chain Monte Carlo sample. As long as the Markov chain mixes sufficiently well, sample is roughly a random sample from the distribution of network statistics specified by the model with the parameter equal to MCMCtheta. If estimate="MPLE" then MCMCtheta equals the MPLE.
loglikelihood

The approximate change in log-likelihood in the last iteration. The value is only approximate because it is estimated based on the MCMC random sample.
gradient

The value of the gradient vector of the approximated loglikelihood function, evaluated at the maximizer. This vector should be very close to zero.
covar

Approximate covariance matrix for the MLE, based on the inverse Hessian of the approximated loglikelihood evaluated at the maximizer.
failure

Logical: Did the MCMC estimation fail?
network

Network passed on the left-hand side of formula. If target.stats are passed, it is replaced by the network returned by san().
newnetworks

If argument newnetwork is "all", a list of the final networks at the end of the MCMC simulation, one for each thread.
newnetwork

If argument newnetwork is "one" or "all", the first (possibly only) element of newnetworks.
coef.init

The initial value of θ\theta.
est.cov

The covariance matrix of the model statistics in the final MCMC sample.
coef.hist, steplen.hist, stats.hist, stats.obs.hist

For the MCMLE method, the history of coefficients, Hummel step lengths, and average model statistics for each iteration..

control

The control list passed to the call.
etamap

The set of functions mapping the true parameter theta to the canonical parameter eta (irrelevant except in a curved exponential family model)
formula

The original formula passed to ergm().
target.stats

The target.stats used during estimation (passed through from the Arguments)
target.esteq

Used for curved models to preserve the target mean values of the curved terms. It is identical to target.stats for non-curved models.
constraints

Constraints used during estimation (passed through from the Arguments)
reference

The reference measure used during estimation (passed through from the Arguments)
estimate

The estimation method used (passed through from the Arguments).
offset

vector of logical telling which model parameters are to be set at a fixed value (i.e., not estimated).
drop

If control$drop=TRUE, a numeric vector indicating which terms were dropped due to to extreme values of the corresponding statistics on the observed network, and how:

0

The term was not dropped.

-1

The term was at its minimum and the coefficient was fixed at -Inf.

+1

The term was at its maximum and the coefficient was fixed at +Inf.
estimable

A logical vector indicating which terms could not be estimated due to a constraints constraint fixing that term at a constant value.

info

A list with miscellaneous information that would typically be accessed by the user via methods; in general, it should not be accessed directly. Current elements include:

terms_dind

Logical indicator of whether the model terms are all dyad-independent.

space_dind

Logical indicator of whether the sample space (constraints) are all dyad-independent.

n_info_dyads

Number of “informative” dyads: those that are observed (not missing) and not constrained by sample space constraints; one of the measures of sample size.

obs

Logical indicator of whether an observational (missing data) process was involved in estimation.

valued

Logical indicator of whether the model is valued.
null.lik

Log-likelihood of the null model. Valid only for unconstrained models.
mle.lik

The approximate log-likelihood for the MLE. The value is only approximate because it is estimated based on the MCMC random sample.

Methods (by generic)

  • is.na(ergm): Return TRUE if the ERGM was fit to a partially observed network and/or an observational process, such as missing (NA) dyads.

  • anyNA(ergm): Alias to the is.na() method.

  • nobs(ergm): Return the number of informative dyads of a model fit.

  • print(ergm): Print the call, the estimate, and the method used to obtain it.

  • vcov(ergm): extracts the variance-covariance matrix of parameter estimates.

Notes on model specification

Although each of the statistics in a given model is a summary statistic for the entire network, it is rarely necessary to calculate statistics for an entire network in a proposed Metropolis-Hastings step. Thus, for example, if the triangle term is included in the model, a census of all triangles in the observed network is never taken; instead, only the change in the number of triangles is recorded for each edge toggle.

In the implementation of ergm(), the model is initialized in R, then all the model information is passed to a C program that generates the sample of network statistics using MCMC. This sample is then returned to R, which then uses one of several algorithms, selected by ⁠main.method=⁠ control.ergm() parameter to update the estimate.

The mechanism for proposing new networks for the MCMC sampling scheme, which is a Metropolis-Hastings algorithm, depends on two things: The constraints, which define the set of possible networks that could be proposed in a particular Markov chain step, and the weights placed on these possible steps by the proposal distribution. The former may be controlled using the constraints argument described above. The latter may be controlled using the prop.weights argument to the control.ergm() function.

The package is designed so that the user could conceivably add additional proposal types.

References

Hunter DR, Handcock MS, Butts CT, Goodreau SM, Morris M (2008). “ergm: A Package to Fit, Simulate and Diagnose Exponential-Family Models for Networks.” Journal of Statistical Software, 24(3), 1–29. doi:10.18637/jss.v024.i03.

Krivitsky PN, Hunter DR, Morris M, Klumb C (2023). “ergm 4: New Features for Analyzing Exponential-Family Random Graph Models.” Journal of Statistical Software, 105(6), 1–44. doi:10.18637/jss.v105.i06.

Admiraal R, Handcock MS (2007). networksis: Simulate bipartite graphs with fixed marginals through sequential importance sampling. Statnet Project, Seattle, WA. Version 1. https://statnet.org.

Bender-deMoll S, Morris M, Moody J (2008). Prototype Packages for Managing and Animating Longitudinal Network Data: dynamicnetwork and rSoNIA. Journal of Statistical Software, 24(7). doi:10.18637/jss.v024.i07

Butts CT (2007). sna: Tools for Social Network Analysis. R package version 2.3-2. https://cran.r-project.org/package=sna.

Butts CT (2008). network: A Package for Managing Relational Data in R. Journal of Statistical Software, 24(2). doi:10.18637/jss.v024.i02

Butts C (2015). network: The Statnet Project (https://statnet.org). R package version 1.12.0, https://cran.r-project.org/package=network.

Goodreau SM, Handcock MS, Hunter DR, Butts CT, Morris M (2008a). A statnet Tutorial. Journal of Statistical Software, 24(8). doi:10.18637/jss.v024.i08

Goodreau SM, Kitts J, Morris M (2008b). Birds of a Feather, or Friend of a Friend? Using Exponential Random Graph Models to Investigate Adolescent Social Networks. Demography, 45, in press.

Handcock, M. S. (2003) Assessing Degeneracy in Statistical Models of Social Networks, Working Paper #39, Center for Statistics and the Social Sciences, University of Washington. https://csss.uw.edu/research/working-papers/assessing-degeneracy-statistical-models-social-networks

Handcock MS (2003b). degreenet: Models for Skewed Count Distributions Relevant to Networks. Statnet Project, Seattle, WA. Version 1.0, https://statnet.org.

Handcock MS and Gile KJ (2010). Modeling Social Networks from Sampled Data. Annals of Applied Statistics, 4(1), 5-25. doi:10.1214/08-AOAS221

Handcock MS, Hunter DR, Butts CT, Goodreau SM, Morris M (2003a). ergm: A Package to Fit, Simulate and Diagnose Exponential-Family Models for Networks. Statnet Project, Seattle, WA. Version 2, https://statnet.org.

Handcock MS, Hunter DR, Butts CT, Goodreau SM, Morris M (2003b). statnet: Software Tools for the Statistical Modeling of Network Data. Statnet Project, Seattle, WA. Version 2, https://statnet.org.

Hunter, D. R. and Handcock, M. S. (2006) Inference in curved exponential family models for networks, Journal of Computational and Graphical Statistics.

Hunter DR, Handcock MS, Butts CT, Goodreau SM, Morris M (2008b). ergm: A Package to Fit, Simulate and Diagnose Exponential-Family Models for Networks. Journal of Statistical Software, 24(3). doi:10.18637/jss.v024.i03

Karwa V, Krivitsky PN, and Slavkovi\'c AB (2017). Sharing Social Network Data: Differentially Private Estimation of Exponential-Family Random Graph Models. Journal of the Royal Statistical Society, Series C, 66(3):481–500. doi:10.1111/rssc.12185

Krivitsky PN (2012). Exponential-Family Random Graph Models for Valued Networks. Electronic Journal of Statistics, 2012, 6, 1100-1128. doi:10.1214/12-EJS696

Morris M, Handcock MS, Hunter DR (2008). Specification of Exponential-Family Random Graph Models: Terms and Computational Aspects. Journal of Statistical Software, 24(4). doi:10.18637/jss.v024.i04

Snijders, T.A.B. (2002), Markov Chain Monte Carlo Estimation of Exponential Random Graph Models. Journal of Social Structure. Available from https://www.cmu.edu/joss/content/articles/volume3/Snijders.pdf.

See Also

network, %v%, %n%, ergmTerm, ergmMPLE, summary.ergm()

Examples

#
# load the Florentine marriage data matrix
#
data(flo)
#
# attach the sociomatrix for the Florentine marriage data
# This is not yet a network object.
#
flo
#
# Create a network object out of the adjacency matrix
#
flomarriage <- network(flo,directed=FALSE)
flomarriage
#
# print out the sociomatrix for the Florentine marriage data
#
flomarriage[,]
#
# create a vector indicating the wealth of each family (in thousands of lira) 
# and add it as a covariate to the network object
#
flomarriage %v% "wealth" <- c(10,36,27,146,55,44,20,8,42,103,48,49,10,48,32,3)
flomarriage
#
# create a plot of the social network
#
plot(flomarriage)
#
# now make the vertex size proportional to their wealth
#
plot(flomarriage, vertex.cex=flomarriage %v% "wealth" / 20, main="Marriage Ties")
#
# Use 'data(package = "ergm")' to list the data sets in a
#
data(package="ergm")
#
# Load a network object of the Florentine data
#
data(florentine)
#
# Fit a model where the propensity to form ties between
# families depends on the absolute difference in wealth
#
gest <- ergm(flomarriage ~ edges + absdiff("wealth"))
summary(gest)
#
# add terms for the propensity to form 2-stars and triangles
# of families 
#
gest <- ergm(flomarriage ~ kstar(1:2) + absdiff("wealth") + triangle)
summary(gest)

# import synthetic network that looks like a molecule
data(molecule)
# Add a attribute to it to mimic the atomic type
molecule %v% "atomic type" <- c(1,1,1,1,1,1,2,2,2,2,2,2,2,3,3,3,3,3,3,3)
#
# create a plot of the social network
# colored by atomic type
#
plot(molecule, vertex.col="atomic type",vertex.cex=3)

# measure tendency to match within each atomic type
gest <- ergm(molecule ~ edges + kstar(2) + triangle + nodematch("atomic type"))
summary(gest)

# compare it to differential homophily by atomic type
gest <- ergm(molecule ~ edges + kstar(2) + triangle
                        + nodematch("atomic type",diff=TRUE))
summary(gest)


# Extract parameter estimates as a numeric vector:
coef(gest)
# Sources of variation in parameter estimates:
vcov(gest, sources="model")
vcov(gest, sources="estimation")
vcov(gest, sources="all") # the default

Internal Function to Sample Networks and Network Statistics

Description

This is an internal function, not normally called directly by the user. The ergm_MCMC_sample function samples networks and network statistics using an MCMC algorithm via MCMC_wrapper and is capable of running in multiple threads using ergm_MCMC_slave.

The ergm_MCMC_slave function calls the actual C routine and does minimal preprocessing.

Usage

ergm_MCMC_sample(
  state,
  control,
  theta = NULL,
  verbose = FALSE,
  ...,
  eta = ergm.eta(theta, (if (is.ergm_state(state)) as.ergm_model(state) else
    as.ergm_model(state[[1]]))$etamap)
)

ergm_MCMC_slave(
  state,
  eta,
  control,
  verbose,
  ...,
  burnin = NULL,
  samplesize = NULL,
  interval = NULL
)

Arguments

state

an ergm_state representing the sampler state, containing information about the network, the model, the proposal, and (optionally) initial statistics, or a list thereof.
control

A list of control parameters for algorithm tuning, typically constructed with control.ergm(), control.simulate.ergm(), etc., which have different defaults. Their documentation gives the the list of recognized control parameters and their meaning. The more generic utility snctrl() (StatNet ConTRoL) also provides argument completion for the available control functions and limited argument name checking.
theta

the (possibly curved) parameters of the model.
verbose

A logical or an integer to control the amount of progress and diagnostic information to be printed. FALSE/0 produces minimal output, with higher values producing more detail. Note that very high values (5+) may significantly slow down processing.
...

additional arugments.
eta

the natural parameters of the model; by default constructed from theta.
burnin, samplesize, interval

MCMC paramters that can be used to temporarily override those in the control list.

Value

ergm_MCMC_sample returns a list containing:

stats

an mcmc.list with sampled statistics.
networks

a list of final sampled networks, one for each thread.
status

status code, propagated from ergm_MCMC_slave().
final.interval

adaptively determined MCMC interval.
final.effectiveSize

adaptively determined target ESS (non-trivial if control$MCMC.effectiveSize is specified via a matrix).
sampnetworks

If control$MCMC.save_networks is set and is TRUE, a list of lists of ergm_states corresponding to the sampled networks.

ergm_MCMC_slave returns the MCMC sample as a list of the following:

s

the matrix of statistics.
state

an ergm_state object for the new network.
status

success or failure code: 0 is success, 1 for too many edges, and 2 for a Metropolis-Hastings proposal failing, -1 for ergm_model or ergm_proposal not passed and missing from the cache.

Note

ergm_MCMC_sample and ergm_MCMC_slave replace ergm.getMCMCsample and ergm.mcmcslave respectively. They differ slightly in their argument names and in their return formats. For example, ergm_MCMC_sample expects ergm_state rather than network/model/proposal, and theta or eta rather than eta0; and it does not return statsmatrix or newnetwork elements. Rather, if parallel processing is not in effect, stats is an mcmc.list with one chain and networks is a list with one element.

Note that unless stats is a part of the ergm_state, the returned stats will be relative to the original network, i.e., the calling function must shift the statistics if required.

At this time, repeated calls to ergm_MCMC_sample will not produce the same sequence of networks as a single long call, even with the same starting seeds. This is because the network sampling algorithms rely on the internal state of the network representation in C, which may not be reconstructed exactly the same way when "resuming". This behaviour may change in the future.

Examples

# This example illustrates constructing "ingredients" for calling
# ergm_MCMC_sample() from calls to simulate.ergm(). One can also
# construct an ergm_state object directly from ergm_model(),
# ergm_proposal(), etc., but the approach shown here is likely to
# be the least error-prone and the most robust to future API
# changes.
#
# The regular simulate() call hierarchy is
#
# simulate_formula.network(formula) ->
#   simulate.ergm_model(ergm_model) ->
#     simulate.ergm_state_full(ergm_state)
#
# They take an argument, return.args=, that will interrupt the call
# and have it return its arguments. We can use it to obtain
# low-level inputs robustly.

data(florentine)
control <- control.simulate(MCMC.burnin = 2, MCMC.interval = 1)


# FYI: Obtain input for simulate.ergm_model():
sim.mod <- simulate(flomarriage~absdiff("wealth"), constraints=~edges,
                    coef = NULL, nsim=3, control=control,
                    return.args="ergm_model")
names(sim.mod)
str(sim.mod$object,1) # ergm_model

# Obtain input for simulate.ergm_state_full():
sim.state <- simulate(flomarriage~absdiff("wealth"), constraints=~edges,
                      coef = NULL, nsim=3, control=control,
                      return.args="ergm_state")
names(sim.state)
str(sim.state$object, 1) # ergm_state

# This control parameter would be set by nsim in the regular
# simulate() call:
control$MCMC.samplesize <- 3

# Capture intermediate networks; can also be left NULL for just the
# statistics:
control$MCMC.save_networks <- TRUE

# Simulate starting from this state:
out <- ergm_MCMC_sample(sim.state$object, control, theta = -1, verbose=6)
names(out)
out$stats # Sampled statistics
str(out$networks, 1) # Updated ergm_state (one per thread)
# List (an element per thread) of lists of captured ergm_states,
# one for each sampled network:
str(out$sampnetworks, 2)
lapply(out$sampnetworks[[1]], as.network) # Converted to networks.

# One more, picking up where the previous sampler left off, but see Note:
control$MCMC.samplesize <- 1
str(ergm_MCMC_sample(out$networks, control, theta = -1, verbose=6), 2)

Plot MCMC list using lattice package graphics

Description

Plot MCMC list using lattice package graphics

Usage

ergm_plot.mcmc.list(x, main = NULL, vars.per.page = 3, ...)

Arguments

x

an mcmc.list object containing the mcmc diagnostic samples.
main

character, main plot heading title.
vars.per.page

Number of rows (one variable per row) per plotting page. Ignored if latticeExtra package is not installed.
...

additional arguments, currently unused.

Note

This is not a method at this time.

A rudimentary cache for large objects

Description

This cache is intended to store large, infrequently changing data structures such as ergm_models and ergm_proposals on worker nodes.

Usage

ergm_state_cache(
  comm = c("pass", "all", "clear", "insert", "get", "check", "list"),
  key,
  object
)

Arguments

comm

a character string giving the desired function; see the default argument above for permitted values and Details for meanings; partial matching is supported.
key

a character string, typically a digest::digest() of the object or a random string.
object

the object to be stored.

Supported tasks are, respectively, to do nothing (the default), return all entries (mainly useful for testing), clear the cache, insert into cache, retrieve an object by key, check if a key is present, or list keys defined.

Deleting an entry can be accomplished by inserting a NULL for that key.

Cache is limited to a hard-coded size (currently 4). This should accommodate an ergm_model and an ergm_proposal for unconstrained and constrained MCMC. When additional objects are stored, the oldest object is purged and garbage-collected.

Note

If called via, say, clusterMap(cl, ergm_state_cache, ...) the function will not accomplish anything. This is because parallel package will serialise the ergm_state_cache() function object, send it to the remote node, evaluate it there, and fetch the return value. This will leave the environment of the worker's ergm_state_cache() unchanged. To actually evaluate it on the worker nodes, it is recommended to wrap it in an empty function whose environment is set to globalenv(). See Examples below.

Examples

## Not run: 
# Wrap ergm_state_cache() and call it explicitly from ergm:
call_ergm_state_cache <- function(...) ergm::ergm_state_cache(...)

# Reset the function's environment so that it does not get sent to
# worker nodes (who have their own instance of ergm namespace
# loaded).
environment(call_ergm_state_cache) <- globalenv()

# Now, call the the wrapper function, with ... below replaced by
# lists of desired arguments.
clusterMap(cl, call_ergm_state_cache, ...)

## End(Not run)

Return a symmetrized version of a binary network

Description

Return a symmetrized version of a binary network

Usage

ergm_symmetrize(x, rule = c("weak", "strong", "upper", "lower"), ...)

## Default S3 method:
ergm_symmetrize(x, rule = c("weak", "strong", "upper", "lower"), ...)

## S3 method for class 'network'
ergm_symmetrize(x, rule = c("weak", "strong", "upper", "lower"), ...)

Arguments

x

an object representing a network.
rule

a string specifying how the network is to be symmetrized; see sna::symmetrize() for details; for the network method, it can also be a function or a list; see Details.
...

additional arguments to sna::symmetrize().

Details

The network method requires more flexibility, in order to specify how the edge attributes are handled. Therefore, rule can be one of the following types:

a character vector

The string is interpreted as in sna::symmetrize(). For edge attributes, "weak" takes the maximum value and "strong" takes the minimum value" for ordered attributes, and drops the unordered.

a function

The function is evaluated on a data.frame constructed by joining (via merge()) the edge tibble with all attributes and NA indicators with itself reversing tail and head columns, and appending original columns with ".th" and the reversed columns with ".ht". It is then evaluated for each attribute in turn, given two arguments: the data frame and the name of the attribute.

a list

The list must have exactly one unnamed element, and the remaining elements must be named with the names of edge attributes. The elements of the list are interpreted as above, allowing each edge attribute to be handled differently. Unnamed arguments are dropped.

Methods (by class)

  • ergm_symmetrize(default): The default method, passing the input on to sna::symmetrize().

  • ergm_symmetrize(network): A method for network objects, which preserves network and vertex attributes, and handles edge attributes.

Note

This was originally exported as a generic to overwrite sna::symmetrize(). By developer's request, it has been renamed; eventually, sna or network packages will export the generic instead.

Examples

data(sampson)
samplike[1,2] <- NA
samplike[4.1] <- NA
sm <- as.matrix(samplike)

tst <- function(x,y){
  mapply(identical, x, y)
}

stopifnot(all(tst(as.logical(as.matrix(ergm_symmetrize(samplike, "weak"))), sm | t(sm))),
          all(tst(as.logical(as.matrix(ergm_symmetrize(samplike, "strong"))), sm & t(sm))),
          all(tst(c(as.matrix(ergm_symmetrize(samplike, "upper"))),
                  sm[cbind(c(pmin(row(sm),col(sm))),c(pmax(row(sm),col(sm))))])),
          all(tst(c(as.matrix(ergm_symmetrize(samplike, "lower"))),
                  sm[cbind(c(pmax(row(sm),col(sm))),c(pmin(row(sm),col(sm))))])))

Global options and term options for the ergm package

Description

Options set via the built-in options() functions that affect ergm estimation and options that control the behavior of some terms.

Global options and defaults

ergm.eval.loglik = TRUE

Whether ergm() and similar functions will evaluate the likelihood of the fitted model. Can be overridden for a specific call by passing eval.loglik argument directly.

ergm.loglik.warn_dyads = TRUE

Whether log-likelihood evaluation should issue a warning when the effective number of dyads that can vary in the sample space is poorly defined, such as if the degree sequence is constrained.

ergm.cluster.retries = 5

ergm's parallel routines implement rudimentary fault-tolerance. This option controls the number of retries for a cluster call before giving up.

ergm.term = list()

The default term options below.

Term options

Term options can be set in three places, in the order of precedence from high to low:

  1. As a term argument (not always). For example, gw.cutoff below can be set in a gwesp term by gwesp(..., cutoff=X).

  2. For functions such as summary that take ergm formulas but do not take a control list, the named arguments passed in as .... E.g, summary(nw~gwesp(.5,fix=TRUE), gw.cutoff=60) will evaluate the GWESP statistic with its cutoff set to 60.

  3. As an element in a ⁠term.options=⁠ list passed via a control function such as control.ergm() or, for functions that do not, in a list with that argument name. E.g., summary(nw~gwesp(.5,fix=TRUE), term.options=list(gw.cutoff=60)) has the same effect.

  4. As an element in a global option list ergm.term above.

The following options are in use by terms in the ergm package:

version

A string that can be interpreted as an R package version. If set, the term will attempt to emulate its behavior as it was that version of ergm. Not all past version behaviors are available.

gw.cutoff

In geometrically weighted terms (gwesp, gwdegree, etc.) the highest number of shared partners, degrees, etc. for which to compute the statistic. This usually defaults to 30.

cache.sp

Whether the gwesp, dgwesp, and similar terms need should use a cache for the dyadwise number of shared partners. This usually improves performance significantly at a modest memory cost, and therefore defaults to TRUE, but it can be disabled.

interact.dependent

Whether to allow and how to handle the user attempting to interact dyad-dependent terms (e.g., absdiff("age"):triangles or absdiff("age")*triangles as opposed to absdiff("age"):nodefactor("sex")). Possible values are "error" (the default), "message", and "warning", for their respective actions, and "silent" for simply processing the term.

Parallel Processing in the ergm Package

Description

Using clusters multiple CPUs or CPU cores to speed up ERGM estimation and simulation.

The ergm.getCluster function is usually called internally by the ergm process (in ergm_MCMC_sample()) and will attempt to start the appropriate type of cluster indicated by the control.ergm() settings. It will also check that the same version of ergm is installed on each node.

The ergm.stopCluster shuts down a cluster, but only if ergm.getCluster was responsible for starting it.

The ergm.restartCluster restarts and returns a cluster, but only if ergm.getCluster was responsible for starting it.

nthreads is a simple generic to obtain the number of parallel processes represented by its argument, keeping in mind that having no cluster (e.g., NULL) represents one thread.

Usage

ergm.getCluster(control = NULL, verbose = FALSE, stop_on_exit = parent.frame())

ergm.stopCluster(..., verbose = FALSE)

ergm.restartCluster(control = NULL, verbose = FALSE)

set.MT_terms(n)

get.MT_terms()

nthreads(clinfo = NULL, ...)

## S3 method for class 'cluster'
nthreads(clinfo = NULL, ...)

## S3 method for class ''NULL''
nthreads(clinfo = NULL, ...)

## S3 method for class 'control.list'
nthreads(clinfo = NULL, ...)

Arguments

control

a control.ergm() (or similar) list of parameter values from which the parallel settings should be read; can also be NULL, in which case an existing cluster is used if started, or no cluster otherwise.
verbose

A logical or an integer to control the amount of progress and diagnostic information to be printed. FALSE/0 produces minimal output, with higher values producing more detail. Note that very high values (5+) may significantly slow down processing.
stop_on_exit

An environment or NULL. If an environment, defaulting to that of the calling function, the cluster will be stopped when the calling the frame in question exits.
...

not currently used
n

an integer specifying the number of threads to use; 0 (the starting value) disables multithreading, and −1-1 or NA sets it to the number of CPUs detected.
clinfo

a cluster or another object.

Details

For estimation that require MCMC, ergm can take advantage of multiple CPUs or CPU cores on the system on which it runs, as well as computing clusters through one of two mechanisms:

Running MCMC chains in parallel

Packages parallel and snow are used to to facilitate this, all cluster types that they support are supported.

The number of nodes used and the parallel API are controlled using the parallel and parallel.type arguments passed to the control functions, such as control.ergm().

The ergm.getCluster() function is usually called internally by the ergm process (in ergm_MCMC_sample()) and will attempt to start the appropriate type of cluster indicated by the control.ergm() settings. The ergm.stopCluster() is helpful if the user has directly created a cluster.

Further details on the various cluster types are included below.

Multithreaded evaluation of model terms

Rather than running multiple MCMC chains, it is possible to attempt to accelerate sampling by evaluating qualified terms' change statistics in multiple threads run in parallel. This is done using the OpenMP API.

However, this introduces a nontrivial amont of computational overhead. See below for a list of the major factors affecting whether it is worthwhile.

Generally, the two approaches should not be used at the same time without caution. In particular, by default, cluster slave nodes will not “inherit” the multithreading setting; but ⁠parallel.inherit.MT=⁠ control parameter can override that. Their relative advantages and disadvantages are as follows:

  • Multithreading terms cannot take advantage of clusters but only of CPUs and cores.

  • Parallel MCMC chains produce several independent chains; multithreading still only produces one.

  • Multithreading terms actually accellerates sampling, including the burn-in phase; parallel MCMC's multiple burn-in runs are effectively “wasted”.

Value

set.MT_terms() returns the previous setting, invisibly.

get.MT_terms() returns the current setting.

Different types of clusters

PSOCK clusters

The parallel package is used with PSOCK clusters by default, to utilize multiple cores on a system. The number of cores on a system can be determined with the detectCores() function.

This method works with the base installation of R on all platforms, and does not require additional software.

For more advanced applications, such as clusters that span multiple machines on a network, the clusters can be initialized manually, and passed into ergm() and others using the parallel control argument. See the second example below.

MPI clusters

To use MPI to accelerate ERGM sampling, pass the control parameter parallel.type="MPI". ergm requires the snow and Rmpi packages to communicate with an MPI cluster.

Using MPI clusters requires the system to have an existing MPI installation. See the MPI documentation for your particular platform for instructions.

To use ergm() across multiple machines in a high performance computing environment, see the section "User initiated clusters" below.

User initiated clusters

A cluster can be passed into ergm() with the parallel control parameter. ergm() will detect the number of nodes in the cluster, and use all of them for MCMC sampling. This method is flexible: it will accept any cluster type that is compatible with snow or parallel packages.

When is multithreading terms worthwhile?

  • The more terms with statistics the model has, the more benefit from parallel execution.

  • The more expensive the terms in the model are, the more benefit from parallel execution. For example, models with terms like gwdsp will generally get more benefit than models where all terms are dyad-independent.

  • Sampling more dense networks will generally get more benefit than sparse networks. Network size has little, if any, effect.

  • More CPUs/cores usually give greater speed-up, but only up to a point, because the amount of overhead grows with the number of threads; it is often better to “batch” the terms into a smaller number of threads than possible.

  • Any other workload on the system will have a more severe effect on multithreaded execution. In particular, do not run more threads than CPUs/cores that you want to allocate to the tasks.

  • Under Windows, even compiling with OpenMP appears to introduce unacceptable amounts of overhead, so it is disabled for Windows at compile time. To enable, delete src/Makevars.win and recompile from scratch.

Note

The this is a setting global to the ergm package and all of its C functions, including when called from other packages via the Linking-To mechanism.

Examples

# Uses 2 SOCK clusters for MCMLE estimation
data(faux.mesa.high)
nw <- faux.mesa.high
fauxmodel.01 <- ergm(nw ~ edges + isolates + gwesp(0.2, fixed=TRUE), 
                     control=control.ergm(parallel=2, parallel.type="PSOCK"))
summary(fauxmodel.01)

Calculate all possible vectors of statistics on a network for an ERGM

Description

ergm.allstats calculates the sufficient statistics of an ERGM over the network's sample space.

ergm.exact() uses ergm.allstats() to calculate the exact loglikelihood, evaluated at eta.

Usage

ergm.allstats(formula, constraints = ~., zeroobs = TRUE, force = FALSE, ...)

ergm.exact(eta, formula, constraints = ~., statmat = NULL, weights = NULL, ...)

Arguments

formula, constraints

An ERGM formula and (optionally) a constraint specification formulas. See ergm(). This function supports only dyad-independent constraints.
zeroobs

Logical: Should the vectors be centered so that the network passed in the formula has the zero vector as its statistics?
force

Logical: Should the algorithm be run even if it is determined that the problem may be very large, thus bypassing the warning message that normally terminates the function in such cases?
...

further arguments, passed to ergm_model().
eta

vector of canonical parameter values at which the loglikelihood should be evaluated.
statmat, weights

outputs from ergm.allstats(): if passed, used in lieu of running it.

Details

The mechanism for doing this is a recursive algorithm, where the number of levels of recursion is equal to the number of possible dyads that can be changed from 0 to 1 and back again. The algorithm starts with the network passed in formula, then recursively toggles each edge twice so that every possible network is visited.

ergm.allstats() and ergm.exact() should only be used for small networks, since the number of possible networks grows extremely fast with the number of nodes. An error results if it is used on a network with more than 31 free dyads, which corresponds to a directed network of more than 6 nodes or an undirected network of more than 8 nodes; use force=TRUE to override this error.

In case ergm.exact() is to be called repeatedly, for instance by an optimization routine, it is preferable to call ergm.allstats() first, then pass statmat and weights explicitly to avoid repeatedly calculating these objects.

Value

ergm.allstats() returns a list object with these two elements:

weights

integer of counts, one for each row of statmat telling how many networks share the corresponding vector of statistics.
statmat

matrix in which each row is a unique vector of statistics.

ergm.exact() returns the exact value of the loglikelihood, evaluated at eta.

Examples

# Count by brute force all the edge statistics possible for a 7-node 
# undirected network
mynw <- network.initialize(7, dir = FALSE)
system.time(a <- ergm.allstats(mynw~edges))

# Summarize results
rbind(t(a$statmat), .freq. = a$weights)

# Each value of a$weights is equal to 21-choose-k, 
# where k is the corresponding statistic (and 21 is 
# the number of dyads in an 7-node undirected network).  
# Here's a check of that fact:
as.vector(a$weights - choose(21, t(a$statmat)))

# Dyad-independent constraints are also supported:
system.time(a <- ergm.allstats(mynw~edges, constraints = ~fixallbut(cbind(1:2,2:3))))
rbind(t(a$statmat), .freq. = a$weights)


# Simple ergm.exact output for this network.
# We know that the loglikelihood for my empty 7-node network
# should simply be -21*log(1+exp(eta)), so we may check that
# the following two values agree:
-21*log(1+exp(.1234)) 
ergm.exact(.1234, mynw~edges, statmat=a$statmat, weights=a$weights)

Bridge sampling to evaluate ERGM log-likelihoods and log-likelihood ratios

Description

ergm.bridge.llr uses bridge sampling with geometric spacing to estimate the difference between the log-likelihoods of two parameter vectors for an ERGM via repeated calls to simulate.formula.ergm().

ergm.bridge.0.llk is a convenience wrapper that returns the log-likelihood of configuration θ\theta relative to the reference measure. That is, the configuration with θ=0\theta=0 is defined as having log-likelihood of 0.

ergm.bridge.dindstart.llk is a wrapper that uses a dyad-independent ERGM as a starting point for bridge sampling to estimate the log-likelihood for a given dyad-dependent model and parameter configuration. Note that it only handles binary ERGMs (response=NULL) and with constraints (⁠constraints=⁠) that that do not induce dyadic dependence.

Usage

ergm.bridge.llr(
  object,
  response = NULL,
  reference = ~Bernoulli,
  constraints = ~.,
  from,
  to,
  obs.constraints = ~. - observed,
  target.stats = NULL,
  basis = ergm.getnetwork(object),
  verbose = FALSE,
  ...,
  llronly = FALSE,
  control = control.ergm.bridge()
)

ergm.bridge.0.llk(
  object,
  response = NULL,
  reference = ~Bernoulli,
  coef,
  ...,
  llkonly = TRUE,
  control = control.ergm.bridge(),
  basis = ergm.getnetwork(object)
)

ergm.bridge.dindstart.llk(
  object,
  response = NULL,
  constraints = ~.,
  coef,
  obs.constraints = ~. - observed,
  target.stats = NULL,
  dind = NULL,
  coef.dind = NULL,
  basis = ergm.getnetwork(object),
  ...,
  llkonly = TRUE,
  control = control.ergm.bridge(),
  verbose = FALSE
)

Arguments

object

A model formula. See ergm() for details.
response

Either a character string, a formula, or NULL (the default), to specify the response attributes and whether the ERGM is binary or valued. Interpreted as follows:

NULL

Model simple presence or absence, via a binary ERGM.

character string

The name of the edge attribute whose value is to be modeled. Type of ERGM will be determined by whether the attribute is logical (TRUE/FALSE) for binary or numeric for valued.

a formula

must be of the form NAME~EXPR|TYPE (with | being literal). EXPR is evaluated in the formula's environment with the network's edge attributes accessible as variables. The optional NAME specifies the name of the edge attribute into which the results should be stored, with the default being a concise version of EXPR. Normally, the type of ERGM is determined by whether the result of evaluating EXPR is logical or numeric, but the optional TYPE can be used to override by specifying a scalar of the type involved (e.g., TRUE for binary and 1 for valued).
reference

A one-sided formula specifying the reference measure (h(y)h(y)) to be used. (Defaults to ~Bernoulli.)
constraints, obs.constraints

One-sided formulas specifying one or more constraints on the support of the distribution of the networks being simulated and on the observation process respectively. See the documentation for similar arguments for ergm() for more information.
from, to

The initial and final parameter vectors.
target.stats

A vector of sufficient statistics to be used in place of those of the network in the formula.
basis

An optional network object to start the Markov chain. If omitted, the default is the left-hand-side of the object.
verbose

A logical or an integer to control the amount of progress and diagnostic information to be printed. FALSE/0 produces minimal output, with higher values producing more detail. Note that very high values (5+) may significantly slow down processing.
...

Further arguments to ergm.bridge.llr and simulate.formula.ergm().
llronly

Logical: If TRUE, only the estiamted log-ratio will be returned by ergm.bridge.llr.
control

A list of control parameters for algorithm tuning, typically constructed with control.ergm.bridge(). Its documentation gives the the list of recognized control parameters and their meaning. The more generic utility snctrl() (StatNet ConTRoL) also provides argument completion for the available control functions and limited argument name checking.
coef

A vector of coefficients for the configuration of interest.
llkonly

Whether only the estiamted log-likelihood should be returned by the ergm.bridge.0.llk and ergm.bridge.dindstart.llk. (Defaults to TRUE.)
dind

A one-sided formula with the dyad-independent model to use as a starting point. Defaults to the dyad-independent terms found in the formula object with an overal density term (edges) added if not redundant.
coef.dind

Parameter configuration for the dyad-independent starting point. Defaults to the MLE of dind.

Value

If llronly=TRUE or llkonly=TRUE, these functions return the scalar log-likelihood-ratio or the log-likelihood. Otherwise, they return a list with the following components:

llr

The estimated log-ratio.
llr.vcov

The estimated variance of the log-ratio due to MCMC approximation.
llrs

A list of lists (1 per attempt) of the estimated log-ratios for each of the bridge.nsteps bridges.
llrs.vcov

A list of lists (1 per attempt) of the estimated variances of the estimated log-ratios for each of the bridge.nsteps bridges.
paths

A list of lists (1 per attempt) with two elements: theta, a numeric matrix with bridge.nsteps rows, with each row being the respective bridge's parameter configuration; and weight, a vector of length bridge.nsteps containing its weight.
Dtheta.Du

The gradient vector of the parameter values with respect to position of the bridge.

ergm.bridge.0.llk result list also includes an llk element, with the log-likelihood itself (with the reference distribution assumed to have likelihood 0).

ergm.bridge.dindstart.llk result list also includes an llk element, with the log-likelihood itself and an llk.dind element, with the log-likelihood of the nearest dyad-independent model.

References

Hunter, D. R. and Handcock, M. S. (2006) Inference in curved exponential family models for networks, Journal of Computational and Graphical Statistics.

See Also

simulate.formula.ergm()

Obtain the set of informative dyads based on the network structure.

Description

Note that this function is not recommended for general use, since it only supports only one way of specifying observational structure—through NA edges. It is likely to be deprecated in the future.

Usage

ergm.design(nw, ...)

Arguments

nw

a network object.
...

term options.

Value

ergm.design returns a rlebdm of informative (non-missing, non fixed) dyads.

Acquire and verify the network from the LHS of an ergm formula and verify that it is a valid network.

Description

The function function ensures that the network in a given formula is valid; if so, the network is returned; if not, execution is halted with warnings.

Usage

ergm.getnetwork(formula, loopswarning = TRUE)

Arguments

formula

a two-sided formula whose LHS is a network, an object that can be coerced to a network, or an expression that evaluates to one.
loopswarning

whether warnings about loops should be printed (TRUE or FALSE); defaults to TRUE.

Value

A network object constructed by evaluating the LHS of the model formula in the formula's environment.

A function to apply a given series of changes to a network.

Description

Gives the network a series of proposals it can't refuse. Returns the statistics of the network, and, optionally, the final network.

Usage

ergm.godfather(
  object,
  changes = NULL,
  ...,
  end.network = FALSE,
  stats.start = FALSE,
  changes.only = FALSE,
  verbose = FALSE,
  basis = NULL,
  formula = NULL
)

## S3 method for class 'formula'
ergm.godfather(
  object,
  changes = NULL,
  response = NULL,
  ...,
  end.network = FALSE,
  stats.start = FALSE,
  changes.only = FALSE,
  verbose = FALSE,
  control = NULL,
  basis = ergm.getnetwork(object)
)

## S3 method for class 'ergm_model'
ergm.godfather(
  object,
  changes = NULL,
  ...,
  end.network = FALSE,
  stats.start = FALSE,
  changes.only = FALSE,
  verbose = FALSE,
  control = NULL,
  basis = NULL
)

## S3 method for class 'ergm_state'
ergm.godfather(
  object,
  changes = NULL,
  ...,
  end.network = FALSE,
  stats.start = FALSE,
  verbose = FALSE,
  control = NULL
)

Arguments

object

An ergm()-style formula, with a network on its LHS, an ergm_model() or the object appropriate to the method.
changes

Either a matrix with three columns: tail, head, and new value, describing the changes to be made; or a list of such matrices to apply these changes in a sequence. For binary network models, the third column may be omitted. In that case, the changes are treated as toggles. Note that if a list is passed, it must either be all of changes or all of toggles.
...

additional arguments to ergm_model().
end.network

Whether to return a network that results. Defaults to FALSE.
stats.start

Whether to return the network statistics at start (before any changes are applied) as the first row of the statistics matrix. Defaults to FALSE, to produce output similar to that of simulate for ERGMs when output="stats", where initial network's statistics are not returned.
changes.only

Whether to return network statistics or only their changes relative to the initial network.
verbose

A logical or an integer to control the amount of progress and diagnostic information to be printed. FALSE/0 produces minimal output, with higher values producing more detail. Note that very high values (5+) may significantly slow down processing.
basis

a value (usually a network) to override the LHS of the formula.
formula

Deprecated; replaced with object for consistency.
response

Either a character string, a formula, or NULL (the default), to specify the response attributes and whether the ERGM is binary or valued. Interpreted as follows:

NULL

Model simple presence or absence, via a binary ERGM.

character string

The name of the edge attribute whose value is to be modeled. Type of ERGM will be determined by whether the attribute is logical (TRUE/FALSE) for binary or numeric for valued.

a formula

must be of the form NAME~EXPR|TYPE (with | being literal). EXPR is evaluated in the formula's environment with the network's edge attributes accessible as variables. The optional NAME specifies the name of the edge attribute into which the results should be stored, with the default being a concise version of EXPR. Normally, the type of ERGM is determined by whether the result of evaluating EXPR is logical or numeric, but the optional TYPE can be used to override by specifying a scalar of the type involved (e.g., TRUE for binary and 1 for valued).
control

Deprecated; arguments such as term.options can be passed directly.

Value

If end.network==FALSE (the default), an mcmc object with the requested network statistics associed with the network series produced by applying the specified changes. Its mcmc attributes encode the timing information: so start(out) gives the time point associated with the first row returned, and end(out) out the last. The "thinning interval" is always 1.

If end.network==TRUE, return a network object, representing the final network, with a matrix of statistics described in the previous paragraph attached to it as an attr-style attribute "stats".

Note

ergm.godfather.ergm_model() is a lower-level interface, providing an ergm.godfather() method for the ergm_model class. The basis argument is required.

ergm.godfather.ergm_model() is a lower-level interface, providing an ergm.godfather() method for the ergm_model class. The basis argument is required.

See Also

tergm.godfather() in tergm, simulate.ergm(), simulate.formula()

Examples

data(florentine)
ergm.godfather(flomarriage~edges+absdiff("wealth")+triangles,
               changes=list(cbind(1:2,2:3),
                            cbind(3,5),
                            cbind(3,5),
                            cbind(1:2,2:3)),
               stats.start=TRUE)

Sample Space Constraints for Exponential-Family Random Graph Models

Description

This page describes how to specify the constraints on the network sample space (the set of possible networks YY, the set of networks yy for which h(y)>0h(y)>0) and sometimes the baseline weights h(y)h(y) to functions in the ergm package. It also provides an indexed list of the constraints visible to the ergm's API. Constraints can also be searched via search.ergmConstraints, and help for an individual constraint can be obtained with ⁠ergmConstraint?<constraint>⁠ or help("<constraint>-ergmConstraint").

Specifying constraints

In an exponential-family random graph model (ERGM), the probability or density of a given network, y∈Yy \in Y, on a set of nodes is

h(y)exp⁡[η(θ)⋅g(y)]/κ(θ),h(y) \exp[\eta(\theta) \cdot g(y)] / \kappa(\theta),

where h(y)h(y) is the reference distribution (particularly for valued network models), g(y)g(y) is a vector of network statistics for yy, η(θ)\eta(\theta) is a natural parameter vector of the same length (with η(θ)≡θ\eta(\theta)\equiv\theta for most terms), ⋅\cdot is the dot product, and κ(θ)\kappa(\theta) is the normalizing constant for the distribution. A complete ERGM specification requires a list of network statistics g(y)g(y) and (if applicable) their η(θ)\eta(\theta) mappings provided by a formula of ergmTerms; and, optionally, sample space Y\mathcal{Y} and reference distribution h(y)h(y) information provided by ergmConstraints and, for valued ERGMs, by ergmReferences. Constraints typically affect YY, or, equivalently, set h(y)=0h(y)=0 for some yy, but some (“soft” constraints) set h(y)h(y) to values other than 0 and 1.

A constraints formula is a one- or two-sided formula whose left-hand side is an optional direct selection of the InitErgmProposal function and whose right-hand side is a series of one or more terms separated by "+" and "-" operators, specifying the constraint.

The sample space (over and above the reference distribution) is determined by iterating over the constraints terms from left to right, each term updating it as follows:

  • If the constraint introduces complex dependence structure (e.g., constrains degree or number of edges in the network), then this constraint always restricts the sample space. It may only have a "+" sign.

  • If the constraint only restricts the set of dyads that may vary in the sample space (e.g., block-diagonal structure or fixing specific dyads at specific values) and has a "+" sign, the set of dyads that may vary is restricted to those that may vary according to this constraint and all the constraints to date.

  • If the constraint only restricts the set of dyads that may vary in the sample space but has a "-" sign, the set of dyads that may vary is expanded to those that may vary according to this constraint or all the constraints up to date.

For example, a constraints formula ~a-b+c-d with all constraints dyadic will allow dyads permitted by either a or b but only if they are also permitted by c; as well as all dyads permitted by d. If A, B, C, and D were logical matrices, the matrix of variable dyads would be equal to ((A|B)&C)|D.

Terms with a positive sign can be viewed as "adding" a constraint while those with a negative sign can be viewed as "relaxing" a constraint.

Inheriting constraints from LHS network

By default, %ergmlhs% attributes constraints or constraints.obs (depending on which constraint) attached to the LHS of the model formula or the ⁠basis=⁠ argument will be added in front of the specified constraints formula. This is the desired behaviour most of the time, since those constraints are usually determined by how the network was constructed (e.g., structural zeros in a block-diagonal network).

For those situations in which this is not the desired behavior, a . term (with a positive sign or no sign at all) can be used to manually set the position of the inherited constraints in the formula, and a -. (minus-dot) term anywhere in the constraints formula will suppress the inherited formula altogether.

Constraints visible to the package

Term Package Description Concepts
ergm Preserve the actor degree for bipartite networks bipartite
ergm Preserve the receiver degree for bipartite networks bipartite
ergm Constrain maximum and minimum vertex degree directed undirected
ergm Block-diagonal structure constraint directed dyad-independent undirected
ergm Constrain blocks of dyads defined by mixing type on a vertex attribute. directed dyad-independent undirected
ergm Preserve the degree distribution of the given network directed undirected
ergm Preserve the degree of each vertex of the given network directed undirected
ergm A soft constraint to adjust the sampled distribution for dyad-level noise with known perturbation probabilities directed dyad-independent soft undirected
ergm Constrain fixed or varying dyad-independent terms directed dyad-independent operator undirected
ergm Preserve the edge count of the given network
ergm Preserve values of dyads incident on vertices with given attribute directed dyad-independent undirected
ergm Preserve the dyad status in all but the given edges directed dyad-independent undirected
ergm Fix specific dyads directed dyad-independent undirected
ergm Preserve the hamming distance to the given network (BROKEN: Do NOT Use) directed undirected
ergm Preserve the indegree distribution directed
ergm Preserve indegree for directed networks directed
ergm Preserve the observed dyads of the given network directed dyad-independent undirected
ergm Preserve the outdegree distribution directed
ergm Preserve outdegree for directed networks directed

All constraints

Term bip dir undir dyad-indep soft op
b1degrees ✔
b2degrees ✔
bd ✔ ✔
blockdiag ✔ ✔ ✔
blocks ✔ ✔ ✔
degreedist ✔ ✔
degrees ✔ ✔
dyadnoise ✔ ✔ ✔ ✔
Dyads ✔ ✔ ✔ ✔
edges
egocentric ✔ ✔ ✔
fixallbut ✔ ✔ ✔
fixedas ✔ ✔ ✔
hamming ✔ ✔
idegreedist ✔
idegrees ✔
observed ✔ ✔ ✔
odegreedist ✔
odegrees ✔

Constraints by keywords

Jump to keyword: bipartite directed undirected dyad-independent soft operator

bipartite

b1degrees b2degrees

directed

bd blockdiag blocks degreedist degrees dyadnoise Dyads egocentric fixallbut fixedas hamming idegreedist idegrees observed odegreedist odegrees

undirected

bd blockdiag blocks degreedist degrees dyadnoise Dyads egocentric fixallbut fixedas hamming observed

dyad-independent

blockdiag blocks dyadnoise Dyads egocentric fixallbut fixedas observed

soft

dyadnoise

operator

Dyads

References

  • Goodreau SM, Handcock MS, Hunter DR, Butts CT, Morris M (2008a). A statnet Tutorial. Journal of Statistical Software, 24(8). doi:10.18637/jss.v024.i08

  • Hunter, D. R. and Handcock, M. S. (2006) Inference in curved exponential family models for networks, Journal of Computational and Graphical Statistics.

  • Hunter DR, Handcock MS, Butts CT, Goodreau SM, Morris M (2008b). ergm: A Package to Fit, Simulate and Diagnose Exponential-Family Models for Networks. Journal of Statistical Software, 24(3). doi:10.18637/jss.v024.i03

  • Karwa V, Krivitsky PN, and Slavkovi\'c AB (2016). Sharing Social Network Data: Differentially Private Estimation of Exponential-Family Random Graph Models. Journal of the Royal Statistical Society, Series C, 66(3): 481-500. doi:10.1111/rssc.12185

  • Krivitsky PN (2012). Exponential-Family Random Graph Models for Valued Networks. Electronic Journal of Statistics, 6, 1100-1128. doi:10.1214/12-EJS696

  • Morris M, Handcock MS, Hunter DR (2008). Specification of Exponential-Family Random Graph Models: Terms and Computational Aspects. Journal of Statistical Software, 24(4). doi:10.18637/jss.v024.i04

MCMC Hints for Exponential-Family Random Graph Models

Description

This page describes how to provide to the ergm's MCMC algorithms information about the sample space. Hints can also be searched via search.ergmHints, and help for an individual hint can be obtained with ⁠ergmHint?<hint>⁠ or help("<hint>-ergmHint").

“Hints” for MCMC

In an exponential-family random graph model (ERGM), the probability or density of a given network, y∈Yy \in Y, on a set of nodes is

h(y)exp⁡[η(θ)⋅g(y)]/κ(θ),h(y) \exp[\eta(\theta) \cdot g(y)] / \kappa(\theta),

where h(y)h(y) is the reference distribution (particularly for valued network models), g(y)g(y) is a vector of network statistics for yy, η(θ)\eta(\theta) is a natural parameter vector of the same length (with η(θ)≡θ\eta(\theta)\equiv\theta for most terms), ⋅\cdot is the dot product, and κ(θ)\kappa(\theta) is the normalizing constant for the distribution. A complete ERGM specification requires a list of network statistics g(y)g(y) and (if applicable) their η(θ)\eta(\theta) mappings provided by a formula of ergmTerms; and, optionally, sample space Y\mathcal{Y} and reference distribution h(y)h(y) information provided by ergmConstraints and, for valued ERGMs, by ergmReferences.

It is often the case that there is additional information available about the distribution of networks being modelled. For example, you may be aware that the network is sparse or that there are strata among the dyads. “Hints”, typically passed on the right-hand side of MCMC.prop and obs.MCMC.prop arguments to control.ergm(), control.simulate.ergm(), and others, allow this information to be provided. By default, hint sparse is in effect.

Unlike constraints, model terms, and reference distributions, “hints” do not affect the specification of the model. That is, regardless of what “hints” may or may not be in effect, the sample space and the probabilities within it are the same. However, “hints” may affect the MCMC proposal distribution used by the samplers.

Note that not all proposals support all “hints”: and if the most suitable proposal available cannot incorporate a particular “hint”, a warning message will be printed.

“Hints” use the same underlying API as constraints, and, if present, %ergmlhs% attributes constraints and constraints.obs will be substituted in its place.

Hints available to the package

The following hints are known to ergm at this time:

Term Package Description Concepts
ergm Sparse network dyad-independent
ergm Stratify Proposed Toggles by Mixing Type on a Vertex Attribute dyad-independent
ergm Network with strong clustering (triad-closure) effects

References

  • Goodreau SM, Handcock MS, Hunter DR, Butts CT, Morris M (2008a). A statnet Tutorial. Journal of Statistical Software, 24(8). doi:10.18637/jss.v024.i08

  • Hunter, D. R. and Handcock, M. S. (2006) Inference in curved exponential family models for networks, Journal of Computational and Graphical Statistics.

  • Hunter DR, Handcock MS, Butts CT, Goodreau SM, Morris M (2008b). ergm: A Package to Fit, Simulate and Diagnose Exponential-Family Models for Networks. Journal of Statistical Software, 24(3). doi:10.18637/jss.v024.i03

  • Karwa V, Krivitsky PN, and Slavkovi\'c AB (2016). Sharing Social Network Data: Differentially Private Estimation of Exponential-Family Random Graph Models. Journal of the Royal Statistical Society, Series C, 66(3): 481-500. doi:10.1111/rssc.12185

  • Krivitsky PN (2012). Exponential-Family Random Graph Models for Valued Networks. Electronic Journal of Statistics, 6, 1100-1128. doi:10.1214/12-EJS696

  • Morris M, Handcock MS, Hunter DR (2008). Specification of Exponential-Family Random Graph Models: Terms and Computational Aspects. Journal of Statistical Software, 24(4). doi:10.18637/jss.v024.i04

Keywords defined for Exponential-Family Random Graph Models

Description

This collects all defined keywords defined for the ERGM and derived packages

Possible keywords defined by the ERGM and derived packages

name short description popular package
binary bin suitable for binary ERGMs TRUE ergm
bipartite bip suitable for bipartite networks TRUE ergm
categorical nodal attribute cat nodal attr involves a categorical nodal attribute FALSE ergm
categorical dyadic attribute cat dyad attr involves a categorical dyadic attribute FALSE ergm
categorical triadic attribute cat triad attr involves a categorical triadic attribute FALSE ergm
continuous cont a continuous distribution for edge values FALSE ergm
curved curved is a curved term FALSE ergm
directed dir suitable for directed networks TRUE ergm
discrete discrete a discrete distribution for edge values FALSE ergm
dyad-independent dyad-indep does not induce dyadic dependence TRUE ergm
finite fin finite edge values only FALSE ergm
frequently-used freq is frequently used FALSE ergm
nonnegative nneg only meaningful for nonnegative edge values FALSE ergm
operator op a term operator TRUE ergm
positive pos only meaningful for positive edge values FALSE ergm
quantitative nodal attribute quant nodal attr involves a quantitative nodal attribute FALSE ergm
quantitative dyadic attribute quant dyad attr involves a quantitative dyadic attribute FALSE ergm
quantitative triadic attribute quant triad attr involves a quantitative triadic attribute FALSE ergm
soft soft a constraint that does not necessarily forbid specific networks outright but reweights their probabilities FALSE ergm
triad-related triad rel involves triangles, two-paths, and other triadic structures FALSE ergm
valued val suitable for valued ERGMs TRUE ergm
undirected undir suitable for undirected networks TRUE ergm

ERGM Predictors and response for logistic regression calculation of MPLE

Description

Return the predictor matrix, response vector, and vector of weights that can be used to calculate the MPLE for an ERGM.

Usage

ergmMPLE(
  formula,
  constraints = ~.,
  obs.constraints = ~-observed,
  output = c("matrix", "array", "dyadlist", "fit"),
  expand.bipartite = FALSE,
  control = control.ergm(),
  verbose = FALSE,
  ...,
  basis = ergm.getnetwork(formula)
)

Arguments

formula, constraints, obs.constraints

An ERGM formula and (optionally) a constraint specification formulas. See ergm(). This function supports only dyad-independent constraints.
output

Character, partially matched. See Value.
expand.bipartite

Logical. Specifies whether the output matrices (or array slices) representing dyads for bipartite networks are represented as rectangular matrices with first mode vertices in rows and second mode in columns, or as square matrices with dimension equalling the total number of vertices, containing with structural NAs or 0s within each mode.
control

A list of control parameters for algorithm tuning, typically constructed with control.ergm(). Its documentation gives the the list of recognized control parameters and their meaning. The more generic utility snctrl() (StatNet ConTRoL) also provides argument completion for the available control functions and limited argument name checking.
verbose

A logical or an integer to control the amount of progress and diagnostic information to be printed. FALSE/0 produces minimal output, with higher values producing more detail. Note that very high values (5+) may significantly slow down processing.
...

Additional arguments, to be passed to lower-level functions.
basis

a value (usually a network) to override the LHS of the formula.

Details

The MPLE for an ERGM is calculated by first finding the matrix of change statistics. Each row of this matrix is associated with a particular pair (ordered or unordered, depending on whether the network is directed or undirected) of nodes, and the row equals the change in the vector of network statistics (as defined in formula) when that pair is toggled from a 0 (no edge) to a 1 (edge), holding all the rest of the network fixed. The MPLE results if we perform a logistic regression in which the predictor matrix is the matrix of change statistics and the response vector is the observed network (i.e., each entry is either 0 or 1, depending on whether the corresponding edge exists or not).

Using output="matrix", note that the result of the fit may be obtained from the glm() function, as shown in the examples below.

Value

If output=="matrix" (the default), then only the response, predictor, and weights are returned; thus, the MPLE may be found by hand or the vector of change statistics may be used in some other way. To save space, the algorithm will automatically search for any duplicated rows in the predictor matrix (and corresponding response values). ergmMPLE function will return a list with three elements, response, predictor, and weights, respectively the response vector, the predictor matrix, and a vector of weights, which are really counts that tell how many times each corresponding response, predictor pair is repeated.

If output=="dyadlist", as "matrix", but rather than coalescing the duplicated rows, every relation in the network that is not fixed and is observed will have its own row in predictor and element in response and weights, and predictor matrix will have two additional rows at the start, tail and head, indicating to which dyad the row and the corresponding elements pertain.

If output=="array", a list with similarly named three elements is returned, but response is formatted into a sociomatrix; predictor is a 3-dimensional array of with cell predictor[t,h,k] containing the change score of term k for dyad (t,h); and weights is also formatted into a sociomatrix, with an element being 1 if it is to be added into the pseudolikelihood and 0 if it is not.

In particular, for a unipartite network, cells corresponding to self-loops, i.e., predictor[i,i,k] will be NA and weights[i,i] will be 0; and for a unipartite undirected network, lower triangle of each predictor[,,k] matrix will be set to NA, with the lower triangle of weights being set to 0.

To all of the above output types, attr(., "etamap") is attached containing the mapping and offset information.

If output=="fit", then ergmMPLE simply calls the ergm() function with the estimate="MPLE" option set, returning an object of class ergm that gives the fitted pseudolikelihood model.

See Also

ergm(), glm()

Examples

data(faux.mesa.high)
formula <- faux.mesa.high ~ edges + nodematch("Sex") + nodefactor("Grade")
mplesetup <- ergmMPLE(formula)

# Obtain MPLE coefficients "by hand":
coef(glm(mplesetup$response ~ . - 1, data = data.frame(mplesetup$predictor),
         weights = mplesetup$weights, family="binomial"))

# Check that the coefficients agree with the output of the ergm function:
coef(ergmMPLE(formula, output="fit"))

# We can also format the predictor matrix into an array:
mplearray <- ergmMPLE(formula, output="array")

# The resulting matrices are big, so only print the first 8 actors:
mplearray$response[1:8,1:8]
mplearray$predictor[1:8,1:8,]
mplearray$weights[1:8,1:8]

# Constraints are handled:
faux.mesa.high%v%"block" <- seq_len(network.size(faux.mesa.high)) %/% 4
mplearray <- ergmMPLE(faux.mesa.high~edges, constraints=~blockdiag("block"), output="array")
mplearray$response[1:8,1:8]
mplearray$predictor[1:8,1:8,]
mplearray$weights[1:8,1:8]

# Or, a dyad list:
faux.mesa.high%v%"block" <- seq_len(network.size(faux.mesa.high)) %/% 4
mplearray <- ergmMPLE(faux.mesa.high~edges, constraints=~blockdiag("block"), output="dyadlist")
mplearray$response[1:8]
mplearray$predictor[1:8,]
mplearray$weights[1:8]

# Curved terms produce predictors on the canonical scale:
formula2 <- faux.mesa.high ~ gwesp
mplearray <- ergmMPLE(formula2, output="array")
# The resulting matrices are big, so only print the first 5 actors:
mplearray$response[1:5,1:5]
mplearray$predictor[1:5,1:5,1:3]
mplearray$weights[1:5,1:5]

Metropolis-Hastings Proposal Methods for ERGM MCMC

Description

This page describes the low-level Metropolis–Hastings (MH) proposal algorithms. They are rarely invoked directly by the user but are rather selected based on the provided sample space constraints and hints about the network process. They can also be searched via search.ergmProposals, and help for an individual proposal can be obtained with ⁠ergmProposal?<proposal>⁠ or help("<proposal>-ergmProposal").

Details

ergm uses a Metropolis-Hastings (MH) algorithm to control the behavior of the Markov Chain Monte Carlo (MCMC) for sampling networks. The MCMC chain is intended to step around the sample space of possible networks, generating a network at regular intervals to evaluate the statistics in the model. For each MCMC step, one or more toggles are proposed to change the dyads to the opposite value. The probability of accepting the proposed change is determined by the MH acceptance ratio. The role of the different MH methods implemented in ergm() is to vary how the sets of dyads are selected for toggle proposals. This is used in some cases to improve the performance (speed and mixing) of the algorithm, and in other cases to constrain the sample space.

Proposals available to the package

Proposal Reference Enforces May_Enforce Priority Weight Class
BDStratTNT Bernoulli sparse bdmax blocks strat -3 BDStratTNT cross-sectional
BDStratTNT Bernoulli bdmax sparse blocks strat 5 BDStratTNT cross-sectional
BDStratTNT Bernoulli blocks sparse bdmax strat 5 BDStratTNT cross-sectional
BDStratTNT Bernoulli strat sparse bdmax blocks 5 BDStratTNT cross-sectional
CondB1Degree Bernoulli b1degrees 0 random cross-sectional
CondB2Degree Bernoulli b2degrees 0 random cross-sectional
CondDegree Bernoulli degrees 0 random cross-sectional
CondDegree Bernoulli idegrees odegrees 0 random cross-sectional
CondDegree Bernoulli b1degrees b2degrees 0 random cross-sectional
CondDegreeDist Bernoulli degreedist 0 random cross-sectional
CondDegreeMix Bernoulli degreesmix 0 random cross-sectional
CondInDegree Bernoulli idegrees 0 random cross-sectional
CondInDegreeDist Bernoulli idegreedist 0 random cross-sectional
CondOutDegree Bernoulli odegrees 0 random cross-sectional
CondOutDegreeDist Bernoulli odegreedist 0 random cross-sectional
ConstantEdges Bernoulli edges .dyads bd 0 random cross-sectional
DiscUnif DiscUnif 0 random cross-sectional
DiscUnif2 DiscUnif -1 random2 cross-sectional
DiscUnifNonObserved DiscUnif observed 0 random cross-sectional
DistRLE StdNormal .dyads 0 random cross-sectional
DistRLE Unif .dyads 0 random cross-sectional
DistRLE Unif .dyads -3 random cross-sectional
DistRLE DiscUnif .dyads -3 random cross-sectional
DistRLE StdNormal .dyads -3 random cross-sectional
DistRLE Poisson .dyads -3 random cross-sectional
DistRLE Binomial .dyads -3 random cross-sectional
dyadnoise Bernoulli dyadnoise 0 random cross-sectional
dyadnoiseTNT Bernoulli dyadnoise sparse 1 TNT cross-sectional
HammingConstantEdges Bernoulli edges hamming 0 random cross-sectional
HammingTNT Bernoulli hamming sparse 0 random cross-sectional
randomtoggle Bernoulli .dyads bd -2 random cross-sectional
SPDyad Bernoulli sparse triadic .dyads bd 0 TNT cross-sectional
StdNormal StdNormal 0 random cross-sectional
TNT Bernoulli sparse .dyads bd 0 TNT cross-sectional
Unif Unif 0 random cross-sectional
UnifNonObserved Unif observed 0 random cross-sectional

Note that .dyads is a meta-constraint, indicating that the proposal supports an arbitrary dyad-level constraint combination.

References

  • Goodreau SM, Handcock MS, Hunter DR, Butts CT, Morris M (2008a). A statnet Tutorial. Journal of Statistical Software, 24(8). doi:10.18637/jss.v024.i08

  • Hunter, D. R. and Handcock, M. S. (2006) Inference in curved exponential family models for networks. Journal of Computational and Graphical Statistics.

  • Hunter DR, Handcock MS, Butts CT, Goodreau SM, Morris M (2008b). ergm: A Package to Fit, Simulate and Diagnose Exponential-Family Models for Networks. Journal of Statistical Software, 24(3). doi:10.18637/jss.v024.i03

  • Krivitsky PN (2012). Exponential-Family Random Graph Models for Valued Networks. Electronic Journal of Statistics, 2012, 6, 1100-1128. doi:10.1214/12-EJS696

  • Morris M, Handcock MS, Hunter DR (2008). Specification of Exponential-Family Random Graph Models: Terms and Computational Aspects. Journal of Statistical Software, 24(4). doi:10.18637/jss.v024.i04

See Also

ergm package, ergm, ergmConstraint, ergmHint, ergm_proposal

Reference Measures for Exponential-Family Random Graph Models

Description

This page describes how to specify the reference measures (baseline distributions) (the set of possible networks YY and the baseline weights h(y)h(y) to functions in the ergm package. It also provides an indexed list of the references visible to the ergm's API. References can also be searched via search.ergmReferences(), and help for an individual reference can be obtained with ⁠ergmReference?<reference>⁠ or help("<reference>-ergmReference").

Specifying reference measures

In an exponential-family random graph model (ERGM), the probability or density of a given network, y∈Yy \in Y, on a set of nodes is

h(y)exp⁡[η(θ)⋅g(y)]/κ(θ),h(y) \exp[\eta(\theta) \cdot g(y)] / \kappa(\theta),

where h(y)h(y) is the reference distribution (particularly for valued network models), g(y)g(y) is a vector of network statistics for yy, η(θ)\eta(\theta) is a natural parameter vector of the same length (with η(θ)≡θ\eta(\theta)\equiv\theta for most terms), ⋅\cdot is the dot product, and κ(θ)\kappa(\theta) is the normalizing constant for the distribution. A complete ERGM specification requires a list of network statistics g(y)g(y) and (if applicable) their η(θ)\eta(\theta) mappings provided by a formula of ergmTerms; and, optionally, sample space Y\mathcal{Y} and reference distribution h(y)h(y) information provided by ergmConstraints and, for valued ERGMs, by ergmReferences.

The reference measure (Y,h(y))(Y,h(y)) is specified on the right-hand side of a one-sided formula passed typically as the reference argument.

Reference measures visible to the package

Term Package Description Concepts
ergm Bernoulli reference discrete finite nonnegative
ergm Discrete Uniform reference discrete finite
ergm Standard Normal reference continuous
ergm Continuous Uniform reference continuous

All references

Term bin discrete fin nneg cont
Bernoulli ✔ ✔ ✔ ✔
DiscUnif ✔ ✔
StdNormal ✔
Unif ✔

References by keywords

Jump to keyword: binary discrete finite nonnegative continuous

binary

Bernoulli

discrete

Bernoulli DiscUnif

finite

Bernoulli DiscUnif

nonnegative

Bernoulli

continuous

StdNormal Unif

References

  • Hunter DR, Handcock MS, Butts CT, Goodreau SM, Morris M (2008b). ergm: A Package to Fit, Simulate and Diagnose Exponential-Family Models for Networks. Journal of Statistical Software, 24(3). doi:10.18637/jss.v024.i03

  • Krivitsky PN (2012). Exponential-Family Random Graph Models for Valued Networks. Electronic Journal of Statistics, 2012, 6, 1100-1128. doi:10.1214/12-EJS696

See Also

ergm, network, sna, summary.ergm, print.ergm, ⁠\%v\%⁠, ⁠\%n\%⁠

Terms used in Exponential Family Random Graph Models

Description

This page explains how to specify the network statistics g(y)g(y) to functions in the ergm package and packages that extend it. It also provides an indexed list of the possible terms (and hence network statistics) visible to the ergm API. Terms can also be searched via search.ergmTerms, and help for an individual term can be obtained with ⁠ergmTerm?<term>⁠ or help("<term>-ergmTerm").

Specifying models

In an exponential-family random graph model (ERGM), the probability or density of a given network, y∈Yy \in Y, on a set of nodes is

h(y)exp⁡[η(θ)⋅g(y)]/κ(θ),h(y) \exp[\eta(\theta) \cdot g(y)] / \kappa(\theta),

where h(y)h(y) is the reference distribution (particularly for valued network models), g(y)g(y) is a vector of network statistics for yy, η(θ)\eta(\theta) is a natural parameter vector of the same length (with η(θ)≡θ\eta(\theta)\equiv\theta for most terms), ⋅\cdot is the dot product, and κ(θ)\kappa(\theta) is the normalizing constant for the distribution. A complete ERGM specification requires a list of network statistics g(y)g(y) and (if applicable) their η(θ)\eta(\theta) mappings provided by a formula of ergmTerms; and, optionally, sample space Y\mathcal{Y} and reference distribution h(y)h(y) information provided by ergmConstraints and, for valued ERGMs, by ergmReferences.

Network statistics g(y)g(y) and mappings η(θ)\eta(\theta) are specified by a formula object, of the form ⁠y ~ <term 1> + <term 2> ...⁠, where y is a network object or a matrix that can be coerced to a network object, and ⁠<term 1>⁠, ⁠<term 2>⁠, etc, are each terms chosen from the list given below. To create a network object in , use the network function, then add nodal attributes to it using the ⁠%v%⁠ operator if necessary.

Term operators

Operator terms like B() and F() take formulas with other ergm terms as their arguments and transform them by modifying their inputs (e.g., the network they evaluate) and/or their outputs.

By convention, their names are capitalized and CamelCased.

Interactions

For binary ERGMs, interactions between ergm terms can be specified in a manner similar to lm and others, as using the : and * operators. However, they must be interpreted carefully, especially for dyad-dependent terms. (Interactions involving curved terms are not supported at this time.)

Generally, if term a has pap_a statistics and b has pbp_b, a:b will add pa×pbp_a \times p_b statistics to the model, corresponding to each element of ga(y)g_a(y) interacted with each element of gb(y)g_b(y).

The interaction is defined as follows. Dyad-independent terms can be expressed in the general form g(y;x)=∑i,jg(y;x)=\sum_{i,j}xi,jyi,jx_{i,j}y_{i,j} for some edge covariate matrix xx,

ga:b(y)=∑i,jxa,i,jxb,i,jyi,j.g_{a:b}(y)=\sum_{i,j} x_{a,i,j}x_{b,i,j}y_{i,j}.

In other words, rather than being a product of their sufficient statistics (ga(y)gb(y)g_{a}(y)g_{b}(y)), it is a dyadwise product of their dyad-level effects.

This means that an interaction between two dyad-independent terms can be interpreted the same way as it would be in the corresponding logistic regression for each potential edge. However, for undirected networks in particular, this may lead to somewhat counterintuitive results. For example, given two nodal covariates "a" and "b" (whose values for node ii are denoted aia_i and bib_i, respectively), nodecov("a") adds one statistic of the form ∑i,j(ai+aj)yi,j\sum_{i,j} (a_{i}+a_{j}) y_{i,j} and analogously for nodecov("b"), so nodecov("a"):nodecov("b") produces

∑i,j(ai+aj)(bi+bj)yi,j.\sum_{i,j} (a_{i}+a_{j}) (b_{i}+b_{j}) y_{i,j}.

Binary and valued ERGM terms

ergm functions such as ergm and simulate (for ERGMs) may operate in two modes: binary and weighted/valued, with the latter activated by passing a non-NULL value as the response argument, giving the edge attribute name to be modeled/simulated.

Generalizations of binary terms

Binary ERGM statistics cannot be used directly in valued mode and vice versa. However, a substantial number of binary ERGM statistics — particularly the ones with dyadic independence — have simple generalizations to valued ERGMs, and have been adapted in ergm. They have the same form as their binary ERGM counterparts, with an additional argument: form, which, at this time, has two possible values: "sum" (the default) and "nonzero". The former creates a statistic of the form ∑i,jxi,jyi,j\sum_{i,j} x_{i,j} y_{i,j}, where yi,jy_{i,j} is the value of dyad (i,j)(i,j) and xi,jx_{i,j} is the term's covariate associated with it. The latter computes the binary version, with the edge considered to be present if its value is not 0. Valued version of some binary ERGM terms have an argument threshold, which sets the value above which a dyad is conidered to have a tie. (Value less than or equal to threshold is considered a nontie.)

The B() operator term documented below can be used to pass other binary terms to valued models, and is more flexible, at the cost of being somewhat slower.

Nodal attribute levels and indices

Terms taking a categorical nodal covariate also take the levels argument. (There are analogous b1levels and b2levels arguments for some terms that apply to bipartite networks, and the levels2 argument for mixing terms.) The levels argument can be used to control the set and the ordering of attribute levels.

Terms that allow the selection of nodes do so with the nodes argument, which is interpreted in the same way as the levels argument, where the categories are the relevant nodal indices themselves.

Both levels and nodes use the new level selection UI. (See Specifying Vertex attributes and Levels (⁠? nodal_attributes⁠) for details.)

Legacy arguments

The legacy base and keep arguments are deprecated as of version 3.10, and replaced by the levels UI. The levels argument provides consistent and flexible mechanisms for specifying which attribute levels to exclude (previously handled by base) and include (previously handled by keep). If levels or nodes argument is given, then base and keep arguments are ignored. The legacy arguments will most likely be removed in a future version.

Note that this exact behavior is new in version 3.10, and it differs slightly from older versions: previously if both levels and base/keep were given, levels argument was applied first and then applied the base/keep argument. Since version 3.10, base/keep would be ignored, even if old term behavior is invoked (as described in the next section).

Term versioning

When a term's behavior has changed from prior version, it is often possible to invoke the old behavior by setting and/or passing a version term option, giving the verison (constructed by as.package_version) desired.

Custom ergm terms

Users and other packages may build custom terms, and package ergm.userterms (https://github.com/statnet/ergm.userterms) provides tools for implementing them.

The current recommendation for any package implementing additional terms is to document the term with Roxygen comments and a name in the form termName-ergmTerm. This ensures that help("ergmTerm") will list ERGM terms available from all loaded packages.

Terms included in the ergm package

As noted above, a cross-referenced HTML version of the term documentation is also available via vignette('ergm-term-crossRef') and terms can also be searched via search.ergmTerms.

Term index (plain)

Term Package Description Concepts
ergm Absolute difference in nodal attribute directed dyad-independent quantitative nodal attribute undirected
ergm Categorical absolute difference in nodal attribute categorical nodal attribute directed dyad-independent undirected
ergm Alternating k-star categorical nodal attribute curved undirected
ergm Asymmetric dyads directed dyad-independent triad-related
ergm Number of dyads with values greater than or equal to a threshold directed dyad-independent undirected
ergm Number of dyads with values less than or equal to a threshold directed dyad-independent undirected
ergm Edge covariate by attribute pairing directed dyad-independent undirected
ergm Concurrent node count for the first mode in a bipartite network bipartite categorical nodal attribute undirected
ergm Main effect of a covariate for the first mode in a bipartite network bipartite dyad-independent frequently-used quantitative nodal attribute undirected
ergm Degree range for the first mode in a bipartite network bipartite undirected
ergm Degree for the first mode in a bipartite network bipartite categorical nodal attribute frequently-used undirected
b1dsp(d) (bin)
 ergm Dyadwise shared partners for dyads in the first bipartition bipartite undirected
ergm Factor attribute effect for the first mode in a bipartite network bipartite categorical nodal attribute dyad-independent frequently-used undirected
ergm Minimum degree for the first mode in a bipartite network bipartite undirected
ergm Nodal attribute-based homophily effect for the first mode in a bipartite network bipartite categorical nodal attribute dyad-independent frequently-used undirected
ergm Degree bipartite dyad-independent undirected
ergm k-stars for the first mode in a bipartite network bipartite categorical nodal attribute undirected
ergm Mixing matrix for k-stars centered on the first mode of a bipartite network bipartite categorical nodal attribute undirected
ergm Two-star census for central nodes centered on the first mode of a bipartite network bipartite categorical nodal attribute undirected
ergm Concurrent node count for the second mode in a bipartite network bipartite frequently-used undirected
ergm Main effect of a covariate for the second mode in a bipartite network bipartite dyad-independent frequently-used quantitative nodal attribute undirected
ergm Degree range for the second mode in a bipartite network bipartite undirected
ergm Degree for the second mode in a bipartite network bipartite categorical nodal attribute frequently-used undirected
b2dsp(d) (bin)
 ergm Dyadwise shared partners for dyads in the second bipartition bipartite undirected
ergm Factor attribute effect for the second mode in a bipartite network bipartite categorical nodal attribute dyad-independent frequently-used undirected
ergm Minimum degree for the second mode in a bipartite network bipartite undirected
ergm Nodal attribute-based homophily effect for the second mode in a bipartite network bipartite categorical nodal attribute dyad-independent frequently-used undirected
ergm Degree bipartite dyad-independent undirected
ergm k-stars for the second mode in a bipartite network bipartite categorical nodal attribute undirected
ergm Mixing matrix for k-stars centered on the second mode of a bipartite network bipartite categorical nodal attribute undirected
ergm Two-star census for central nodes centered on the second mode of a bipartite network bipartite categorical nodal attribute undirected
balance (bin)
 ergm Balanced triads directed triad-related undirected
ergm Coincident node count for the second mode in a bipartite (aka two-mode) network bipartite undirected
ergm Concurrent node count categorical nodal attribute undirected
ergm Concurrent tie count categorical nodal attribute undirected
ergm Cyclic triples categorical nodal attribute directed triad-related
ergm k-Cycle Census directed undirected
ergm Cyclical ties directed undirected
ergm Cyclical weights directed nonnegative undirected
degcor (bin)
 ergm Degree Correlation undirected
ergm Degree Cross-Product undirected
ergm Degree range categorical nodal attribute undirected
ergm Degree categorical nodal attribute frequently-used undirected
degree1.5 (bin)
 ergm Degree to the 3/2 power undirected
density (bin)
 ergm Density directed dyad-independent undirected
ergm Difference bipartite directed dyad-independent frequently-used quantitative nodal attribute undirected
ergm Directed dyadwise shared partners directed
ergm Dyadic covariate directed dyad-independent quantitative dyadic attribute undirected
ergm Edge covariate directed dyad-independent frequently-used quantitative dyadic attribute undirected
edges (bin)
nonzero (val)
edges (val)
 ergm Number of edges in the network directed dyad-independent undirected
ergm Number of dyads with values equal to a specific value (within tolerance) directed dyad-independent undirected
ergm Directed edgewise shared partners directed
ergm Number of dyads with values strictly greater than a threshold directed dyad-independent undirected
ergm Geometrically weighted degree distribution for the first mode in a bipartite network bipartite curved undirected
ergm Geometrically weighted dyadwise shared partner distribution for dyads in the first bipartition bipartite curved undirected
ergm Geometrically weighted degree distribution for the second mode in a bipartite network bipartite curved undirected
ergm Geometrically weighted dyadwise shared partner distribution for dyads in the second bipartition bipartite curved undirected
ergm Geometrically weighted degree distribution curved frequently-used undirected
ergm Geometrically weighted dyadwise shared partner distribution directed
ergm Geometrically weighted edgewise shared partner distribution directed
ergm Geometrically weighted in-degree distribution curved directed
ergm Geometrically weighted non-edgewise shared partner distribution directed
ergm Geometrically weighted out-degree distribution curved directed
ergm Hamming distance directed dyad-independent undirected
ergm In-degree range categorical nodal attribute directed
ergm In-degree categorical nodal attribute directed frequently-used
idegree1.5 (bin)
 ergm In-degree to the 3/2 power directed
ergm Number of dyads whose values are in an interval directed dyad-independent undirected
ergm Intransitive triads directed triad-related
ergm Isolated edges bipartite undirected
isolates (bin)
 ergm Isolates directed frequently-used undirected
ergm In-stars categorical nodal attribute directed
ergm k-stars categorical nodal attribute undirected
ergm Triangles within neighborhoods categorical dyadic attribute directed triad-related undirected
m2star (bin)
 ergm Mixed 2-stars, a.k.a 2-paths directed
meandeg (bin)
 ergm Mean vertex degree directed dyad-independent undirected
ergm Mixing matrix cells and margins categorical nodal attribute directed dyad-independent frequently-used undirected
ergm Mutuality directed frequently-used
ergm Near simmelian triads directed triad-related
ergm Main effect of a covariate directed dyad-independent frequently-used quantitative nodal attribute undirected
ergm Covariance of undirected dyad values incident on each actor directed
ergm Factor attribute effect categorical nodal attribute directed dyad-independent frequently-used undirected
ergm Main effect of a covariate for in-edges directed frequently-used quantitative nodal attribute
ergm Covariance of in-dyad values incident on each actor directed
ergm Factor attribute effect for in-edges categorical nodal attribute directed dyad-independent frequently-used
ergm Uniform homophily and differential homophily categorical nodal attribute directed dyad-independent frequently-used undirected
ergm Nodal attribute mixing categorical nodal attribute directed dyad-independent frequently-used undirected
ergm Main effect of a covariate for out-edges directed dyad-independent quantitative nodal attribute
ergm Covariance of out-dyad values incident on each actor directed
ergm Factor attribute effect for out-edges categorical nodal attribute directed dyad-independent
ergm Directed non-edgewise shared partners directed
ergm Out-degree range categorical nodal attribute directed
ergm Out-degree categorical nodal attribute directed frequently-used
odegree1.5 (bin)
 ergm Out-degree to the 3/2 power directed
opentriad (bin)
 ergm Open triads triad-related undirected
ergm k-Outstars categorical nodal attribute directed
ergm Receiver effect directed dyad-independent
ergm Sender effect directed dyad-independent
simmelian (bin)
 ergm Simmelian triads directed triad-related
ergm Ties in simmelian triads directed triad-related
ergm Number of ties between actors with similar attribute values directed dyad-independent quantitative nodal attribute undirected
ergm Number of dyads with values strictly smaller than a threshold directed dyad-independent undirected
ergm Undirected degree categorical nodal attribute dyad-independent undirected
sum(pow) (val)
 ergm Sum of dyad values (optionally taken to a power) directed undirected
ergm Three-trails directed triad-related undirected
transitive (bin)
 ergm Transitive triads directed triad-related
ergm Transitive ties categorical nodal attribute directed triad-related undirected
ergm Transitive weights directed nonnegative triad-related undirected
ergm Triad census directed triad-related undirected
ergm Triangles categorical nodal attribute directed frequently-used triad-related undirected
ergm Triangle percentage categorical nodal attribute triad-related undirected
ergm Transitive triples categorical nodal attribute directed triad-related
twopath (bin)
 ergm 2-Paths directed undirected

Term index (operator)

Term Package Description Concepts
ergm Wrap binary terms for use in valued models operator
ergm Impose a curved structure on term parameters operator
ergm Exponentiate a network's statistic operator
ergm Filtering on arbitrary one-term model operator
For(...) (bin)
 ergm A for operator for terms operator
ergm Modify terms' coefficient names operator
ergm Take a natural logarithm of a network's statistic operator
ergm Filtering on nodematch operator
ergm Terms with fixed coefficients operator
ergm A product (or an arbitrary power combination) of one or more formulas operator
ergm Evaluation on an induced subgraph operator
ergm A sum (or an arbitrary linear combination) of one or more formulas operator
ergm Evaluation on symmetrized (undirected) network directed operator

Frequently-used terms

Term bin bip dir dyad-indep op val undir
b1cov ✔ ✔ ✔ ✔ ✔
b1degree ✔ ✔ ✔
b1factor ✔ ✔ ✔ ✔ ✔
b1nodematch ✔ ✔ ✔ ✔
b2concurrent ✔ ✔ ✔
b2cov ✔ ✔ ✔ ✔ ✔
b2degree ✔ ✔ ✔
b2factor ✔ ✔ ✔ ✔ ✔
b2nodematch ✔ ✔ ✔ ✔
degree ✔ ✔
diff ✔ ✔ ✔ ✔ ✔ ✔
edgecov ✔ ✔ ✔ ✔ ✔
gwdegree ✔ ✔
idegree ✔ ✔
isolates ✔ ✔ ✔
mm ✔ ✔ ✔ ✔ ✔
mutual ✔ ✔ ✔
nodecov ✔ ✔ ✔ ✔ ✔
nodefactor ✔ ✔ ✔ ✔ ✔
nodeicov ✔ ✔ ✔
nodeifactor ✔ ✔ ✔ ✔
nodematch ✔ ✔ ✔ ✔ ✔
nodemix ✔ ✔ ✔ ✔ ✔
odegree ✔ ✔
triangle ✔ ✔ ✔

Operator terms

Term bin bip dir dyad-indep val undir
B ✔
Curve ✔ ✔
Exp ✔ ✔
F ✔
For ✔
Label ✔ ✔
Log ✔ ✔
NodematchFilter ✔
Offset ✔
Prod ✔ ✔
S ✔
Sum ✔ ✔
Symmetrize ✔ ✔

All terms

Term dir dyad-indep quant nodal attr undir bin val cat nodal attr curved triad rel op bip freq nneg quant dyad attr cat dyad attr
absdiff ✔ ✔ ✔ ✔ ✔ ✔
absdiffcat ✔ ✔ ✔ ✔ ✔ ✔
altkstar ✔ ✔ ✔ ✔
asymmetric ✔ ✔ ✔ ✔
atleast ✔ ✔ ✔ ✔
atmost ✔ ✔ ✔ ✔
attrcov ✔ ✔ ✔ ✔
B ✔ ✔
b1concurrent ✔ ✔ ✔ ✔
b1cov ✔ ✔ ✔ ✔ ✔ ✔ ✔
b1degrange ✔ ✔ ✔
b1degree ✔ ✔ ✔ ✔ ✔
b1dsp ✔ ✔ ✔
b1factor ✔ ✔ ✔ ✔ ✔ ✔ ✔
b1mindegree ✔ ✔ ✔
b1nodematch ✔ ✔ ✔ ✔ ✔ ✔
b1sociality ✔ ✔ ✔ ✔ ✔
b1star ✔ ✔ ✔ ✔
b1starmix ✔ ✔ ✔ ✔
b1twostar ✔ ✔ ✔ ✔
b2concurrent ✔ ✔ ✔ ✔
b2cov ✔ ✔ ✔ ✔ ✔ ✔ ✔
b2degrange ✔ ✔ ✔
b2degree ✔ ✔ ✔ ✔ ✔
b2dsp ✔ ✔ ✔
b2factor ✔ ✔ ✔ ✔ ✔ ✔ ✔
b2mindegree ✔ ✔ ✔
b2nodematch ✔ ✔ ✔ ✔ ✔ ✔
b2sociality ✔ ✔ ✔ ✔ ✔
b2star ✔ ✔ ✔ ✔
b2starmix ✔ ✔ ✔ ✔
b2twostar ✔ ✔ ✔ ✔
balance ✔ ✔ ✔ ✔
coincidence ✔ ✔ ✔
concurrent ✔ ✔ ✔
concurrentties ✔ ✔ ✔
ctriple ✔ ✔ ✔ ✔
Curve ✔ ✔ ✔
cycle ✔ ✔ ✔
cyclicalties ✔ ✔ ✔ ✔
cyclicalweights ✔ ✔ ✔ ✔
degcor ✔ ✔
degcrossprod ✔ ✔
degrange ✔ ✔ ✔
degree ✔ ✔ ✔ ✔
degree1.5 ✔ ✔
density ✔ ✔ ✔ ✔
diff ✔ ✔ ✔ ✔ ✔ ✔ ✔ ✔
dsp ✔ ✔
dyadcov ✔ ✔ ✔ ✔ ✔
edgecov ✔ ✔ ✔ ✔ ✔ ✔ ✔
edges ✔ ✔ ✔ ✔ ✔
equalto ✔ ✔ ✔ ✔
esp ✔ ✔
Exp ✔ ✔ ✔
F ✔ ✔
For ✔ ✔
greaterthan ✔ ✔ ✔ ✔
gwb1degree ✔ ✔ ✔ ✔
gwb1dsp ✔ ✔ ✔ ✔
gwb2degree ✔ ✔ ✔ ✔
gwb2dsp ✔ ✔ ✔ ✔
gwdegree ✔ ✔ ✔ ✔
gwdsp ✔ ✔
gwesp ✔ ✔
gwidegree ✔ ✔ ✔
gwnsp ✔ ✔
gwodegree ✔ ✔ ✔
hamming ✔ ✔ ✔ ✔
idegrange ✔ ✔ ✔
idegree ✔ ✔ ✔ ✔
idegree1.5 ✔ ✔
ininterval ✔ ✔ ✔ ✔
intransitive ✔ ✔ ✔
isolatededges ✔ ✔ ✔
isolates ✔ ✔ ✔ ✔
istar ✔ ✔ ✔
kstar ✔ ✔ ✔
Label ✔ ✔ ✔
localtriangle ✔ ✔ ✔ ✔ ✔
Log ✔ ✔ ✔
m2star ✔ ✔
meandeg ✔ ✔ ✔ ✔
mm ✔ ✔ ✔ ✔ ✔ ✔ ✔
mutual ✔ ✔ ✔ ✔
nearsimmelian ✔ ✔ ✔
nodecov ✔ ✔ ✔ ✔ ✔ ✔ ✔
nodecovar ✔ ✔
nodefactor ✔ ✔ ✔ ✔ ✔ ✔ ✔
nodeicov ✔ ✔ ✔ ✔ ✔
nodeicovar ✔ ✔
nodeifactor ✔ ✔ ✔ ✔ ✔ ✔
nodematch ✔ ✔ ✔ ✔ ✔ ✔ ✔
NodematchFilter ✔ ✔
nodemix ✔ ✔ ✔ ✔ ✔ ✔ ✔
nodeocov ✔ ✔ ✔ ✔ ✔
nodeocovar ✔ ✔
nodeofactor ✔ ✔ ✔ ✔ ✔
nsp ✔ ✔
odegrange ✔ ✔ ✔
odegree ✔ ✔ ✔ ✔
odegree1.5 ✔ ✔
Offset ✔ ✔
opentriad ✔ ✔ ✔
ostar ✔ ✔ ✔
Prod ✔ ✔ ✔
receiver ✔ ✔ ✔ ✔
S ✔ ✔
sender ✔ ✔ ✔ ✔
simmelian ✔ ✔ ✔
simmelianties ✔ ✔ ✔
smalldiff ✔ ✔ ✔ ✔ ✔
smallerthan ✔ ✔ ✔ ✔
sociality ✔ ✔ ✔ ✔ ✔
sum ✔ ✔ ✔
Sum ✔ ✔ ✔
Symmetrize ✔ ✔ ✔
threetrail ✔ ✔ ✔ ✔
transitive ✔ ✔ ✔
transitiveties ✔ ✔ ✔ ✔ ✔
transitiveweights ✔ ✔ ✔ ✔ ✔
triadcensus ✔ ✔ ✔ ✔
triangle ✔ ✔ ✔ ✔ ✔ ✔
tripercent ✔ ✔ ✔ ✔
ttriple ✔ ✔ ✔ ✔
twopath ✔ ✔ ✔

Terms by keywords

Jump to keyword: directed dyad-independent quantitative nodal attribute undirected binary valued categorical nodal attribute curved triad-related operator bipartite frequently-used nonnegative quantitative dyadic attribute categorical dyadic attribute

directed

absdiff absdiffcat asymmetric atleast atmost attrcov balance ctriple cycle cyclicalties cyclicalweights density diff dsp dyadcov edgecov edges equalto esp greaterthan gwdsp gwesp gwidegree gwnsp gwodegree hamming idegrange idegree idegree1.5 ininterval intransitive isolates istar localtriangle m2star meandeg mm mutual nearsimmelian nodecov nodecovar nodefactor nodeicov nodeicovar nodeifactor nodematch nodemix nodeocov nodeocovar nodeofactor nsp odegrange odegree odegree1.5 ostar receiver sender simmelian simmelianties smalldiff smallerthan sum Symmetrize threetrail transitive transitiveties transitiveweights triadcensus triangle ttriple twopath

dyad-independent

absdiff absdiffcat asymmetric atleast atmost attrcov b1cov b1factor b1nodematch b1sociality b2cov b2factor b2nodematch b2sociality density diff dyadcov edgecov edges equalto greaterthan hamming ininterval meandeg mm nodecov nodefactor nodeifactor nodematch nodemix nodeocov nodeofactor receiver sender smalldiff smallerthan sociality

quantitative nodal attribute

absdiff b1cov b2cov diff nodecov nodeicov nodeocov smalldiff

undirected

absdiff absdiffcat altkstar atleast atmost attrcov b1concurrent b1cov b1degrange b1degree b1dsp b1factor b1mindegree b1nodematch b1sociality b1star b1starmix b1twostar b2concurrent b2cov b2degrange b2degree b2dsp b2factor b2mindegree b2nodematch b2sociality b2star b2starmix b2twostar balance coincidence concurrent concurrentties cycle cyclicalties cyclicalweights degcor degcrossprod degrange degree degree1.5 density diff dyadcov edgecov edges equalto greaterthan gwb1degree gwb1dsp gwb2degree gwb2dsp gwdegree hamming ininterval isolatededges isolates kstar localtriangle meandeg mm nodecov nodefactor nodematch nodemix opentriad smalldiff smallerthan sociality sum threetrail transitiveties transitiveweights triadcensus triangle tripercent twopath

binary

absdiff absdiffcat altkstar asymmetric attrcov b1concurrent b1cov b1degrange b1degree b1dsp b1factor b1mindegree b1nodematch b1sociality b1star b1starmix b1twostar b2concurrent b2cov b2degrange b2degree b2dsp b2factor b2mindegree b2nodematch b2sociality b2star b2starmix b2twostar balance coincidence concurrent concurrentties ctriple Curve cycle cyclicalties degcor degcrossprod degrange degree degree1.5 density diff dsp dyadcov edgecov edges esp Exp F For gwb1degree gwb1dsp gwb2degree gwb2dsp gwdegree gwdsp gwesp gwidegree gwnsp gwodegree hamming idegrange idegree idegree1.5 intransitive isolatededges isolates istar kstar Label localtriangle Log m2star meandeg mm mutual nearsimmelian nodecov nodefactor nodeicov nodeifactor nodematch NodematchFilter nodemix nodeocov nodeofactor nsp odegrange odegree odegree1.5 Offset opentriad ostar Prod receiver S sender simmelian simmelianties smalldiff sociality Sum Symmetrize threetrail transitive transitiveties triadcensus triangle tripercent ttriple twopath

valued

absdiff absdiffcat atleast atmost B b1cov b1factor b1sociality b2cov b2factor b2sociality Curve cyclicalties cyclicalweights diff edgecov edges equalto Exp greaterthan ininterval Label Log mm mutual nodecov nodecovar nodefactor nodeicov nodeicovar nodeifactor nodematch nodemix nodeocov nodeocovar nodeofactor Prod receiver sender smallerthan sociality sum Sum transitiveweights

categorical nodal attribute

absdiffcat altkstar b1concurrent b1degree b1factor b1nodematch b1star b1starmix b1twostar b2degree b2factor b2nodematch b2star b2starmix b2twostar concurrent concurrentties ctriple degrange degree idegrange idegree istar kstar mm nodefactor nodeifactor nodematch nodemix nodeofactor odegrange odegree ostar sociality transitiveties triangle tripercent ttriple

curved

altkstar gwb1degree gwb1dsp gwb2degree gwb2dsp gwdegree gwidegree gwodegree

triad-related

asymmetric balance ctriple intransitive localtriangle nearsimmelian opentriad simmelian simmelianties threetrail transitive transitiveties transitiveweights triadcensus triangle tripercent ttriple

operator

B Curve Exp F For Label Log NodematchFilter Offset Prod S Sum Symmetrize

bipartite

b1concurrent b1cov b1degrange b1degree b1dsp b1factor b1mindegree b1nodematch b1sociality b1star b1starmix b1twostar b2concurrent b2cov b2degrange b2degree b2dsp b2factor b2mindegree b2nodematch b2sociality b2star b2starmix b2twostar coincidence diff gwb1degree gwb1dsp gwb2degree gwb2dsp isolatededges

frequently-used

b1cov b1degree b1factor b1nodematch b2concurrent b2cov b2degree b2factor b2nodematch degree diff edgecov gwdegree idegree isolates mm mutual nodecov nodefactor nodeicov nodeifactor nodematch nodemix odegree triangle

nonnegative

cyclicalweights transitiveweights

quantitative dyadic attribute

dyadcov edgecov

categorical dyadic attribute

localtriangle

References

  • Krivitsky P. N., Hunter D. R., Morris M., Klumb C. (2021). "ergm 4.0: New features and improvements." arXiv:2106.04997. https://arxiv.org/abs/2106.04997

  • Bomiriya, R. P, Bansal, S., and Hunter, D. R. (2014). Modeling Homophily in ERGMs for Bipartite Networks. Submitted.

  • Butts, CT. (2008). "A Relational Event Framework for Social Action." Sociological Methodology, 38(1).

  • Davis, J.A. and Leinhardt, S. (1972). The Structure of Positive Interpersonal Relations in Small Groups. In J. Berger (Ed.), Sociological Theories in Progress, Volume 2, 218–251. Boston: Houghton Mifflin.

  • Holland, P. W. and S. Leinhardt (1981). An exponential family of probability distributions for directed graphs. Journal of the American Statistical Association, 76: 33–50.

  • Hunter, D. R. and M. S. Handcock (2006). Inference in curved exponential family models for networks. Journal of Computational and Graphical Statistics, 15: 565–583.

  • Hunter, D. R. (2007). Curved exponential family models for social networks. Social Networks, 29: 216–230.

  • Krackhardt, D. and Handcock, M. S. (2007). Heider versus Simmel: Emergent Features in Dynamic Structures. Lecture Notes in Computer Science, 4503, 14–27.

  • Krivitsky P. N. (2012). Exponential-Family Random Graph Models for Valued Networks. Electronic Journal of Statistics, 2012, 6, 1100-1128. doi:10.1214/12-EJS696

  • Robins, G; Pattison, P; and Wang, P. (2009). "Closure, Connectivity, and Degree Distributions: Exponential Random Graph (p*) Models for Directed Social Networks." Social Networks, 31:105-117.

  • Snijders T. A. B., G. G. van de Bunt, and C. E. G. Steglich. Introduction to Stochastic Actor-Based Models for Network Dynamics. Social Networks, 2010, 32(1), 44-60. doi:10.1016/j.socnet.2009.02.004

  • Morris M, Handcock MS, and Hunter DR. Specification of Exponential-Family Random Graph Models: Terms and Computational Aspects. Journal of Statistical Software, 2008, 24(4), 1-24. doi:10.18637/jss.v024.i04

  • Snijders, T. A. B., P. E. Pattison, G. L. Robins, and M. S. Handcock (2006). New specifications for exponential random graph models, Sociological Methodology, 36(1): 99-153.

See Also

ergm package, search.ergmTerms, ergm, network, %v%, %n%

Examples

## Not run: 
ergm(flomarriage ~ kstar(1:2) + absdiff("wealth") + triangle)

ergm(molecule ~ edges + kstar(2:3) + triangle
                      + nodematch("atomic type",diff=TRUE)
                      + triangle + absdiff("atomic type"))

## End(Not run)

Directed edgewise shared partners

Description

This term adds one network statistic to the model for each element in d where the ii th such statistic equals the number of edges in the network with exactly d[i] shared partners.

Usage

# binary: desp(d, type="OTP")

# binary: esp(d, type="OTP")

Arguments

d

a vector of distinct integers
type

A string indicating the type of shared partner or path to be considered for directed networks: "OTP" (default for directed), "ITP", "RTP", "OSP", and "ISP"; has no effect for undirected. See the section below on Shared partner types for details.

Shared partner types

While there is only one shared partner configuration in the undirected case, nine distinct configurations are possible for directed graphs, selected using the type argument. Currently, terms may be defined with respect to five of these configurations; they are defined here as follows (using terminology from Butts (2008) and the relevent package):

  • Outgoing Two-path ("OTP"): vertex kk is an OTP shared partner of ordered pair (i,j)(i,j) iff i→k→ji \to k \to j. Also known as "transitive shared partner".

  • Incoming Two-path ("ITP"): vertex kk is an ITP shared partner of ordered pair (i,j)(i,j) iff j→k→ij \to k \to i. Also known as "cyclical shared partner"

  • Reciprocated Two-path ("RTP"): vertex kk is an RTP shared partner of ordered pair (i,j)(i,j) iff i↔k↔ji \leftrightarrow k \leftrightarrow j.

  • Outgoing Shared Partner ("OSP"): vertex kk is an OSP shared partner of ordered pair (i,j)(i,j) iff i→k,j→ki \to k, j \to k.

  • Incoming Shared Partner ("ISP"): vertex kk is an ISP shared partner of ordered pair (i,j)(i,j) iff k→i,k→jk \to i, k \to j.

By default, outgoing two-paths ("OTP") are calculated. Note that Robins et al. (2009) define closely related statistics to several of the above, using slightly different terminology.

Note

This term takes an additional term option (see options?ergm), cache.sp, controlling whether the implementation will cache the number of shared partners for each dyad in the network; this is usually enabled by default.

This term can only be used with directed networks.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

directed, binary

Exponentiate a network's statistic

Description

Evaluate the terms specified in formula and exponentiates them with base ee .

Usage

# binary: Exp(formula)

# valued: Exp(formula)

Arguments

formula

a one-sided ergm()-style formula with the terms to be evaluated

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

operator, binary, valued

Filtering on arbitrary one-term model

Description

Evaluates the given formula on a network constructed by taking yy and removing any edges for which fi,j(yi,j)=0f_{i,j}(y_{i,j}) = 0 .

Usage

# binary: F(formula, filter)

Arguments

formula

a one-sided ergm()-style formula with the terms to be evaluated
filter

must contain one binary ergm term, with the following properties:

  • dyadic independence;

  • dyadwise contribution of 0 for a 0-valued dyad.

Formally, this means that it is expressable as

g(y)=∑i,jfi,j(yi,j),g(y) = \sum_{i,j} f_{i,j}(y_{i,j}),

where for all ii, jj, and yy, fi,j(yi,j)f_{i,j}(y_{i,j}) for which fi,j(0)=0f_{i,j}(0)=0. For convenience, the term in specified can be a part of a simple logical or comparison operation: (e.g., ~!nodematch("A") or ~abs("X")>3), which filters on fi,j(yi,j)◯0f_{i,j}(y_{i,j}) \bigcirc 0 instead.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

operator, binary

Faux desert High School as a network object

Description

This data set represents a simulation of a directed in-school friendship network. The network is named faux.desert.high.

Usage

data(faux.desert.high)

Format

faux.desert.high is a network object with 107 vertices (students, in this case) and 439 directed edges (friendship nominations). To obtain additional summary information about it, type summary(faux.desert.high).

The vertex attributes are Grade, Sex, and Race. The Grade attribute has values 7 through 12, indicating each student's grade in school. The Race attribute is based on the answers to two questions, one on Hispanic identity and one on race, and takes six possible values: White (non-Hisp.), Black (non-Hisp.), Hispanic, Asian (non-Hisp.), Native American, and Other (non-Hisp.)

Licenses and Citation

If the source of the data set does not specified otherwise, this data set is protected by the Creative Commons License https://creativecommons.org/licenses/by-nc-nd/2.5/.

When publishing results obtained using this data set, the original authors (Resnick et al, 1997) should be cited. In addition this package should be cited as:

Mark S. Handcock, David R. Hunter, Carter T. Butts, Steven M. Goodreau, and Martina Morris. 2003 statnet: Software tools for the Statistical Modeling of Network Data
https://statnet.org.

Source

The data set is simulation based upon an ergm model fit to data from one school community from the AddHealth Study, Wave I (Resnick et al., 1997). It was constructed as follows:

The school in question (a single school with 7th through 12th grades) was selected from the Add Health "structure files." Documentation on these files can be found here: https://addhealth.cpc.unc.edu/documentation/codebooks/.

The stucture file contains directed out-ties representing each instance of a student who named another student as a friend. Students could nominate up to 5 male and 5 female friends. Note that registered students who did not take the AddHealth survey or who were not listed by name on the schools' student roster are not included in the stucture files. In addition, we removed any students with missing values for race, grade or sex.

The following ergm() specification was fit to the original data (with code updated for modern syntax): 

 desert.fit <- ergm(original.net ~ edges + mutual +
absdiff("grade") + nodefactor("race", base=5) + nodefactor("grade", base=3)
+ nodefactor("sex") + nodematch("race", diff = TRUE) + nodematch("grade",
diff = TRUE) + nodematch("sex", diff = FALSE) + idegree(0:1) + odegree(0:1)
+ gwesp(0.1,fixed=T), constraints = ~bd(maxout=10), control =
control.ergm(MCMLE.steplength = .25, MCMC.burnin = 100000, MCMC.interval =
10000, MCMC.samplesize = 2500, MCMLE.maxit = 100), verbose=T)

Then the faux.desert.high dataset was created by simulating a single network from the above model fit: 

 faux.desert.high <- simulate(desert.fit, nsim=1,
                 control=snctrl(MCMC.burnin=1e+8),
                 constraints = ~edges)

References

Resnick M.D., Bearman, P.S., Blum R.W. et al. (1997). Protecting adolescents from harm. Findings from the National Longitudinal Study on Adolescent Health, Journal of the American Medical Association, 278: 823-32.

See Also

network, plot.network(), ergm(), faux.desert.high, faux.mesa.high, faux.magnolia.high

Faux dixon High School as a network object

Description

This data set represents a simulation of a directed in-school friendship network. The network is named faux.dixon.high.

Usage

data(faux.dixon.high)

Format

faux.dixon.high is a network object with 248 vertices (students, in this case) and 1197 directed edges (friendship nominations). To obtain additional summary information about it, type summary(faux.dixon.high).

The vertex attributes are Grade, Sex, and Race. The Grade attribute has values 7 through 12, indicating each student's grade in school. The Race attribute is based on the answers to two questions, one on Hispanic identity and one on race, and takes six possible values: White (non-Hisp.), Black (non-Hisp.), Hispanic, Asian (non-Hisp.), Native American, and Other (non-Hisp.)

Licenses and Citation

If the source of the data set does not specified otherwise, this data set is protected by the Creative Commons License https://creativecommons.org/licenses/by-nc-nd/2.5/.

When publishing results obtained using this data set, the original authors (Resnick et al, 1997) should be cited. In addition this package should be cited as:

Mark S. Handcock, David R. Hunter, Carter T. Butts, Steven M. Goodreau, and Martina Morris. 2003 statnet: Software tools for the Statistical Modeling of Network Data
https://statnet.org.

Source

The data set is simulation based upon an ergm model fit to data from one school community from the AddHealth Study, Wave I (Resnick et al., 1997). It was constructed as follows:

The school in question (a single school with 7th through 12th grades) was selected from the Add Health "structure files." Documentation on these files can be found here: https://addhealth.cpc.unc.edu/documentation/codebooks/.

The stucture file contains directed out-ties representing each instance of a student who named another student as a friend. Students could nominate up to 5 male and 5 female friends. Note that registered students who did not take the AddHealth survey or who were not listed by name on the schools' student roster are not included in the stucture files. In addition, we removed any students with missing values for race, grade or sex.

The following ergm() specification was fit to the original data (with code updated for modern syntax): 

 dixon.fit <- ergm(original.net ~ edges + mutual +
absdiff("grade") + nodefactor("race", base=5) + nodefactor("grade", base=3)
+ nodefactor("sex") + nodematch("race", diff = TRUE) + nodematch("grade",
diff = TRUE) + nodematch("sex", diff = FALSE) + idegree(0:1) + odegree(0:1)
+ gwesp(0.1,fixed=T), constraints = ~bd(maxout=10), control =
control.ergm(MCMLE.steplength = .25, MCMC.burnin = 100000, MCMC.interval =
10000, MCMC.samplesize = 2500, MCMLE.maxit = 100), verbose=T)

Then the faux.dixon.high dataset was created by simulating a single network from the above model fit: 

 faux.dixon.high <- simulate(dixon.fit, nsim=1, burnin=1e+8,
constraint = "edges")

References

Resnick M.D., Bearman, P.S., Blum R.W. et al. (1997). Protecting adolescents from harm. Findings from the National Longitudinal Study on Adolescent Health, Journal of the American Medical Association, 278: 823-32.

See Also

network, plot.network(), ergm(), faux.desert.high, faux.mesa.high, faux.magnolia.high

Goodreau's Faux Magnolia High School as a network object

Description

This data set represents a simulation of an in-school friendship network. The network is named faux.magnolia.high because the school commnunities on which it is based are large and located in the southern US.

Usage

data(faux.magnolia.high)

Format

faux.magnolia.high is a network object with 1461 vertices (students, in this case) and 974 undirected edges (mutual friendships). To obtain additional summary information about it, type summary(faux.magnolia.high).

The vertex attributes are Grade, Sex, and Race. The Grade attribute has values 7 through 12, indicating each student's grade in school. The Race attribute is based on the answers to two questions, one on Hispanic identity and one on race, and takes six possible values: White (non-Hisp.), Black (non-Hisp.), Hispanic, Asian (non-Hisp.), Native American, and Other (non-Hisp.)

Licenses and Citation

If the source of the data set does not specified otherwise, this data set is protected by the Creative Commons License https://creativecommons.org/licenses/by-nc-nd/2.5/.

When publishing results obtained using this data set, the original authors (Resnick et al, 1997) should be cited. In addition this package should be cited as:

Mark S. Handcock, David R. Hunter, Carter T. Butts, Steven M. Goodreau, and Martina Morris. 2003 statnet: Software tools for the Statistical Modeling of Network Data
https://statnet.org.

Source

The data set is based upon a model fit to data from two school communities from the AddHealth Study, Wave I (Resnick et al., 1997). It was constructed as follows:

The two schools in question (a junior and senior high school in the same community) were combined into a single network dataset. Students who did not take the AddHealth survey or who were not listed on the schools' student rosters were eliminated, then an undirected link was established between any two individuals who both named each other as a friend. All missing race, grade, and sex values were replaced by a random draw with weights determined by the size of the attribute classes in the school.

The following ergm() specification was fit to the original data: 

 magnolia.fit <- ergm (magnolia ~ edges +
nodematch("Grade",diff=T) + nodematch("Race",diff=T) +
nodematch("Sex",diff=F) + absdiff("Grade") + gwesp(0.25,fixed=T),
control=control.ergm(MCMC.burnin=10000, MCMC.interval=1000, MCMLE.maxit=25,
                     MCMC.samplesize=2500, MCMLE.steplength=0.25))

Then the faux.magnolia.high dataset was created by simulating a single network from the above model fit: 

 faux.magnolia.high <- simulate (magnolia.fit, nsim=1,
                 control = snctrl(MCMC.burnin=100000000), constraints = ~edges)

References

Resnick M.D., Bearman, P.S., Blum R.W. et al. (1997). Protecting adolescents from harm. Findings from the National Longitudinal Study on Adolescent Health, Journal of the American Medical Association, 278: 823-32.

See Also

network, plot.network(), ergm(), faux.mesa.high

Goodreau's Faux Mesa High School as a network object

Description

This data set (formerly called “fauxhigh”) represents a simulation of an in-school friendship network. The network is named faux.mesa.high because the school commnunity on which it is based is in the rural western US, with a student body that is largely Hispanic and Native American.

Usage

data(faux.mesa.high)

Format

faux.mesa.high is a network object with 205 vertices (students, in this case) and 203 undirected edges (mutual friendships). To obtain additional summary information about it, type summary(faux.mesa.high).

The vertex attributes are Grade, Sex, and Race. The Grade attribute has values 7 through 12, indicating each student's grade in school. The Race attribute is based on the answers to two questions, one on Hispanic identity and one on race, and takes six possible values: White (non-Hisp.), Black (non-Hisp.), Hispanic, Asian (non-Hisp.), Native American, and Other (non-Hisp.)

Licenses and Citation

If the source of the data set does not specified otherwise, this data set is protected by the Creative Commons License https://creativecommons.org/licenses/by-nc-nd/2.5/.

When publishing results obtained using this data set, the original authors (Resnick et al, 1997) should be cited. In addition this package should be cited as:

Mark S. Handcock, David R. Hunter, Carter T. Butts, Steven M. Goodreau, and Martina Morris. 2003 statnet: Software tools for the Statistical Modeling of Network Data
https://statnet.org.

Source

The data set is based upon a model fit to data from one school community from the AddHealth Study, Wave I (Resnick et al., 1997). It was constructed as follows:

A vector representing the sex of each student in the school was randomly re-ordered. The same was done with the students' response to questions on race and grade. These three attribute vectors were permuted independently. Missing values for each were randomly assigned with weights determined by the size of the attribute classes in the school.

The following ergm() specification was used to fit a model to the original data: 

 ~ edges + nodefactor("Grade") + nodefactor("Race") +
nodefactor("Sex") + nodematch("Grade",diff=TRUE) +
nodematch("Race",diff=TRUE) + nodematch("Sex",diff=FALSE) +
gwdegree(1.0,fixed=TRUE) + gwesp(1.0,fixed=TRUE) + gwdsp(1.0,fixed=TRUE)

The resulting model fit was then applied to a network with actors possessing the permuted attributes and with the same number of edges as in the original data.

The processes for handling missing data and defining the race attribute are described in Hunter, Goodreau & Handcock (2008).

References

Hunter D.R., Goodreau S.M. and Handcock M.S. (2008). Goodness of Fit of Social Network Models, Journal of the American Statistical Association.

Resnick M.D., Bearman, P.S., Blum R.W. et al. (1997). Protecting adolescents from harm. Findings from the National Longitudinal Study on Adolescent Health, Journal of the American Medical Association, 278: 823-32.

See Also

network, plot.network(), ergm(), faux.magnolia.high

Convert a curved ERGM into a corresponding "fixed" ERGM.

Description

The generic fix.curved converts an ergm object or formula of a model with curved terms to the variant in which the curved parameters are fixed. Note that each term has to be treated as a special case.

Usage

fix.curved(object, ...)

## S3 method for class 'ergm'
fix.curved(object, ...)

## S3 method for class 'formula'
fix.curved(object, theta, ...)

Arguments

object

An ergm object or an ERGM formula. The curved terms of the given formula (or the formula used in the fit) must have all of their arguments passed by name.
...

Unused at this time.
theta

Curved model parameter configuration.

Details

Some ERGM terms such as gwesp and gwdegree have two forms: a curved form, for which their decay or similar parameters are to be estimated, and whose canonical statistics is a vector of the term's components (esp(1), esp(2), ... and degree(1), degree(2), ..., respectively) and a "fixed" form where the decay or similar parameters are fixed, and whose canonical statistic is just the term itself. It is often desirable to fit a model estimating the curved parameters but simulate the "fixed" statistic.

This function thus takes in a fit or a formula and performs this mapping, returning a "fixed" model and parameter specification. It only works for curved ERGM terms included with the ergm package. It does not work with curved terms not included in ergm.

Value

A list with the following components:

formula

The "fixed" formula.
theta

The "fixed" parameter vector.

See Also

ergm(), simulate.ergm()

Examples

data(sampson)
gest<-ergm(samplike~edges+gwesp(),
           control=control.ergm(MCMLE.maxit=2))
summary(gest)
# A statistic for esp(1),...,esp(16)
simulate(gest,output="stats")

tmp<-fix.curved(gest)
tmp
# A gwesp() statistic only
simulate(tmp$formula, coef=tmp$theta, output="stats")

Preserve the dyad status in all but the given edges

Description

Preserve the dyad status in all but free.dyads.

Usage

# fixallbut(free.dyads)

Arguments

free.dyads

edgelist or network. Networks will be converted to the corresponding edgelist.

See Also

ergmConstraint for index of constraints and hints currently visible to the package.

Keywords

directed, dyad-independent, undirected

Fix specific dyads

Description

Fix the dyads in fixed.dyads at their current value, preserve the edges in present, and preclude the edges in absent.

Usage

# fixedas(fixed.dyads, present, absent)

Arguments

fixed.dyads, present, absent

a two-column edge list or a network

Details

present and absent differ from fixed.dyads in that they check that the specified edges are in fact present and/or absent and stop with an error if not.

See Also

ergmConstraint for index of constraints and hints currently visible to the package.

Keywords

directed, dyad-independent, undirected

Florentine Family Marriage and Business Ties Data as a "network" object

Description

This is a data set of marriage and business ties among Renaissance Florentine families. The data is originally from Padgett (1994) via UCINET and stored as a network object.

Usage

data(florentine)

Details

Breiger & Pattison (1986), in their discussion of local role analysis, use a subset of data on the social relations among Renaissance Florentine families (person aggregates) collected by John Padgett from historical documents. The two relations are business ties (flobusiness - specifically, recorded financial ties such as loans, credits and joint partnerships) and marriage alliances (flomarriage).

As Breiger & Pattison point out, the original data are symmetrically coded. This is acceptable perhaps for marital ties, but is unfortunate for the financial ties (which are almost certainly directed). To remedy this, the financial ties can be recoded as directed relations using some external measure of power - for instance, a measure of wealth. Both graphs provide vertex information on (1) wealth each family's net wealth in 1427 (in thousands of lira); (2) priorates the number of priorates (seats on the civic council) held between 1282- 1344; and (3) totalties the total number of business or marriage ties in the total dataset of 116 families (see Breiger & Pattison (1986), p 239).

Substantively, the data include families who were locked in a struggle for political control of the city of Florence around 1430. Two factions were dominant in this struggle: one revolved around the infamous Medicis (9), the other around the powerful Strozzis (15).

Source

Padgett, John F. 1994. Marriage and Elite Structure in Renaissance Florence, 1282-1500. Paper delivered to the Social Science History Association.

References

Wasserman, S. and Faust, K. (1994) Social Network Analysis: Methods and Applications, Cambridge University Press, Cambridge, England.

Breiger R. and Pattison P. (1986). Cumulated social roles: The duality of persons and their algebras, Social Networks, 8, 215-256.

See Also

flo, network, plot.network, ergm

A for operator for terms

Description

This operator evaluates the formula given to it, substituting the specified loop counter variable with each element in a sequence.

Usage

# binary: For(...)

Arguments

...

in any order,

  • one unnamed one-sided ergm()-style formula with the terms to be evaluated, containing one or more placeholders VAR and

  • one or more named expressions of the form VAR = SEQ specifying the placeholder and its range. See Details below.

Details

Placeholders are specified in the style of foreach::foreach(), as VAR = SEQ. VAR can be any valid R variable name, and SEQ can be a vector, a list, a function of one argument, or a one-sided formula. The vector or list will be used directly, whereas a function will be called with the network as its argument to produce the list, and the formula will be used analogously to purrr::as_mapper(), its RHS evaluated in an environment in which the network itself will be accessible as . or .nw.

If more than one named expression is given, they will be expanded as one would expect in a nested for loop: earlier expressions will form the outer loops and later expressions the inner loops.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

operator, binary

Examples

#
# The following are equivalent ways to compute differential
# homophily.
#

data(sampson)
(groups <- sort(unique(samplike%v%"group"))) # Sorted list of groups.

# The "normal" way:
summary(samplike ~ nodematch("group", diff=TRUE))

# One element at a time, specifying a list:
summary(samplike ~ For(~nodematch("group", levels=., diff=TRUE),
                       . = groups))

# One element at a time, specifying a function that returns a list:
summary(samplike ~ For(~nodematch("group", levels=., diff=TRUE),
                       . = function(nw) sort(unique(nw%v%"group"))))

# One element at a time, specifying a formula whose RHS expression
# returns a list:
summary(samplike ~ For(~nodematch("group", levels=., diff=TRUE),
                       . = ~sort(unique(.%v%"group"))))

#
# Multiple iterators are possible, in any order. Here, absdiff() is
# being computed for each combination of attribute and power.
#

data(florentine)

# The "normal" way:
summary(flomarriage ~ absdiff("wealth", pow=1) + absdiff("priorates", pow=1) +
                      absdiff("wealth", pow=2) + absdiff("priorates", pow=2) +
                      absdiff("wealth", pow=3) + absdiff("priorates", pow=3))

# With a loop; note that the attribute (a) is being iterated within
# power (.):
summary(flomarriage ~ For(. = 1:3, a = c("wealth", "priorates"), ~absdiff(a, pow=.)))

Goodreau's four node network as a "network" object

Description

This is an example thought of by Steve Goodreau. It is a directed network of four nodes and five ties stored as a network object.

Usage

data(g4)

Details

It is interesting because the maximum likelihood estimator of the model with out degree 3 in it exists, but the maximum psuedolikelihood estimator does not.

Source

Steve Goodreau

See Also

florentine, network, plot.network, ergm

Examples

data(g4)
summary(ergm(g4 ~ odegree(3), estimate="MPLE"))
summary(ergm(g4 ~ odegree(3), control=control.ergm(init=0)))

Multivariate version of coda's coda::geweke.diag().

Description

Rather than comparing each mean independently, compares them jointly. Note that it returns an htest object, not a geweke.diag object.

Usage

geweke.diag.mv(x, frac1 = 0.1, frac2 = 0.5, split.mcmc.list = FALSE, ...)

Arguments

x

an mcmc, mcmc.list, or just a matrix with observations in rows and variables in columns.
frac1, frac2

the fraction at the start and, respectively, at the end of the sample to compare.
split.mcmc.list

when given an mcmc.list, whether to test each chain individually.
...

additional arguments, passed on to approx.hotelling.diff.test(), which passes them to spectrum0.mvar(), etc.; in particular, ⁠order.max=⁠ can be used to limit the order of the AR model used to estimate the effective sample size.

Value

An object of class htest, inheriting from that returned by approx.hotelling.diff.test(), but with p-value considered to be 0 on insufficient sample size.

Note

If approx.hotelling.diff.test() returns an error, then assume that burn-in is insufficient.

See Also

coda::geweke.diag(), approx.hotelling.diff.test()

Conduct Goodness-of-Fit Diagnostics on a Exponential Family Random Graph Model

Description

gof() calculates pp-values for geodesic distance, degree, and reachability summaries to diagnose the goodness-of-fit of exponential family random graph models. See ergm() for more information on these models.

Usage

gof(object, ...)

## S3 method for class 'ergm'
gof(
  object,
  ...,
  coef = coefficients(object),
  GOF = NULL,
  constraints = object$constraints,
  control = control.gof.ergm(),
  verbose = FALSE
)

## S3 method for class 'formula'
gof(
  object,
  ...,
  coef = NULL,
  GOF = NULL,
  constraints = ~.,
  basis = eval_lhs.formula(object),
  control = NULL,
  unconditional = TRUE,
  verbose = FALSE
)

## S3 method for class 'gof'
print(x, ...)

## S3 method for class 'gof'
plot(
  x,
  ...,
  cex.axis = 0.7,
  plotlogodds = FALSE,
  main = "Goodness-of-fit diagnostics",
  normalize.reachability = FALSE,
  verbose = FALSE
)

Arguments

object

Either a formula or an ergm object. See documentation for ergm().
...

Additional arguments, to be passed to lower-level functions.
coef

When given either a formula or an object of class ergm, coef are the parameters from which the sample is drawn. By default set to a vector of 0.
GOF

formula; an formula object, of the form ~ <model terms> specifying the statistics to use to diagnosis the goodness-of-fit of the model. They do not need to be in the model formula specified in formula, and typically are not. Currently supported terms are the degree distribution (“degree” for undirected graphs, “idegree” and/or “odegree” for directed graphs, and “b1degree” and “b2degree” for bipartite undirected graphs), geodesic distances (“distance”), shared partner distributions (“espartners” and “dspartners”), the triad census (“triadcensus”), and the terms of the original model (“model”). The default formula for undirected networks is ~ degree + espartners + distance + model, and the default formula for directed networks is ~ idegree + odegree + espartners + distance + model. By default a “model” term is added to the formula. It is a very useful overall validity check and a reminder of the statistical variation in the estimates of the mean value parameters. To omit the “model” term, add “- model” to the formula.
constraints

A one-sided formula specifying one or more constraints on the support of the distribution of the networks being modeled. See the help for similarly-named argument in ergm() for more information. For gof.formula, defaults to unconstrained. For gof.ergm, defaults to the constraints with which object was fitted.
control

A list of control parameters for algorithm tuning, typically constructed with control.gof.formula() or control.gof.ergm(), which have different defaults. Their documentation gives the the list of recognized control parameters and their meaning. The more generic utility snctrl() (StatNet ConTRoL) also provides argument completion for the available control functions and limited argument name checking.
verbose

A logical or an integer to control the amount of progress and diagnostic information to be printed. FALSE/0 produces minimal output, with higher values producing more detail. Note that very high values (5+) may significantly slow down processing.
basis

a value (usually a network) to override the LHS of the formula.
unconditional

logical; if TRUE, the simulation is unconditional on the observed dyads. if not TRUE, the simulation is conditional on the observed dyads. This is primarily used internally when the network has missing data and a conditional GoF is produced.
x

an object of class gof for printing or plotting.
cex.axis

Character expansion of the axis labels relative to that for the plot.
plotlogodds

Plot the odds of a dyad having given characteristics (e.g., reachability, minimum geodesic distance, shared partners). This is an alternative to the probability of a dyad having the same property.
main

Title for the goodness-of-fit plots.
normalize.reachability

Should the reachability proportion be normalized to make it more comparable with the other geodesic distance proportions.

Details

A sample of graphs is randomly drawn from the specified model. The first argument is typically the output of a call to ergm() and the model used for that call is the one fit.

For GOF = ~model, the model's observed sufficient statistics are plotted as quantiles of the simulated sample. In a good fit, the observed statistics should be near the sample median (0.5).

By default, the sample consists of 100 simulated networks, but this sample size (and many other settings) can be changed using the control argument described above.

Value

gof(), gof.ergm(), and gof.formula() return an object of class gof.ergm, which inherits from class gof. This is a list of the tables of statistics and pp-values. This is typically plotted using plot.gof().

Methods (by class)

  • gof(ergm): Perform simulation to evaluate goodness-of-fit for a specific ergm() fit.

  • gof(formula): Perform simulation to evaluate goodness-of-fit for a model configuration specified by a formula, coefficient, constraints, and other settings.

Methods (by generic)

  • print(gof): print.gof() summaries the diagnostics such as the degree distribution, geodesic distances, shared partner distributions, and reachability for the goodness-of-fit of exponential family random graph models. (summary.gof is a deprecated alias that may be repurposed in the future.)

  • plot(gof): plot.gof() plots diagnostics such as the degree distribution, geodesic distances, shared partner distributions, and reachability for the goodness-of-fit of exponential family random graph models.

Note

For gof.ergm and gof.formula, default behavior depends on the directedness of the network involved; if undirected then degree, espartners, and distance are used as default properties to examine. If the network in question is directed, “degree” in the above is replaced by idegree and odegree.

See Also

ergm(), network(), simulate.ergm(), summary.ergm()

Examples

data(florentine)
gest <- ergm(flomarriage ~ edges + kstar(2))
gest
summary(gest)

# test the gof.ergm function
gofflo <- gof(gest)
gofflo

# Plot all three on the same page
# with nice margins
par(mfrow=c(1,3))
par(oma=c(0.5,2,1,0.5))
plot(gofflo)

# And now the log-odds
plot(gofflo, plotlogodds=TRUE)

# Use the formula version of gof
gofflo2 <-gof(flomarriage ~ edges + kstar(2), coef=c(-1.6339, 0.0049))
plot(gofflo2)

Number of dyads with values strictly greater than a threshold

Description

Adds the number of statistics equal to the length of threshold equaling to the number of dyads whose values exceed the corresponding element of threshold .

Usage

# valued: greaterthan(threshold=0)

Arguments

threshold

a vector of numerical values

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

directed, dyad-independent, undirected, valued

Geometrically weighted degree distribution for the first mode in a bipartite network

Description

This term adds one network statistic to the model equal to the weighted degree distribution with decay controlled by the decay parameter, which should be non-negative, for nodes in the first mode of a bipartite network. The first mode of a bipartite network object is sometimes known as the "actor" mode.

This term can only be used with undirected bipartite networks.

Usage

# binary: gwb1degree(decay, fixed=FALSE, attr=NULL, cutoff=30, levels=NULL)

Arguments

decay

nonnegative decay parameter for the first mode degree frequencies; required if fixed=TRUE and ignored with a warning otherwise.
fixed

optional argument indicating whether the decay parameter is fixed at the given value, or is to be fit as a curved exponential-family model (see Hunter and Handcock, 2006). The default is FALSE , which means the scale parameter is not fixed and thus the model is a curved exponential family.
attr

a vertex attribute specification (see Specifying Vertex attributes and Levels (?nodal_attributes) for details.)
cutoff

This optional argument sets the number of underlying degree terms to use in computing the statistics when fixed=FALSE, in order to reduce the computational burden. Its default value can also be controlled by the gw.cutoff term option control parameter. (See ?control.ergm.)
levels

TODO (See Specifying Vertex attributes and Levels (?nodal_attributes) for details.)

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

bipartite, curved, undirected, binary

Geometrically weighted dyadwise shared partner distribution for dyads in the first bipartition

Description

This term adds one network statistic to the model equal to the geometrically weighted dyadwise shared partner distribution for dyads in the first bipartition with decay parameter decay parameter, which should be non-negative. This term can only be used with bipartite networks.

Usage

# binary: gwb1dsp(decay=0, fixed=FALSE, cutoff=30)

Arguments

decay

nonnegative decay parameter for the shared partner counts; required if fixed=TRUE and ignored with a warning otherwise.
fixed

optional argument indicating whether the decay parameter is fixed at the given value, or is to be fit as a curved exponential-family model (see Hunter and Handcock, 2006). The default is FALSE , which means the scale parameter is not fixed and thus the model is a curved exponential family.
cutoff

This optional argument sets the number of underlying b1dsp terms to use in computing the statistics when fixed=FALSE, in order to reduce the computational burden. Its default value can also be controlled by the gw.cutoff term option control parameter. (See ?control.ergm.)

Note

This term takes an additional term option (see options?ergm), cache.sp, controlling whether the implementation will cache the number of shared partners for each dyad in the network; this is usually enabled by default.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

bipartite, curved, undirected, binary

Geometrically weighted degree distribution for the second mode in a bipartite network

Description

This term adds one network statistic to the model equal to the weighted degree distribution with decay controlled by the which should be non-negative, for nodes in the second mode of a bipartite network. The second mode of a bipartite network object is sometimes known as the "event" mode.

Usage

# binary: gwb2degree(decay, fixed=FALSE, attr=NULL, cutoff=30, levels=NULL)

Arguments

decay

nonnegative decay parameter for the second mode degree frequencies; required if fixed=TRUE and ignored with a warning otherwise.
fixed

optional argument indicating whether the decay parameter is fixed at the given value, or is to be fit as a curved exponential-family model (see Hunter and Handcock, 2006). The default is FALSE , which means the scale parameter is not fixed and thus the model is a curved exponential family.
attr

a vertex attribute specification (see Specifying Vertex attributes and Levels (?nodal_attributes) for details.)
cutoff

This optional argument sets the number of underlying degree terms to use in computing the statistics when fixed=FALSE, in order to reduce the computational burden. Its default value can also be controlled by the gw.cutoff term option control parameter. (See ?control.ergm.)
levels

TODO (See Specifying Vertex attributes and Levels (?nodal_attributes) for details.)

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

bipartite, curved, undirected, binary

Geometrically weighted dyadwise shared partner distribution for dyads in the second bipartition

Description

This term adds one network statistic to the model equal to the geometrically weighted dyadwise shared partner distribution for dyads in the second bipartition with decay parameter decay parameter, which should be non-negative. This term can only be used with bipartite networks.

Usage

# binary: gwb2dsp(decay=0, fixed=FALSE, cutoff=30)

Arguments

decay

nonnegative decay parameter for the shared partner counts; required if fixed=TRUE and ignored with a warning otherwise.
fixed

optional argument indicating whether the decay parameter is fixed at the given value, or is to be fit as a curved exponential-family model (see Hunter and Handcock, 2006). The default is FALSE , which means the scale parameter is not fixed and thus the model is a curved exponential family.
cutoff

This optional argument sets the number of underlying b2dsp terms to use in computing the statistics when fixed=FALSE, in order to reduce the computational burden. Its default value can also be controlled by the gw.cutoff term option control parameter. (See ?control.ergm.)

Note

This term takes an additional term option (see options?ergm), cache.sp, controlling whether the implementation will cache the number of shared partners for each dyad in the network; this is usually enabled by default.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

bipartite, curved, undirected, binary

Geometrically weighted degree distribution

Description

This term adds one network statistic to the model equal to the weighted degree distribution with decay controlled by the decay parameter, which should be non-negative.

Usage

# binary: gwdegree(decay, fixed=FALSE, attr=NULL, cutoff=30, levels=NULL)

Arguments

decay

nonnegative decay parameter for the degree frequencies; required if fixed=TRUE and ignored with a warning otherwise.
fixed

optional argument indicating whether the decay parameter is fixed at the given value, or is to be fit as a curved exponential-family model (see Hunter and Handcock, 2006). The default is FALSE , which means the scale parameter is not fixed and thus the model is a curved exponential family.
attr

a vertex attribute specification (see Specifying Vertex attributes and Levels (?nodal_attributes) for details.)
cutoff

This optional argument sets the number of underlying degree terms to use in computing the statistics when fixed=FALSE, in order to reduce the computational burden. Its default value can also be controlled by the gw.cutoff term option control parameter. (See ?control.ergm.)
levels

TODO (See Specifying Vertex attributes and Levels (?nodal_attributes) for details.)

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

curved, frequently-used, undirected, binary

Geometrically weighted dyadwise shared partner distribution

Description

This term adds one network statistic to the model equal to the geometrically weighted dyadwise shared partner distribution with decay parameter decay parameter.

Usage

# binary: dgwdsp(decay, fixed=FALSE, cutoff=30, type="OTP")

# binary: gwdsp(decay, fixed=FALSE, cutoff=30, type="OTP")

Arguments

decay

nonnegative decay parameter for the shared partner or selected directed analogue count; required if fixed=TRUE and ignored with a warning otherwise.
fixed

optional argument indicating whether the decay parameter is fixed at the given value, or is to be fit as a curved exponential-family model (see Hunter and Handcock, 2006). The default is FALSE , which means the scale parameter is not fixed and thus the model is a curved exponential family.
cutoff

This optional argument sets the number of underlying DSP terms to use in computing the statistics when fixed=FALSE, in order to reduce the computational burden. Its default value can also be controlled by the gw.cutoff term option control parameter. (See ?control.ergm.)
type

A string indicating the type of shared partner or path to be considered for directed networks: "OTP" (default for directed), "ITP", "RTP", "OSP", and "ISP"; has no effect for undirected. See the section below on Shared partner types for details.

Shared partner types

While there is only one shared partner configuration in the undirected case, nine distinct configurations are possible for directed graphs, selected using the type argument. Currently, terms may be defined with respect to five of these configurations; they are defined here as follows (using terminology from Butts (2008) and the relevent package):

  • Outgoing Two-path ("OTP"): vertex kk is an OTP shared partner of ordered pair (i,j)(i,j) iff i→k→ji \to k \to j. Also known as "transitive shared partner".

  • Incoming Two-path ("ITP"): vertex kk is an ITP shared partner of ordered pair (i,j)(i,j) iff j→k→ij \to k \to i. Also known as "cyclical shared partner"

  • Reciprocated Two-path ("RTP"): vertex kk is an RTP shared partner of ordered pair (i,j)(i,j) iff i↔k↔ji \leftrightarrow k \leftrightarrow j.

  • Outgoing Shared Partner ("OSP"): vertex kk is an OSP shared partner of ordered pair (i,j)(i,j) iff i→k,j→ki \to k, j \to k.

  • Incoming Shared Partner ("ISP"): vertex kk is an ISP shared partner of ordered pair (i,j)(i,j) iff k→i,k→jk \to i, k \to j.

By default, outgoing two-paths ("OTP") are calculated. Note that Robins et al. (2009) define closely related statistics to several of the above, using slightly different terminology.

Note

This term takes an additional term option (see options?ergm), cache.sp, controlling whether the implementation will cache the number of shared partners for each dyad in the network; this is usually enabled by default.

The GWDSP statistic is equal to the sum of GWNSP plus GWESP.

The decay parameter was called alpha prior to ergm 3.7.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

directed, binary

Geometrically weighted edgewise shared partner distribution

Description

This term adds a statistic equal to the geometrically weighted edgewise (not dyadwise) shared partner distribution with decay parameter decay parameter.

Usage

# binary: dgwesp(decay, fixed=FALSE, cutoff=30, type="OTP")

# binary: gwesp(decay, fixed=FALSE, cutoff=30, type="OTP")

Arguments

decay

nonnegative decay parameter for the shared partner or selected directed analogue count; required if fixed=TRUE and ignored with a warning otherwise.
fixed

optional argument indicating whether the decay parameter is fixed at the given value, or is to be fit as a curved exponential-family model (see Hunter and Handcock, 2006). The default is FALSE , which means the scale parameter is not fixed and thus the model is a curved exponential family.
cutoff

This optional argument sets the number of underlying ESP terms to use in computing the statistics when fixed=FALSE, in order to reduce the computational burden. Its default value can also be controlled by the gw.cutoff term option control parameter. (See ?control.ergm.)
type

A string indicating the type of shared partner or path to be considered for directed networks: "OTP" (default for directed), "ITP", "RTP", "OSP", and "ISP"; has no effect for undirected. See the section below on Shared partner types for details.

Shared partner types

While there is only one shared partner configuration in the undirected case, nine distinct configurations are possible for directed graphs, selected using the type argument. Currently, terms may be defined with respect to five of these configurations; they are defined here as follows (using terminology from Butts (2008) and the relevent package):

  • Outgoing Two-path ("OTP"): vertex kk is an OTP shared partner of ordered pair (i,j)(i,j) iff i→k→ji \to k \to j. Also known as "transitive shared partner".

  • Incoming Two-path ("ITP"): vertex kk is an ITP shared partner of ordered pair (i,j)(i,j) iff j→k→ij \to k \to i. Also known as "cyclical shared partner"

  • Reciprocated Two-path ("RTP"): vertex kk is an RTP shared partner of ordered pair (i,j)(i,j) iff i↔k↔ji \leftrightarrow k \leftrightarrow j.

  • Outgoing Shared Partner ("OSP"): vertex kk is an OSP shared partner of ordered pair (i,j)(i,j) iff i→k,j→ki \to k, j \to k.

  • Incoming Shared Partner ("ISP"): vertex kk is an ISP shared partner of ordered pair (i,j)(i,j) iff k→i,k→jk \to i, k \to j.

By default, outgoing two-paths ("OTP") are calculated. Note that Robins et al. (2009) define closely related statistics to several of the above, using slightly different terminology.

Note

This term takes an additional term option (see options?ergm), cache.sp, controlling whether the implementation will cache the number of shared partners for each dyad in the network; this is usually enabled by default.

The decay parameter was called alpha prior to ergm 3.7.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

directed, binary

Geometrically weighted in-degree distribution

Description

This term adds one network statistic to the model equal to the weighted in-degree distribution with decay parameter decay parameter, which should be non-negative. This term can only be used with directed networks.

Usage

# binary: gwidegree(decay, fixed=FALSE, attr=NULL, cutoff=30, levels=NULL)

Arguments

decay

nonnegative decay parameter for the indegree frequencies; required if fixed=TRUE and ignored with a warning otherwise.
fixed

optional argument indicating whether the decay parameter is fixed at the given value, or is to be fit as a curved exponential-family model (see Hunter and Handcock, 2006). The default is FALSE , which means the scale parameter is not fixed and thus the model is a curved exponential family.
attr

a vertex attribute specification (see Specifying Vertex attributes and Levels (?nodal_attributes) for details.)
cutoff

This optional argument sets the number of underlying degree terms to use in computing the statistics when fixed=FALSE, in order to reduce the computational burden. Its default value can also be controlled by the gw.cutoff term option control parameter. (See ?control.ergm.)
levels

TODO (See Specifying Vertex attributes and Levels (?nodal_attributes) for details.)

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

curved, directed, binary

Geometrically weighted non-edgewise shared partner distribution

Description

This term is just like gwesp and gwdsp except it adds a statistic equal to the geometrically weighted nonedgewise (that is, over dyads that do not have an edge) shared partner distribution with decay parameter decay parameter.

Usage

# binary: dgwnsp(decay, fixed=FALSE, cutoff=30, type="OTP")

# binary: gwnsp(decay, fixed=FALSE, cutoff=30, type="OTP")

Arguments

decay

nonnegative decay parameter for the shared partner or selected directed analogue count; required if fixed=TRUE and ignored with a warning otherwise.
fixed

optional argument indicating whether the decay parameter is fixed at the given value, or is to be fit as a curved exponential-family model (see Hunter and Handcock, 2006). The default is FALSE , which means the scale parameter is not fixed and thus the model is a curved exponential family.
cutoff

This optional argument sets the number of underlying NSP terms to use in computing the statistics when fixed=FALSE, in order to reduce the computational burden. Its default value can also be controlled by the gw.cutoff term option control parameter. (See ?control.ergm.)
type

A string indicating the type of shared partner or path to be considered for directed networks: "OTP" (default for directed), "ITP", "RTP", "OSP", and "ISP"; has no effect for undirected. See the section below on Shared partner types for details.

Shared partner types

While there is only one shared partner configuration in the undirected case, nine distinct configurations are possible for directed graphs, selected using the type argument. Currently, terms may be defined with respect to five of these configurations; they are defined here as follows (using terminology from Butts (2008) and the relevent package):

  • Outgoing Two-path ("OTP"): vertex kk is an OTP shared partner of ordered pair (i,j)(i,j) iff i→k→ji \to k \to j. Also known as "transitive shared partner".

  • Incoming Two-path ("ITP"): vertex kk is an ITP shared partner of ordered pair (i,j)(i,j) iff j→k→ij \to k \to i. Also known as "cyclical shared partner"

  • Reciprocated Two-path ("RTP"): vertex kk is an RTP shared partner of ordered pair (i,j)(i,j) iff i↔k↔ji \leftrightarrow k \leftrightarrow j.

  • Outgoing Shared Partner ("OSP"): vertex kk is an OSP shared partner of ordered pair (i,j)(i,j) iff i→k,j→ki \to k, j \to k.

  • Incoming Shared Partner ("ISP"): vertex kk is an ISP shared partner of ordered pair (i,j)(i,j) iff k→i,k→jk \to i, k \to j.

By default, outgoing two-paths ("OTP") are calculated. Note that Robins et al. (2009) define closely related statistics to several of the above, using slightly different terminology.

Note

This term takes an additional term option (see options?ergm), cache.sp, controlling whether the implementation will cache the number of shared partners for each dyad in the network; this is usually enabled by default.

The decay parameter was called alpha prior to ergm 3.7.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

directed, binary

Geometrically weighted out-degree distribution

Description

This term adds one network statistic to the model equal to the weighted out-degree distribution with decay parameter decay parameter, which should be non-negative. This term can only be used with directed networks.

Usage

# binary: gwodegree(decay, fixed=FALSE, attr=NULL, cutoff=30, levels=NULL)

Arguments

decay

nonnegative decay parameter for the outdegree frequencies; required if fixed=TRUE and ignored with a warning otherwise.
fixed

optional argument indicating whether the decay parameter is fixed at the given value, or is to be fit as a curved exponential-family model (see Hunter and Handcock, 2006). The default is FALSE , which means the scale parameter is not fixed and thus the model is a curved exponential family.
attr

a vertex attribute specification (see Specifying Vertex attributes and Levels (?nodal_attributes) for details.)
cutoff

This optional argument sets the number of underlying degree terms to use in computing the statistics when fixed=FALSE, in order to reduce the computational burden. Its default value can also be controlled by the gw.cutoff term option control parameter. (See ?control.ergm.)
levels

TODO (See Specifying Vertex attributes and Levels (?nodal_attributes) for details.)

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

curved, directed, binary

Preserve the hamming distance to the given network (BROKEN: Do NOT Use)

Description

This constraint is currently broken. Do not use.

Usage

# hamming

See Also

ergmConstraint for index of constraints and hints currently visible to the package.

Keywords

directed, undirected

Hamming distance

Description

This term adds one statistic to the model equal to the weighted or unweighted Hamming distance of the network from the network specified by x . Unweighted Hamming distance is defined as the total number of pairs (i,j)(i,j) (ordered or unordered, depending on whether the network is directed or undirected) on which the two networks differ. If the optional argument cov is specified, then the weighted Hamming distance is computed instead, where each pair (i,j)(i,j) contributes a pre-specified weight toward the distance when the two networks differ on that pair.

Usage

# binary: hamming(x, cov, attrname=NULL)

Arguments

x

defaults to be the observed network, i.e., the network on the left side of the ∼\sim in the formula that defines the ERGM.
cov

either a matrix of edgewise weights or a network
attrname

option argument that provides the name of the edge attribute to use for weight values when a network is specified in cov

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

directed, dyad-independent, undirected, binary

In-degree range

Description

This term adds one network statistic to the model for each element of from (or to ); the ii th such statistic equals the number of nodes in the network of in-degree greater than or equal to from[i] but strictly less than to[i] , i.e. with in-edge count in semiopen interval ⁠[from,to)⁠ .

This term can only be used with directed networks; for undirected networks (bipartite and not) see degrange . For degrees of specific modes of bipartite networks, see b1degrange and b2degrange . For in-degrees, see idegrange .

Usage

# binary: idegrange(from, to=+Inf, by=NULL, homophily=FALSE, levels=NULL)

Arguments

from, to

vectors of distinct integers. If one of the vectors have length 1, it is recycled to the length of the other. Otherwise, it must have the same length.
by, levels, homophily

the optional argument by specifies a vertex attribute (see Specifying Vertex attributes and Levels (?nodal_attributes) for details). If this is specified and homophily is TRUE , then degrees are calculated using the subnetwork consisting of only edges whose endpoints have the same value of the by attribute. If by is specified and homophily is FALSE (the default), then separate degree range statistics are calculated for nodes having each separate value of the attribute. levels selects which levels of by' to include.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

categorical nodal attribute, directed, binary

In-degree

Description

This term adds one network statistic to the model for each element in d ; the ii th such statistic equals the number of nodes in the network of in-degree d[i] , i.e. the number of nodes with exactly d[i] in-edges. This term can only be used with directed networks; for undirected networks see degree .

Usage

# binary: idegree(d, by=NULL, homophily=FALSE, levels=NULL)

Arguments

d

a vector of distinct integers
by, levels, homophily

the optional argument by specifies a vertex attribute (see Specifying Vertex attributes and Levels (?nodal_attributes) for details). If this is specified and homophily is TRUE , then degrees are calculated using the subnetwork consisting of only edges whose endpoints have the same value of the by attribute. If by is specified and homophily is FALSE (the default), then separate degree range statistics are calculated for nodes having each separate value of the attribute. levels selects which levels of by' to include.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

categorical nodal attribute, directed, frequently-used, binary

In-degree to the 3/2 power

Description

This term adds one network statistic to the model equaling the sum over the actors of each actor's indegree taken to the 3/2 power (or, equivalently, multiplied by its square root). This term is analogous to the term of Snijders et al. (2010), equation (12). This term can only be used with directed networks.

Usage

# binary: idegree1.5

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

directed, binary

Preserve the indegree distribution

Description

Preserve the indegree distribution of the given network.

Usage

# idegreedist

See Also

ergmConstraint for index of constraints and hints currently visible to the package.

Keywords

directed

Preserve indegree for directed networks

Description

For directed networks, preserve the indegree of each vertex of the given network, while allowing outdegree to vary

Usage

# idegrees

See Also

ergmConstraint for index of constraints and hints currently visible to the package.

Keywords

directed

Number of dyads whose values are in an interval

Description

Adds one statistic equaling to the number of dyads whose values are between lower and upper .

Usage

# valued: ininterval(lower=-Inf, upper=+Inf, open=c(TRUE,TRUE))

Arguments

lower

defaults to -Inf
upper

defaults to +Inf
open

a logical vector of length 2 that controls whether the interval is open (exclusive) on the lower and on the upper end, respectively. open can also be specified as one of "[]" , "(]" , "[)" , and "()" .

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

directed, dyad-independent, undirected, valued

Intransitive triads

Description

This term adds one statistic to the model, equal to the number of triads in the network that are intransitive. The intransitive triads are those of type ⁠111D⁠ , 201 , ⁠111U⁠ , ⁠021C⁠ , or ⁠030C⁠ in the categorization of Davis and Leinhardt (1972). For details on the 16 possible triad types, see triad.classify in the sna package. Note the distinction from the ctriple term.

Usage

# binary: intransitive

Note

This term can only be used with directed networks.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

directed, triad-related, binary

Testing for curved exponential family

Description

These functions test whether an ERGM fit, formula, or some other object represents a curved exponential family.

The method for NULL always returns FALSE by convention.

Usage

is.curved(object, ...)

## S3 method for class ''NULL''
is.curved(object, ...)

## S3 method for class 'formula'
is.curved(object, response = NULL, basis = NULL, ...)

## S3 method for class 'ergm'
is.curved(object, ...)

Arguments

object

An ergm object or an ERGM formula.
...

Arguments passed on to lower-level functions.
response

Either a character string, a formula, or NULL (the default), to specify the response attributes and whether the ERGM is binary or valued. Interpreted as follows:

NULL

Model simple presence or absence, via a binary ERGM.

character string

The name of the edge attribute whose value is to be modeled. Type of ERGM will be determined by whether the attribute is logical (TRUE/FALSE) for binary or numeric for valued.

a formula

must be of the form NAME~EXPR|TYPE (with | being literal). EXPR is evaluated in the formula's environment with the network's edge attributes accessible as variables. The optional NAME specifies the name of the edge attribute into which the results should be stored, with the default being a concise version of EXPR. Normally, the type of ERGM is determined by whether the result of evaluating EXPR is logical or numeric, but the optional TYPE can be used to override by specifying a scalar of the type involved (e.g., TRUE for binary and 1 for valued).
basis

See ergm().

Details

Curvature is checked by testing if all model parameters are canonical.

Value

TRUE if the object represents a curved exponential family; FALSE otherwise.

Testing for dyad-independence

Description

These functions test whether an ERGM fit, a formula, or some other object represents a dyad-independent model.

The method for NULL always returns TRUE by convention.

Usage

is.dyad.independent(object, ...)

## S3 method for class ''NULL''
is.dyad.independent(object, ...)

## S3 method for class 'formula'
is.dyad.independent(object, response = NULL, basis = NULL, ...)

## S3 method for class 'ergm_conlist'
is.dyad.independent(object, object.obs = NULL, ...)

## S3 method for class 'ergm'
is.dyad.independent(object, how = c("overall", "terms", "space"), ...)

Arguments

object

The object to be tested for dyadic independence.
...

Unused at this time.
response

Either a character string, a formula, or NULL (the default), to specify the response attributes and whether the ERGM is binary or valued. Interpreted as follows:

NULL

Model simple presence or absence, via a binary ERGM.

character string

The name of the edge attribute whose value is to be modeled. Type of ERGM will be determined by whether the attribute is logical (TRUE/FALSE) for binary or numeric for valued.

a formula

must be of the form NAME~EXPR|TYPE (with | being literal). EXPR is evaluated in the formula's environment with the network's edge attributes accessible as variables. The optional NAME specifies the name of the edge attribute into which the results should be stored, with the default being a concise version of EXPR. Normally, the type of ERGM is determined by whether the result of evaluating EXPR is logical or numeric, but the optional TYPE can be used to override by specifying a scalar of the type involved (e.g., TRUE for binary and 1 for valued).
basis

See ergm().
object.obs

For the ergm_conlist method, the observed data constraint.
how

one of "overall" (the default), "terms", or "space", to specify which aspect of the ERGM is to be tested for dyadic independence.

Details

Dyad independence is determined by checking if all of the constituent parts of the object (formula, ergm terms, constraints, etc.) are flagged as dyad-independent.

Value

TRUE if the model implied by the object is dyad-independent; FALSE otherwise.

Function to check whether an ERGM fit or some aspect of it is valued

Description

Function to check whether an ERGM fit or some aspect of it is valued

Usage

is.valued(object, ...)

## S3 method for class 'ergm_state'
is.valued(object, ...)

## S3 method for class 'edgelist'
is.valued(object, ...)

## S3 method for class 'ergm'
is.valued(object, ...)

## S3 method for class 'network'
is.valued(object, ...)

Arguments

object

the object to be tested.
...

additional arguments for methods, currently unused.

Methods (by class)

  • is.valued(ergm_state): a method for ergm_state objects.

  • is.valued(edgelist): a method for edgelist objects.

  • is.valued(ergm): a method for ergm objects.

  • is.valued(network): a method for network objects that tests whether the network has been instrumented with a valued %ergmlhs% "response" specification, typically by ergm_preprocess_response(). Note that it is not a test for whether a network has edge attributes. This method is primarily for internal use.

Isolated edges

Description

This term adds one statistic to the model equal to the number of isolated edges in the network, i.e., the number of edges each of whose endpoints has degree 1. This term can only be used with undirected networks.

Usage

# binary: isolatededges

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

bipartite, undirected, binary

Isolates

Description

This term adds one statistic to the model equal to the number of isolates in the network. For an undirected network, an isolate is defined to be any node with degree zero. For a directed network, an isolate is any node with both in-degree and out-degree equal to zero.

Usage

# binary: isolates

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

directed, frequently-used, undirected, binary

In-stars

Description

This term adds one network statistic to the model for each element in k . The ii th such statistic counts the number of distinct k[i] -instars in the network, where a kk -instar is defined to be a node NN and a set of kk different nodes {O1,…,Ok}\{O_1, \dots, O_k\} such that the ties (Oj→N)(O_j{\rightarrow}N) exist for j=1,…,kj=1, \dots, k . This term can only be used for directed networks; for undirected networks see kstar . Note that istar(1) is equal to both ostar(1) and edges .

Usage

# binary: istar(k, attr=NULL, levels=NULL)

Arguments

k

a vector of distinct integers
attr, levels

a vertex attribute specification; if attr is specified, then the count is over the instances where all nodes involved have the same value of the attribute. levels specified which values of attr are included in the count. (See Specifying Vertex attributes and Levels (?nodal_attributes) for details.)

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

categorical nodal attribute, directed, binary

Kapferer's tailor shop data

Description

This well-known social network dataset, collected by Bruce Kapferer in Zambia from June 1965 to August 1965, involves interactions among workers in a tailor shop as observed by Kapferer himself.

Usage

data(kapferer)

Format

Two network objects, kapferer and kapferer2. The kapferer dataset contains only the 39 individuals who were present at both data-collection time periods. However, these data only reflect data collected during the first period. The individuals' names are included as a nodal covariate called names.

Details

An interaction is defined by Kapferer as "continuous uninterrupted social activity involving the participation of at least two persons"; only transactions that were relatively frequent are recorded. All of the interactions in this particular dataset are "sociational", as opposed to "instrumental". Kapferer explains the difference (p. 164) as follows:

"I have classed as transactions which were sociational in content those where the activity was markedly convivial such as general conversation, the sharing of gossip and the enjoyment of a drink together. Examples of instrumental transactions are the lending or giving of money, assistance at times of personal crisis and help at work."

Kapferer also observed and recorded instrumental transactions, many of which are unilateral (directed) rather than reciprocal (undirected), though those transactions are not recorded here. In addition, there was a second period of data collection, from September 1965 to January 1966, but these data are also not recorded here. All data are given in Kapferer's 1972 book on pp. 176-179.

During the first time period, there were 43 individuals working in this particular tailor shop; however, the better-known dataset includes only those 39 individuals who were present during both time collection periods. (Missing are the workers named Lenard, Peter, Lazarus, and Laurent.) Thus, we give two separate network datasets here: kapferer is the well-known 39-individual dataset, whereas kapferer2 is the full 43-individual dataset.

Source

Original source: Kapferer, Bruce (1972), Strategy and Transaction in an African Factory, Manchester University Press.

kk-stars

Description

This term adds one network statistic to the model for each element in k . The ii th such statistic counts the number of distinct k[i] -stars in the network, where a kk -star is defined to be a node NN and a set of kk different nodes {O1,…,Ok}\{O_1, \dots, O_k\} such that the ties {N,Oi}\{N, O_i\} exist for i=1,…,ki=1, \dots, k . This term can only be used for undirected networks; for directed networks, see istar , ostar , twopath and m2star . Note that kstar(1) is equal to edges .

Usage

# binary: kstar(k, attr=NULL, levels=NULL)

Arguments

k

a vector of distinct integers
attr, levels

a vertex attribute specification; if attr is specified, then the count is over the instances where all nodes involved have the same value of the attribute. levels specified which values of attr are included in the count. (See Specifying Vertex attributes and Levels (?nodal_attributes) for details.)

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

categorical nodal attribute, undirected, binary

Modify terms' coefficient names

Description

This operator evaluates formula without modification, but modifies its coefficient and/or parameter names based on label and pos .

Usage

# binary: Label(formula, label, pos)

# valued: Label(formula, label, pos)

Arguments

formula

a one-sided ergm()-style formula with the terms to be evaluated
label

a character vector specifying the label for the terms, a list of two character vectors (see Details), or a function through which term names are mapped (or a as_mapper -style formula).
pos

controls how label modifies the term names: one of "prepend" , "replace" , "append" , or "(" , with the latter wrapping the term names in parentheses like a function call with name specified by label .

Details

If pos == "replace":

  • Elements for which is.na(label) == TRUE are preserved.

  • If the model is curved, ⁠label=⁠ can be a either function/mapper or a list with two elements, the first element giving the curved (model) parameter names and second giving the canonical parameter names. NULL leaves the respective name unchanged.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

operator, binary, valued

Triangles within neighborhoods

Description

This term adds one statistic to the model equal to the number of triangles in the network between nodes "close to" each other. For an undirected network, a local triangle is defined to be any set of three edges between nodal pairs {(i,j),(j,k),(k,i)}\{(i,j), (j,k), (k,i)\} that are in the same neighborhood. For a directed network, a triangle is defined as any set of three edges (i→j),(j→k)(i{\rightarrow}j), (j{\rightarrow}k) and either (k→i)(k{\rightarrow}i) or (k←i)(k{\leftarrow}i) where again all nodes are within the same neighborhood.

Usage

# binary: localtriangle(x)

Arguments

x

an undirected network or an symmetric adjacency matrix that specifies whether the two nodes are in the same neighborhood. Note that triangle , with or without an argument, is a special case of localtriangle .

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

categorical dyadic attribute, directed, triad-related, undirected, binary

Take a natural logarithm of a network's statistic

Description

Evaluate the terms specified in formula and takes a natural (base ee ) logarithm of them. Since an ERGM statistic must be finite, log0 specifies the value to be substituted for log(0) . The default value seems reasonable for most purposes.

Usage

# binary: Log(formula, log0=-1/sqrt(.Machine$double.eps))

# valued: Log(formula, log0=-1/sqrt(.Machine$double.eps))

Arguments

formula

a one-sided ergm()-style formula with the terms to be evaluated
log0

the value to be substituted for log(0)

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

operator, binary, valued

A logLik() method for ergm fits.

Description

A function to return the log-likelihood associated with an ergm fit, evaluating it if necessary. If the log-likelihood was not computed for object, produces an error unless eval.loglik=TRUE.

Usage

## S3 method for class 'ergm'
logLik(
  object,
  add = FALSE,
  force.reeval = FALSE,
  eval.loglik = add || force.reeval,
  control = control.logLik.ergm(),
  ...,
  verbose = FALSE
)

## S3 method for class 'ergm'
deviance(object, ...)

## S3 method for class 'ergm'
AIC(object, ..., k = 2)

## S3 method for class 'ergm'
BIC(object, ...)

Arguments

object

An ergm fit, returned by ergm().
add

Logical: If TRUE, instead of returning the log-likelihood, return object with log-likelihood value (and the null likelihood value) set.
force.reeval

Logical: If TRUE, reestimate the log-likelihood even if object already has an estiamte.
eval.loglik

Logical: If TRUE, evaluate the log-likelihood if not set on object.
control

A list of control parameters for algorithm tuning, typically constructed with control.logLik.ergm(). Its documentation gives the the list of recognized control parameters and their meaning. The more generic utility snctrl() (StatNet ConTRoL) also provides argument completion for the available control functions and limited argument name checking.
...

Other arguments to the likelihood functions.
verbose

A logical or an integer to control the amount of progress and diagnostic information to be printed. FALSE/0 produces minimal output, with higher values producing more detail. Note that very high values (5+) may significantly slow down processing.
k

see help for AIC().

Value

The form of the output of logLik.ergm depends on add: add=FALSE (the default), a logLik object. If add=TRUE (the default), an ergm object with the log-likelihood set.

As of version 3.1, all likelihoods for which logLikNull is not implemented are computed relative to the reference measure. (I.e., a null model, with no terms, is defined to have likelihood of 0, and all other models are defined relative to that.)

Functions

References

Hunter, D. R. and Handcock, M. S. (2006) Inference in curved exponential family models for networks, Journal of Computational and Graphical Statistics.

See Also

logLik(), logLikNull(), ergm.bridge.llr(), ergm.bridge.dindstart.llk()

Examples

# See help(ergm) for a description of this model. The likelihood will
# not be evaluated.
data(florentine)
## Not run: 
# The default maximum number of iterations is currently 20. We'll only
# use 2 here for speed's sake.
gest <- ergm(flomarriage ~ kstar(1:2) + absdiff("wealth") + triangle, eval.loglik=FALSE)

gest <- ergm(flomarriage ~ kstar(1:2) + absdiff("wealth") + triangle, eval.loglik=FALSE,
             control=control.ergm(MCMLE.maxit=2))
# Log-likelihood is not evaluated, so no deviance, AIC, or BIC:
summary(gest)
# Evaluate the log-likelihood and attach it to the object.

# The default number of bridges is currently 20. We'll only use 3 here
# for speed's sake.
gest.logLik <- logLik(gest, add=TRUE)

gest.logLik <- logLik(gest, add=TRUE, control=control.logLik.ergm(bridge.nsteps=3))
# Deviances, AIC, and BIC are now shown:
summary(gest.logLik)
# Null model likelihood can also be evaluated, but not for all constraints:
logLikNull(gest) # == network.dyadcount(flomarriage)*log(1/2)

## End(Not run)

Calculate the null model likelihood

Description

Calculate the null model likelihood

Usage

logLikNull(object, ...)

## S3 method for class 'ergm'
logLikNull(object, control = control.logLik.ergm(), ...)

Arguments

object

a fitted model.
...

further arguments to lower-level functions.

logLikNull computes, when possible the log-probability of the data under the null model (reference distribution).
control

A list of control parameters for algorithm tuning, typically constructed with control.logLik.ergm(). Its documentation gives the the list of recognized control parameters and their meaning. The more generic utility snctrl() (StatNet ConTRoL) also provides argument completion for the available control functions and limited argument name checking.

Value

logLikNull returns an object of type logLik if it is able to compute the null model probability, and NA otherwise.

Methods (by class)

  • logLikNull(ergm): A method for ergm fits; currently only implemented for binary ERGMs with dyad-independent sample-space constraints.

Mixed 2-stars, a.k.a 2-paths

Description

This term adds one statistic to the model, equal to the number of mixed 2-stars in the network, where a mixed 2-star is a pair of distinct edges (i→j),(j→k)(i{\rightarrow}j), (j{\rightarrow}k) . A mixed 2-star is sometimes called a 2-path because it is a directed path of length 2 from ii to kk via jj . However, in the case of a 2-path the focus is usually on the endpoints ii and kk , whereas for a mixed 2-star the focus is usually on the midpoint jj . This term can only be used with directed networks; for undirected networks see kstar(2) . See also twopath .

Usage

# binary: m2star

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

directed, binary

Conduct MCMC diagnostics on a model fit

Description

This function prints diagnistic information and creates simple diagnostic plots for MCMC sampled statistics produced from a fit.

Usage

mcmc.diagnostics(object, ...)

## S3 method for class 'ergm'
mcmc.diagnostics(
  object,
  center = TRUE,
  esteq = TRUE,
  vars.per.page = 3,
  which = c("plots", "texts", "summary", "autocorrelation", "crosscorrelation", "burnin"),
  compact = FALSE,
  ...
)

Arguments

object

A model fit object to be diagnosed.
...

Additional arguments, to be passed to plotting functions.
center

Logical: If TRUE, center the samples on the observed statistics.
esteq

Logical: If TRUE, for statistics corresponding to curved ERGM terms, summarize the curved statistics by their negated estimating function values (evaluated at the MLE of any curved parameters) (i.e., ηI′(θ^)⋅(gI(Y)−gI(y))\eta'_{I}(\hat{\theta})\cdot (g_{I}(Y)-g_{I}(y)) for II being indices of the canonical parameters in question), rather than the canonical (sufficient) vectors of the curved statistics relative to the observed (gI(Y)−gI(y)g_{I}(Y)-g_{I}(y)).
vars.per.page

Number of rows (one variable per row) per plotting page. Ignored if latticeExtra package is not installed.
which

A character vector specifying which diagnostics to plot and/or print. Defaults to all of the below if meaningful:

"plots"

Traceplots and density plots of sample values for all statistic or estimating function elements.

"texts"

Shorthand for the following text diagnostics.

"summary"

Summary of network statistic or estimating function elements as produced by coda::summary.mcmc.list().

"autocorrelation"

Autocorrelation of each of the network statistic or estimating function elements.

"crosscorrelation"

Cross-correlations between each pair of the network statistic or estimating function elements.

"burnin"

Burn-in diagnostics, in particular, the Geweke test.

Partial matching is supported. (E.g., which=c("auto","cross") will print autocorrelation and cross-correlations.)
compact

Numeric: For diagnostics that print variables in columns (e.g. correlations, hypothesis test p-values), try to abbreviate variable names to this many characters and round the numbers to compact - 2 digits after the decimal point; 0 or FALSE for no abbreviation.

Details

A pair of plots are produced for each statistic:a trace of the sampled output statistic values on the left and density estimate for each variable in the MCMC chain on the right. Diagnostics printed to the console include correlations and convergence diagnostics.

For ergm() specifically, recent changes in the estimation algorithm mean that these plots can no longer be used to ensure that the mean statistics from the model match the observed network statistics. For that functionality, please use the GOF command: gof(object, GOF=~model).

In fact, an ergm() output object contains the sample of statistics from the last MCMC run as element ⁠$sample⁠. If missing data MLE is fit, the corresponding element is named ⁠$sample.obs⁠. These are objects of mcmc and can be used directly in the coda package to assess MCMC convergence.

More information can be found by looking at the documentation of ergm().

Methods (by class)

  • mcmc.diagnostics(ergm):

References

Raftery, A.E. and Lewis, S.M. (1995). The number of iterations, convergence diagnostics and generic Metropolis algorithms. In Practical Markov Chain Monte Carlo (W.R. Gilks, D.J. Spiegelhalter and S. Richardson, eds.). London, U.K.: Chapman and Hall.

See Also

ergm(), network package, coda package, summary.ergm()

Examples

## Not run: 
#
data(florentine)
#
# test the mcmc.diagnostics function
#
gest <- ergm(flomarriage ~ edges + kstar(2))
summary(gest)

#
# Plot the probabilities first
#
mcmc.diagnostics(gest)
#
# Use coda directly
#
library(coda)
#
plot(gest$sample, ask=FALSE)
#
# A full range of diagnostics is available
# using codamenu()
#

## End(Not run)

Mean vertex degree

Description

This term adds one network statistic to the model equal to the average degree of a node. Note that this term is a constant multiple of both edges and density .

Usage

# binary: meandeg

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

directed, dyad-independent, undirected, binary

Mixing matrix cells and margins

Description

attrs is the rows of the mixing matrix and whose RHS gives that for its columns (which may be different). A one-sided formula (e.g., ~A ) is symmetrized (e.g., A~A ). A two-sided formula with a dot on one side calculates the margins of the mixing matrix, analogously to nodefactor , with A~. calculating the row/sender/b1 margins and .~A calculating the column/receiver/b2 margins. If row and column attributes are the same and the network is undirected, only the cells at or above the diagonal (where row≤column\text{row} \le \text{column}) will be calculated.

Usage

# binary: mm(attrs, levels=NULL, levels2=-1)

# valued: mm(attrs, levels=NULL, levels2=-1, form="sum")

Arguments

attrs

a two-sided formula whose LHS gives the attribute or attribute function (see Specifying Vertex attributes and Levels (?nodal_attributes) for details.) for the rows of the mixing matrix and whose RHS gives for its columns. A one-sided formula (e.g., ~A) is symmetrized (e.g., A~A)
levels

subset of rows and columns to be used. (See Specifying Vertex attributes and Levels (?nodal_attributes) for details.)
levels2

which specific cells of the matrix to include; ?nodal_attributes for details
form

character how to aggregate tie values in a valued ERGM

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

categorical nodal attribute, directed, dyad-independent, frequently-used, undirected, binary, valued

Synthetic network with 20 nodes and 28 edges

Description

This is a synthetic network of 20 nodes that is used as an example within the ergm() documentation. It has an interesting elongated shape

  • reminencent of a chemical molecule. It is stored as a network object.

Usage

data(molecule)

See Also

florentine, sampson, network, plot.network, ergm

Mutuality

Description

In binary ERGMs, equal to the number of pairs of actors ii and jj for which (i→j)(i{\rightarrow}j) and (j→i)(j{\rightarrow}i) both exist. For valued ERGMs, equal to ∑i<jm(yi,j,yj,i)\sum_{i<j} m(y_{i,j},y_{j,i}) , where mm is determined by form argument: "min" for min⁡(yi,j,yj,i)\min(y_{i,j},y_{j,i}) , "nabsdiff" for −∣yi,j,yj,i∣-|y_{i,j},y_{j,i}| , "product" for yi,jyj,iy_{i,j}y_{j,i} , and "geometric" for yi,jyj,i\sqrt{y_{i,j}}\sqrt{y_{j,i}} . See Krivitsky (2012) for a discussion of these statistics. form="threshold" simply computes the binary mutuality after thresholding at threshold .

This term can only be used with directed networks.

Usage

# binary: mutual(same=NULL, by=NULL, diff=FALSE, keep=NULL, levels=NULL)

# valued: mutual(form="min",threshold=0)

Arguments

same

if the optional argument is passed (see Specifying Vertex attributes and Levels (?nodal_attributes) for details), only mutual pairs that match on the attribute are counted; separate counts for each unique matching value can be obtained by using diff=TRUE with same. Only one of same or by may be used. If both parameters are used, by is ignored. This paramer is affected by diff.
by

if the optional argument is passed (see Specifying Vertex attributes and Levels (?nodal_attributes) for details), then each node is counted separately for each mutual pair in which it occurs and the counts are tabulated by unique values of the attribute. This means that the sum of the mutual statistics when by is used will equal twice the standard mutual statistic. Only one of same or by may be used. If both parameters are used, by is ignored. This paramer is not affected by diff.
keep

deprecated
levels

which statistics should be kept whenever the mutual term would ordinarily result in multiple statistics. (See Specifying Vertex attributes and Levels (?nodal_attributes) for details.)
form

character how to aggregate tie values in a valued ERGM

Note

The argument keep is retained for backwards compatibility and may be removed in a future version. When both keep and levels are passed, levels overrides keep.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

directed, frequently-used, binary, valued

Near simmelian triads

Description

This term adds one statistic to the model equal to the number of near Simmelian triads, as defined by Krackhardt and Handcock (2007). This is a sub-graph of size three which is exactly one tie short of being complete.

Usage

# binary: nearsimmelian

Note

This term can only be used with directed networks.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

directed, triad-related, binary

A convenience container for a list of network objects, output by simulate.ergm() among others.

Description

A convenience container for a list of network objects, output by simulate.ergm() among others.

Usage

network.list(object, ...)

## S3 method for class 'network.list'
print(x, stats.print = FALSE, ...)

## S3 method for class 'network.list'
summary(
  object,
  stats.print = TRUE,
  net.print = FALSE,
  net.summary = FALSE,
  ...
)

Arguments

object, x

a list of networks or a network.list object.
...

for network.list, additional attributes to be set on the network list; for others, arguments passed down to lower-level functions.
stats.print

Logical: If TRUE, print network statistics.
net.print

Logical: If TRUE, print network overviews.
net.summary

Logical: If TRUE, print network summaries.

Methods (by generic)

  • print(network.list): A print() method for network lists.

  • summary(network.list): A summary() method for network lists.

See Also

simulate.ergm()

Examples

# Draw from a Bernoulli model with 16 nodes
# and tie probability 0.1
#
g.use <- network(16, density=0.1, directed=FALSE)
#
# Starting from this network let's draw 3 realizations
# of a model with edges and 2-star terms
#
g.sim <- simulate(~edges+kstar(2), nsim=3, coef=c(-1.8, 0.03),
               basis=g.use, control=control.simulate(
                 MCMC.burnin=100000,
                 MCMC.interval=1000))
print(g.sim)
summary(g.sim)

Specifying nodal attributes and their levels

Description

This document describes the ways to specify nodal attributes or functions of nodal attributes and which levels for categorical factors to include. For the helper functions to facilitate this, see nodal_attributes-API.

Usage

LARGEST(l, a)

SMALLEST(l, a)

COLLAPSE_SMALLEST(object, n, into)

Arguments

object, l, a, n, into

COLLAPSE_SMALLEST, LARGEST, and SMALLEST are technically functions but they are generally not called in a standard fashion but rather as a part of an vertex attribute specification or a level specification as described below. The above usage examples are needed to pass R's package checking without warnings; please disregard them, and refer to the sections and examples below instead.

Specifying nodal attributes

Term nodal attribute arguments, typically called attr, attrs, by, or on are interpreted as follows:

a character string

Extract the vertex attribute with this name.

a character vector of length > 1

Extract the vertex attributes and paste them together, separated by dots if the term expects categorical attributes and (typically) combine into a covariate matrix if it expects quantitative attributes.

a function

The function is called on the LHS network and additional arguments to ergm_get_vattr(), expected to return a vector or matrix of appropriate dimension. (Shorter vectors and matrix columns will be recycled as needed.)

a formula

The expression on the RHS of the formula is evaluated in an environment of the vertex attributes of the network, expected to return a vector or matrix of appropriate dimension. (Shorter vectors and matrix columns will be recycled as needed.) Within this expression, the network itself accessible as either . or .nw. For example, nodecov(~abs(Grade-mean(Grade))/network.size(.)) would return the absolute difference of each actor's "Grade" attribute from its network-wide mean, divided by the network size.

an AsIs object created by I()

Use as is, checking only for correct length and type.

Any of these arguments may also be wrapped in or piped through COLLAPSE_SMALLEST(attr, n, into) or, attr %>% COLLAPSE_SMALLEST(n, into), a convenience function that will transform the attribute by collapsing the smallest n categories into one, naming it into. Note that into must be of the same type (numeric, character, etc.) as the vertex attribute in question. If there are ties for nth smallest category, they will be broken in lexicographic order, and a warning will be issued.

The name the nodal attribute receives in the statistic can be overridden by setting a an attr()-style attribute "name".

Specifying categorical attribute levels and their ordering

For categorical attributes, to select which levels are of interest and their ordering, use the argument levels. Selection of nodes (from the appropriate vector of nodal indices) is likewise handled as the selection of levels, using the argument nodes. These arguments are interpreted as follows:

an expression wrapped in I()

Use the given list of levels as is.

a numeric or logical vector

Used for indexing of a list of all possible levels (typically, unique values of the attribute) in default older (typically lexicographic), i.e., sort(unique(attr))[levels]. In particular, levels=TRUE will retain all levels. Negative values exclude. Another special value is LARGEST, which will refer to the most frequent category, so, say, to set such a category as the baseline, pass levels=-LARGEST. In addition, LARGEST(n) will refer to the n largest categories. SMALLEST works analogously. If there are ties in frequencies, they will be broken in lexicographic order, and a warning will be issued. To specify numeric or logical levels literally, wrap in I().

NULL

Retain all possible levels; usually equivalent to passing TRUE.

a character vector

Use as is.

a function

The function is called on the list of unique values of the attribute, the values of the attribute themselves, and the network itself, depending on its arity. Its return value is interpreted as above.

a formula

The expression on the RHS of the formula is evaluated in an environment in which the network itself is accessible as .nw, the list of unique values of the attribute as . or as .levels, and the attribute vector itself as .attr. Its return value is interpreted as above.

a matrix

For mixing effects (i.e., ⁠level2=⁠ arguments), a matrix can be used to select elements of the mixing matrix, either by specifying a logical (TRUE and FALSE) matrix of the same dimension as the mixing matrix to select the corresponding cells or a two-column numeric matrix indicating giving the coordinates of cells to be used.

Note that levels, nodes, and others often have a default that is sensible for the term in question.

Examples

library(magrittr) # for %>%

data(faux.mesa.high)

# Activity by grade with a baseline grade excluded:
summary(faux.mesa.high~nodefactor(~Grade))
# Name overrides:
summary(faux.mesa.high~nodefactor("Form"~Grade)) # Only for terms that don't use the LHS.
summary(faux.mesa.high~nodefactor(~structure(Grade,name="Form")))
# Retain all levels:
summary(faux.mesa.high~nodefactor(~Grade, levels=TRUE)) # or levels=NULL
# Use the largest grade as baseline (also Grade 7):
summary(faux.mesa.high~nodefactor(~Grade, levels=-LARGEST))
# Activity by grade with no baseline smallest two grades (11 and
# 12) collapsed into a new category, labelled 0:
table(faux.mesa.high %v% "Grade")
summary(faux.mesa.high~nodefactor((~Grade) %>% COLLAPSE_SMALLEST(2, 0),
                                  levels=TRUE))

# Handling of tied frequencies
faux.mesa.high %v% "Plans" <-
    sample(rep(c("College", "Trade School", "Apprenticeship", "Undecided"), c(80,80,20,25)))
summary(faux.mesa.high ~ nodefactor("Plans", levels = -LARGEST))

# Mixing between lower and upper grades:
summary(faux.mesa.high~mm(~Grade>=10))
# Mixing between grades 7 and 8 only:
summary(faux.mesa.high~mm("Grade", levels=I(c(7,8))))
# or
summary(faux.mesa.high~mm("Grade", levels=1:2))
# or using levels2 (see ? mm) to filter the combinations of levels,
summary(faux.mesa.high~mm("Grade",
        levels2=~sapply(.levels,
                        function(l)
                          l[[1]]%in%c(7,8) && l[[2]]%in%c(7,8))))

# Here are some less complex ways to specify levels2. This is the
# full list of combinations of sexes in an undirected network:
summary(faux.mesa.high~mm("Sex", levels2=TRUE))
# Select only the second combination:
summary(faux.mesa.high~mm("Sex", levels2=2))
# Equivalently,
summary(faux.mesa.high~mm("Sex", levels2=-c(1,3)))
# or
summary(faux.mesa.high~mm("Sex", levels2=c(FALSE,TRUE,FALSE)))
# Select all *but* the second one:
summary(faux.mesa.high~mm("Sex", levels2=-2))
# Select via a mixing matrix: (Network is undirected and
# attributes are the same on both sides, so we can use either M or
# its transpose.)
(M <- matrix(c(FALSE,TRUE,FALSE,FALSE),2,2))
summary(faux.mesa.high~mm("Sex", levels2=M)+mm("Sex", levels2=t(M)))
# Select via an index of a cell:
idx <- cbind(1,2)
summary(faux.mesa.high~mm("Sex", levels2=idx))
# Or, select by specific attribute value combinations, though note
# the names 'row' and 'col' and the order for undirected networks:
summary(faux.mesa.high~mm("Sex",
                          levels2 = I(list(list(row="M",col="M"),
                                           list(row="M",col="F"),
                                           list(row="F",col="M")))))
# Note the warning: in an undirected network with identical row and
# column attributes, the mixing matrix is symmetric and only the
# upper triangle (where row < column) is valid, so the [M,F] cell
# will get a statistic of 0 with a warning.

# mm() term allows two-sided attribute formulas with different attributes:
summary(faux.mesa.high~mm(Grade~Race, levels2=TRUE))
# It is possible to have collapsing functions in the formula; note
# the parentheses around "~Race": this is because a formula
# operator (~) has lower precedence than pipe (|>):
summary(faux.mesa.high~mm(Grade~(~Race) %>% COLLAPSE_SMALLEST(3,"BWO"), levels2=TRUE))

# Some terms, such as nodecov(), accept matrices of nodal
# covariates. An certain R quirk means that columns whose
# expressions are not typical variable names have their names
# dropped and need to be adjusted. Consider, for example, the
# linear and quadratic effects of grade:
Grade <- faux.mesa.high %v% "Grade"
colnames(cbind(Grade, Grade^2)) # Second column name missing.
colnames(cbind(Grade, Grade2=Grade^2)) # Can be set manually,
colnames(cbind(Grade, `Grade^2`=Grade^2)) # even to non-variable-names.
colnames(cbind(Grade, Grade^2, deparse.level=2)) # Alternatively, deparse.level=2 forces naming.
rm(Grade)

# Therefore, the nodal attribute names are set as follows:
summary(faux.mesa.high~nodecov(~cbind(Grade, Grade^2))) # column names dropped with a warning
summary(faux.mesa.high~nodecov(~cbind(Grade, Grade2=Grade^2))) # column names set manually
summary(faux.mesa.high~nodecov(~cbind(Grade, Grade^2, deparse.level=2))) # using deparse.level=2

# Activity by grade with a random covariate. Note that setting an attribute "name" gives it a name:
randomcov <- structure(I(rbinom(network.size(faux.mesa.high),1,0.5)), name="random")
summary(faux.mesa.high~nodefactor(I(randomcov)))

Main effect of a covariate

Description

This term adds a single network statistic for each quantitative attribute or matrix column to the model equaling the sum of attr(i) and attr(j) for all edges (i,j)(i,j) in the network. For categorical attributes, see nodefactor . Note that for directed networks, nodecov equals nodeicov plus nodeocov .

Usage

# binary: nodecov(attr)

# binary: nodemain

# valued: nodecov(attr, form="sum")

# valued: nodemain(attr, form="sum")

Arguments

attr

a vertex attribute specification (see Specifying Vertex attributes and Levels (?nodal_attributes) for details.)
form

character how to aggregate tie values in a valued ERGM

Note

ergm versions 3.9.4 and earlier used different arguments for this term. See ergm-options for how to invoke the old behaviour.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

directed, dyad-independent, frequently-used, quantitative nodal attribute, undirected, binary, valued

Covariance of undirected dyad values incident on each actor

Description

This term adds one statistic equal to ∑i,j<kyi,jyi,k/(n−2)\sum_{i,j<k} y_{i,j}y_{i,k}/(n-2) . This can be viewed as a valued analog of the star(2) statistic.

Usage

# valued: nodecovar(center, transform)

Arguments

center

If center=TRUE , the y⋅,⋅y_{\cdot,\cdot} s are centered by their mean over the whole network before the calculation. Note that this makes the model non-local, but it may alleviate multimodailty.
transform

If transform="sqrt" , y⋅,⋅y_{\cdot,\cdot} s are repaced by their square roots before the calculation. This makes sense for counts in particular. If center=TRUE as well, they are centered by the mean of the square roots.

Note

Note that this term replaces nodesqrtcovar , which has been deprecated in favor of nodecovar(transform="sqrt") .

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

directed, valued

Factor attribute effect

Description

This term adds multiple network statistics to the model, one for each of (a subset of) the unique values of the attr attribute (or each combination of the attributes given). Each of these statistics gives the number of times a node with that attribute or those attributes appears in an edge in the network.

Usage

# binary: nodefactor(attr, base=1, levels=-1)

# valued: nodefactor(attr, base=1, levels=-1, form="sum")

Arguments

attr

a vertex attribute specification (see Specifying Vertex attributes and Levels (?nodal_attributes) for details.)
base

deprecated
levels

this optional argument controls which levels of the attribute attributes and Levels (?nodal_attributes) for details.)
form

character how to aggregate tie values in a valued ERGM

Note

To include all attribute values is usually not a good idea, because the sum of all such statistics equals the number of edges and hence a linear dependency would arise in any model also including edges. The default, levels=-1, is therefore to omit the first (in lexicographic order) attribute level. To include all levels, pass either levels=TRUE (i.e., keep all levels) or levels=NULL (i.e., do not filter levels).

The argument base is retained for backwards compatibility and may be removed in a future version. When both base and levels are passed, levels overrides base.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

categorical nodal attribute, directed, dyad-independent, frequently-used, undirected, binary, valued

Main effect of a covariate for in-edges

Description

This term adds a single network statistic for each quantitative attribute or matrix column to the model equaling the total value of attr(j) for all edges (i,j)(i,j) in the network. This term may only be used with directed networks. For categorical attributes, see nodeifactor .

Usage

# binary: nodeicov(attr)

# valued: nodeicov(attr, form="sum")

Arguments

attr

a vertex attribute specification (see Specifying Vertex attributes and Levels (?nodal_attributes) for details.)
form

character how to aggregate tie values in a valued ERGM

Note

ergm versions 3.9.4 and earlier used different arguments for this term. See ergm-options for how to invoke the old behaviour.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

directed, frequently-used, quantitative nodal attribute, binary, valued

Covariance of in-dyad values incident on each actor

Description

This term adds one statistic equal to ∑i,j,kyj,iyk,i/(n−2)\sum_{i,j,k} y_{j,i}y_{k,i}/(n-2) . This can be viewed as a valued analog of the istar(2) statistic.

Usage

# valued: nodeicovar(center, transform)

Arguments

center

If center=TRUE , the y⋅,⋅y_{\cdot,\cdot} s are centered by their mean over the whole network before the calculation. Note that this makes the model non-local, but it may alleviate multimodailty.
transform

If transform="sqrt" , y⋅,⋅y_{\cdot,\cdot} s are repaced by their square roots before the calculation. This makes sense for counts in particular. If center=TRUE as well, they are centered by the mean of the square roots.

Note

Note that this term replaces nodeisqrtcovar , which has been deprecated in favor of nodeicovar(transform="sqrt") .

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

directed, valued

Factor attribute effect for in-edges

Description

This term adds multiple network statistics to the model, one for each of (a subset of) the unique values of the attr attribute (or each combination of the attributes given). Each of these statistics gives the number of times a node with that attribute or those attributes appears as the terminal node of a directed tie.

For an analogous term for quantitative vertex attributes, see nodeicov .

Usage

# binary: nodeifactor(attr, base=1, levels=-1)

# valued: nodeifactor(attr, base=1, levels=-1, form="sum")

Arguments

attr

a vertex attribute specification (see Specifying Vertex attributes and Levels (?nodal_attributes) for details.)
base

deprecated
levels

this optional argument controls which levels of the attribute attributes and Levels (?nodal_attributes) for details.)
form

character how to aggregate tie values in a valued ERGM

Note

To include all attribute values is usually not a good idea, because the sum of all such statistics equals the number of edges and hence a linear dependency would arise in any model also including edges. The default, levels=-1, is therefore to omit the first (in lexicographic order) attribute level. To include all levels, pass either levels=TRUE (i.e., keep all levels) or levels=NULL (i.e., do not filter levels).

The argument base is retained for backwards compatibility and may be removed in a future version. When both base and levels are passed, levels overrides base.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

categorical nodal attribute, directed, dyad-independent, frequently-used, binary, valued

Uniform homophily and differential homophily

Description

When diff=FALSE , this term adds one network statistic to the model, which counts the number of edges (i,j)(i,j) for which attr(i)==attr(j) . This is also called “uniform homophily”, because each group is assumed to have the same propensity for within-group ties. When multiple attribute names are given, the statistic counts only ties for which all of the attributes match. When diff=TRUE , pp network statistics are added to the model, where pp is the number of unique values of the attr attribute. The kk th such statistic counts the number of edges (i,j)(i,j) for which ⁠attr(i) == attr(j) == value(k)⁠ , where value(k) is the kk th smallest unique value of the attr attribute. This is also called “differential homophily”, because each group is allowed to have a unique propensity for within-group ties. Note that a statistical test of uniform vs. differential homophily should be conducted using the ANOVA function.

By default, matches on all levels kk are counted. This works for both diff=TRUE and diff=FALSE .

Usage

# binary: nodematch(attr, diff=FALSE, keep=NULL, levels=NULL)

# valued: nodematch(attr, diff=FALSE, keep=NULL, levels=NULL, form="sum")

# valued: match(attr, diff=FALSE, keep=NULL, levels=NULL, form="sum")

Arguments

attr

a vertex attribute specification (see Specifying Vertex attributes and Levels (?nodal_attributes) for details.)
diff

specify if the term has uniform or differential homophily
keep

deprecated
levels

this optional argument controls which levels of the attribute attributes and Levels (?nodal_attributes) for details.)
form

character how to aggregate tie values in a valued ERGM

Note

The argument keep is retained for backwards compatibility and may be removed in a future version. When both keep and levels are passed, levels overrides keep.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

categorical nodal attribute, directed, dyad-independent, frequently-used, undirected, binary, valued

Filtering on nodematch

Description

Evaluates the terms specified in formula on a network constructed by taking yy and removing any edges for which attrname(i)!=attrname(j) .

Usage

# binary: NodematchFilter(formula, attrname)

Arguments

formula

formula to be evaluated
attrname

a character vector giving one or more names of attributes in the network's vertex attribute list.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

operator, binary

Nodal attribute mixing

Description

By default, this term adds one network statistic to the model for each possible pairing of attribute values. The statistic equals the number of edges in the network in which the nodes have that pairing of values. (When multiple attributes are specified, a statistic is added for each combination of attribute values for those attributes.) In other words, this term produces one statistic for every entry in the mixing matrix for the attribute(s). By default, the ordering of the attribute values is lexicographic: alphabetical (for nominal categories) or numerical (for ordered categories).

Usage

# binary: nodemix(attr, base=NULL, b1levels=NULL, b2levels=NULL, levels=NULL, levels2=-1)

# valued: nodemix(attr, base=NULL, b1levels=NULL, b2levels=NULL, levels=NULL,
#                 levels2=-1, form="sum")

Arguments

attr

a vertex attribute specification (see Specifying Vertex attributes and Levels (?nodal_attributes) for details.)
base

deprecated
b1levels, b2levels, levels

control what statistics are included in the model and the order in which they appear. levels applies to unipartite networks; b1levels and b2levels apply to bipartite networks (see Specifying Vertex attributes and Levels (?nodal_attributes) for details)
levels2

similar to the other levels arguments above and applies to all networks. Optionally allows a factor or character matrix to be specified to group certain levels. Level combinations corresponding to NA are excluded. Combinations specified by the same character or level will be grouped together and summarised by the same statistic. If an empty string is specified, the level combinations will be ungrouped. Only the upper triangle needs to be specified for undirected networks. For example, levels2=matrix(c('A', '', NA, 'A'), 2, 2, byrow=TRUE) on an undirected matrix will group homophilous ties while leaving ties between 1 and 2 ungrouped.
form

character how to aggregate tie values in a valued ERGM

Note

The argument base is retained for backwards compatibility and may be removed in a future version. When both base and levels are passed, levels overrides base.

The argument base is retained for backwards compatibility and may be removed in a future version. When both base and levels2 are passed, levels2 overrides base.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

categorical nodal attribute, directed, dyad-independent, frequently-used, undirected, binary, valued

Main effect of a covariate for out-edges

Description

This term adds a single network statistic for each quantitative attribute or matrix column to the model equaling the total value of attr(i) for all edges (i,j)(i,j) in the network. This term may only be used with directed networks. For categorical attributes, see nodeofactor .

Usage

# binary: nodeocov(attr)

# valued: nodeocov(attr, form="sum")

Arguments

attr

a vertex attribute specification (see Specifying Vertex attributes and Levels (?nodal_attributes) for details.)
form

character how to aggregate tie values in a valued ERGM

Note

ergm versions 3.9.4 and earlier used different arguments for this term. See ergm-options for how to invoke the old behaviour.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

directed, dyad-independent, quantitative nodal attribute, binary, valued

Covariance of out-dyad values incident on each actor

Description

This term adds one statistic equal to ∑i,j,kyi,jyi,k/(n−2)\sum_{i,j,k} y_{i,j}y_{i,k}/(n-2) . This can be viewed as a valued analog of the ostar(2) statistic.

Usage

# valued: nodeocovar(center, transform)

Arguments

center

whether the y⋅,⋅y_{\cdot,\cdot} s are centered by their mean over the whole network before the calculation. Note that this makes the model non-local, but it may alleviate multimodailty.
transform

if transform="sqrt" , y⋅,⋅y_{\cdot,\cdot} s are repaced by their square roots before the calculation. This makes sense for counts in particular. If center=TRUE as well, they are centered by the mean of the square roots.

Note

Note that this term replaces nodeosqrtcovar , which has been deprecated in favor of nodeocovar(transform="sqrt") .

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

directed, valued

Factor attribute effect for out-edges

Description

This term adds multiple network statistics to the model, one for each of (a subset of) the unique values of the attr attribute (or each combination of the attributes given). Each of these statistics gives the number of times a node with that attribute or those attributes appears as the node of origin of a directed tie.

Usage

# binary: nodeofactor(attr, base=1, levels=-1)

# valued: nodeofactor(attr, base=1, levels=-1, form="sum")

Arguments

attr

a vertex attribute specification (see Specifying Vertex attributes and Levels (?nodal_attributes) for details.)
base

deprecated
levels

this optional argument controls which levels of the attribute attributes and Levels (?nodal_attributes) for details.)
form

character how to aggregate tie values in a valued ERGM

Note

The argument base is retained for backwards compatibility and may be removed in a future version. When both base and levels are passed, levels overrides base.

To include all attribute values is usually not a good idea, because the sum of all such statistics equals the number of edges and hence a linear dependency would arise in any model also including edges. The default, levels=-1, is therefore to omit the first (in lexicographic order) attribute level. To include all levels, pass either levels=TRUE (i.e., keep all levels) or levels=NULL (i.e., do not filter levels).

This term can only be used with directed networks.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

categorical nodal attribute, directed, dyad-independent, binary, valued

Length of the parameter vector associated with an object or with its terms.

Description

This is a generic that returns the number of parameters associated with a model or a model fit.

Usage

nparam(object, ...)

## Default S3 method:
nparam(object, ...)

## S3 method for class 'ergm'
nparam(object, offset = NA, ...)

Arguments

object

An object for which number of parameters is defined.
...

Additional arguments to methods.
offset

If NA (the default), all model terms are counted; if TRUE, only offset terms are counted; and if FALSE, offset terms are skipped.

Methods (by class)

  • nparam(default): By default, the length of the coef() vector is returned.

  • nparam(ergm): A method to return the number of parameters of an ergm fit.

Directed non-edgewise shared partners

Description

This term adds one network statistic to the model for each element in d where the ii th such statistic equals the number of non-edges in the network with exactly d[i] shared partners.

Usage

# binary: dnsp(d, type="OTP")

# binary: nsp(d, type="OTP")

Arguments

d

a vector of distinct integers
type

A string indicating the type of shared partner or path to be considered for directed networks: "OTP" (default for directed), "ITP", "RTP", "OSP", and "ISP"; has no effect for undirected. See the section below on Shared partner types for details.

Shared partner types

While there is only one shared partner configuration in the undirected case, nine distinct configurations are possible for directed graphs, selected using the type argument. Currently, terms may be defined with respect to five of these configurations; they are defined here as follows (using terminology from Butts (2008) and the relevent package):

  • Outgoing Two-path ("OTP"): vertex kk is an OTP shared partner of ordered pair (i,j)(i,j) iff i→k→ji \to k \to j. Also known as "transitive shared partner".

  • Incoming Two-path ("ITP"): vertex kk is an ITP shared partner of ordered pair (i,j)(i,j) iff j→k→ij \to k \to i. Also known as "cyclical shared partner"

  • Reciprocated Two-path ("RTP"): vertex kk is an RTP shared partner of ordered pair (i,j)(i,j) iff i↔k↔ji \leftrightarrow k \leftrightarrow j.

  • Outgoing Shared Partner ("OSP"): vertex kk is an OSP shared partner of ordered pair (i,j)(i,j) iff i→k,j→ki \to k, j \to k.

  • Incoming Shared Partner ("ISP"): vertex kk is an ISP shared partner of ordered pair (i,j)(i,j) iff k→i,k→jk \to i, k \to j.

By default, outgoing two-paths ("OTP") are calculated. Note that Robins et al. (2009) define closely related statistics to several of the above, using slightly different terminology.

Note

This term takes an additional term option (see options?ergm), cache.sp, controlling whether the implementation will cache the number of shared partners for each dyad in the network; this is usually enabled by default.

This term can only be used with directed networks.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

directed, binary

Preserve the observed dyads of the given network

Description

Preserve the observed dyads of the given network.

Usage

# observed

See Also

ergmConstraint for index of constraints and hints currently visible to the package.

Keywords

directed, dyad-independent, undirected

Out-degree range

Description

This term adds one network statistic to the model for each element of from (or to ); the ii th such statistic equals the number of nodes in the network of out-degree greater than or equal to from[i] but strictly less than to[i] , i.e. with out-edge count in semiopen interval ⁠[from,to)⁠ .

This term can only be used with directed networks; for undirected networks (bipartite and not) see degrange . For degrees of specific modes of bipartite networks, see b1degrange and b2degrange . For in-degrees, see idegrange .

Usage

# binary: odegrange(from, to=+Inf, by=NULL, homophily=FALSE, levels=NULL)

Arguments

from, to

vectors of distinct integers. If one of the vectors have length 1, it is recycled to the length of the other. Otherwise, it must have the same length.
by, levels, homophily

the optional argument by specifies a vertex attribute (see Specifying Vertex attributes and Levels (?nodal_attributes) for details). If this is specified and homophily is TRUE , then degrees are calculated using the subnetwork consisting of only edges whose endpoints have the same value of the by attribute. If by is specified and homophily is FALSE (the default), then separate degree range statistics are calculated for nodes having each separate value of the attribute. levels selects which levels of by' to include.
attr

a vertex attribute specification (see Specifying Vertex attributes and Levels (?nodal_attributes) for details.)

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

categorical nodal attribute, directed, binary

Out-degree

Description

This term adds one network statistic to the model for each element in d ; the ii th such statistic equals the number of nodes in the network of out-degree d[i] , i.e. the number of nodes with exactly d[i] out-edges. This term can only be used with directed networks; for undirected networks see degree .

Usage

# binary: odegree(d, by=NULL, homophily=FALSE, levels=NULL)

Arguments

d

a vector of distinct integers
by, levels, homophily

the optional argument by specifies a vertex attribute (see Specifying Vertex attributes and Levels (?nodal_attributes) for details). If this is specified and homophily is TRUE , then degrees are calculated using the subnetwork consisting of only edges whose endpoints have the same value of the by attribute. If by is specified and homophily is FALSE (the default), then separate degree range statistics are calculated for nodes having each separate value of the attribute. levels selects which levels of by' to include.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

categorical nodal attribute, directed, frequently-used, binary

Out-degree to the 3/2 power

Description

This term adds one network statistic to the model equaling the sum over the actors of each actor's outdegree taken to the 3/2 power (or, equivalently, multiplied by its square root). This term is analogous to the term of Snijders et al. (2010), equation (12). This term can only be used with directed networks.

Usage

# binary: odegree1.5

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

directed, binary

Preserve the outdegree distribution

Description

Preserve the outdegree distribution of the given network.

Usage

# odegreedist

See Also

ergmConstraint for index of constraints and hints currently visible to the package.

Keywords

directed

Preserve outdegree for directed networks

Description

For directed networks, preserve the outdegree of each vertex of the given network, while allowing indegree to vary

Usage

# odegrees

See Also

ergmConstraint for index of constraints and hints currently visible to the package.

Keywords

directed

Terms with fixed coefficients

Description

This operator is analogous to the offset() wrapper, but the coefficients are specified within the term and the curved ERGM mechanism is used internally.

Usage

# binary: Offset(formula, coef, which)

Arguments

formula

a one-sided ergm()-style formula with the terms to be evaluated
coef

coefficients to the formula
which

used to specify which of the parameters in the formula are fixed. It can be a logical vector (recycled as needed), a numeric vector of indices of parameters to be fixed, or a character vector of parameter names.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

operator, binary

Open triads

Description

This term adds one statistic to the model equal to the number of 2-stars minus three times the number of triangles in the network. It is currently only implemented for undirected networks.

Usage

# binary: opentriad

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

triad-related, undirected, binary

k-Outstars

Description

This term adds one network statistic to the model for each element in k . The ii th such statistic counts the number of distinct k[i] -outstars in the network, where a kk -outstar is defined to be a node NN and a set of kk different nodes {O1,…,Ok}\{O_1, \dots, O_k\} such that the ties (N→Oj)(N{\rightarrow}O_j) exist for j=1,…,kj=1, \dots, k . This term can only be used with directed networks; for undirected networks see kstar .

Usage

# binary: ostar(k, attr=NULL, levels=NULL)

Arguments

k

a vector of distinct integers
attr, levels

a vertex attribute specification; if attr is specified, then the count is over the instances where all nodes involved have the same value of the attribute. levels specified which values of attr are included in the count. (See Specifying Vertex attributes and Levels (?nodal_attributes) for details.)

Note

ostar(1) is equal to both istar(1) and edges .

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

categorical nodal attribute, directed, binary

Names of the parameters associated with an object.

Description

This is a generic that returns a vector giving the names of the parameters associated with a model or a model fit.

Usage

param_names(object, ...)

## Default S3 method:
param_names(object, ...)

param_names(object, ...) <- value

Arguments

object

An object for which parameter names are defined.
...

Additional arguments to methods.
value

Specification for the new parameter names.

Methods (by class)

  • param_names(default): By default, the names of the coef() vector is returned.

Functions

  • param_names(object, ...) <- value: a method for modifying parameter names of an object.

ERGM-based tie probabilities

Description

Calculate model-predicted conditional and unconditional tie probabilities for dyads in the given network. Conditional probabilities of a dyad given the state of all the remaining dyads in the graph are computed exactly. Unconditional probabilities are computed through simulating networks using the given model. Currently there are two methods implemented:

  • Method for formula objects requires (1) an ERGM model formula with an existing network object on the left hand side and model terms on the right hand side, and (2) a vector of corresponding parameter values.

  • Method for ergm objects, as returned by ergm(), takes both the formula and parameter values from the fitted model object.

Both methods can limit calculations to specific set of dyads of interest.

Usage

## S3 method for class 'formula'
predict(
  object,
  theta,
  conditional = TRUE,
  type = c("response", "link"),
  nsim = 100,
  output = c("data.frame", "matrix"),
  ...
)

## S3 method for class 'ergm'
predict(object, ...)

Arguments

object

a formula or a fitted ERGM model object
theta

numeric vector of ERGM model parameter values
conditional

logical whether to compute conditional or unconditional predicted probabilities
type

character element, one of "response" (default) or "link" - whether the returned predictions are on the probability scale or on the scale of linear predictor. This is similar to type argument of predict.glm().
nsim

integer, number of simulated networks used for computing unconditional probabilities. Defaults to 100.
output

character, type of object returned. Defaults to "data.frame". See section Value below.
...

other arguments passed to/from other methods. For the predict.formula method, if conditional=TRUE arguments are passed to ergmMPLE(). If conditional=FALSE arguments are passed to simulate_formula().

Value

Type of object returned depends on the argument output. If output="data.frame" the function will return a data frame with columns:

  • tail, head – indices of nodes identifying a dyad

  • p – predicted conditional tie probability

If output="matrix" the function will return an "adjacency matrix" with the predicted probabilities. Diagonal values are 0s.

Examples

# A three-node empty directed network
net <- network.initialize(3, directed=TRUE)

# In homogeneous Bernoulli model with odds of a tie of 1/5 all ties are
# equally likely
predict(net ~ edges, log(1/5))

# Let's add a tie so that `net` has 1 tie out of possible 6 (so odds of 1/5)
net[1,2] <- 1

# Fit the model
fit <- ergm(net ~ edges)

# The p's should be identical
predict(fit)

A product (or an arbitrary power combination) of one or more formulas

Description

This operator evaluates a list of formulas whose corresponnding RHS statistics will be multiplied elementwise. They are required to be nonnegative.

Usage

# binary: Prod(formulas, label)

# valued: Prod(formulas, label)

Arguments

formulas

a list (constructed using list() or c()) of ergm()-style formulas whose RHS gives the statistics to be evaluated, or a single formula.

If a formula in the list has an LHS, it is interpreted as follows:

  • a numeric scalar: Network statistics of this formula will be exponentiated by this.

  • a numeric vector: Corresponding network statistics of this formula will be exponentiated by this.

  • a numeric matrix: Vector of network statistics will be exponentiated by this using the same pattern as matrix multiplication.

  • a character string: One of several predefined multiplicative combinations. Currently supported presets are as follows:

    • "prod": Network statistics of this formula will be multiplied together; equivalent to matrix(1,1,p) , where p is the length of the network statistic vector.

    • "geomean": Network statistics of this formula will be geometrically averaged; equivalent to matrix(1/p,1,p) , where p is the length of the network statistic vector.

label

used to specify the names of the elements of the resulting term product vector. If label is a character vector of length 1, it will be recycled with indices appended. If a function is specified, formulas parameter names are extracted and their list of character vectors is passed label.

Details

Note that each formula must either produce the same number of statistics or be mapped through a matrix to produce the same number of statistics.

A single formula is also permitted. This can be useful if one wishes to, say, scale or multiply together the statistics returned by a formula.

Offsets are ignored unless there is only one formula and the transformation only scales the statistics (i.e., the effective transformation matrix is diagonal).

Curved models are supported, subject to some limitations. In particular, the first model's etamap will be used, overwriting the others. If label is not of length 1, it should have an attr -style attribute "curved" specifying the names for the curved parameters.

Note

The current implementation piggybacks on the Log , Exp , and Sum operators, essentially Exp(~Sum(~Log(formula), label)) . This may result in loss of precision, particularly for extremely large or small statistics. The implementation may change in the future.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

operator, binary, valued

A lack-of-fit test for ERGMs

Description

A simple test reporting the sample quantile of the observed network's probability in the distribution under the MLE. This is a conservative p-value for the null hypothesis of the observed network being a draw from the distribution of interest.

Usage

rank_test.ergm(x, plot = FALSE)

Arguments

x

an ergm() object.
plot

if TRUE, plot the empirical distribution.

Value

The sample quantile of the observed network's probability among the predicted.

Receiver effect

Description

This term adds one network statistic for each node equal to the number of in-ties for that node. This measures the popularity of the node. The term for the first node is omitted by default because of linear dependence that arises if this term is used together with edges , but its coefficient can be computed as the negative of the sum of the coefficients of all the other actors. That is, the average coefficient is zero, following the Holland-Leinhardt parametrization of the $p_1$ model (Holland and Leinhardt, 1981). This term can only be used with directed networks. For undirected networks, see sociality .

Usage

# binary: receiver(base=1, nodes=-1)

# valued: receiver(base=1, nodes=-1, form="sum")

Arguments

base

deprecated
nodes

specify which nodes' statistics should be included or excluded (see Specifying Vertex attributes and Levels (?nodal_attributes) for details)
form

character how to aggregate tie values in a valued ERGM

Note

The argument base is retained for backwards compatibility and may be removed in a future version. When both base and nodes are passed, nodes overrides base.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

directed, dyad-independent, binary, valued

Evaluation on an induced subgraph

Description

This operator takes a two-sided forumla attrs whose LHS gives the attribute or attribute function for which tails and heads will be used to construct the induced subgraph. They must evaluate either to a logical vector equal in length to the number of tails (for LHS) and heads (for RHS) indicating which nodes are to be used to induce the subgraph or a numeric vector giving their indices.

Usage

# binary: S(formula, attrs)

Arguments

formula

a one-sided ergm()-style formula with the terms to be evaluated
attrs

a two-sided formula to be used. A one-sided formula (e.g., ~A ) is symmetrized (e.g., A~A ).

Details

As with indexing vectors, the logical vector will be recycled to the size of the network or the size of the appropriate bipartition, and negative indices will deselect vertices.

When the two sets are identical, the induced subgraph retains the directedness of the original graph. Otherwise, an undirected bipartite graph is induced.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

operator, binary

Longitudinal networks of positive affection within a monastery as a "network" object

Description

Three network objects containing the "liking" nominations of Sampson's (1969) monks at the three time points.

Usage

data(samplk)

Details

Sampson (1969) recorded the social interactions among a group of monks while he was a resident as an experimenter at the cloister. During his stay, a political "crisis in the cloister" resulted in the expulsion of four monks– namely, the three "outcasts," Brothers Elias, Simplicius, Basil, and the leader of the "young Turks," Brother Gregory. Not long after Brother Gregory departed, all but one of the "young Turks" left voluntarily: Brothers John Bosco, Albert, Boniface, Hugh, and Mark. Then, all three of the "waverers" also left: First, Brothers Amand and Victor, then later Brother Romuald. Eventually, Brother Peter and Brother Winfrid also left, leaving only four of the original group.

Of particular interest are the data on positive affect relations ("liking," using the terminology later adopted by White et al. (1976)), in which each monk was asked if he had positive relations to each of the other monks. Each monk ranked only his top three choices (or four, in the case of ties) on "liking". Here, we consider a directed edge from monk A to monk B to exist if A nominated B among these top choices.

The data were gathered at three times to capture changes in group sentiment over time. They represent three time points in the period during which a new cohort had entered the monastery near the end of the study but before the major conflict began. These three time points are labeled T2, T3, and T4 in Tables D5 through D16 in the appendices of Sampson's 1969 dissertation. and the corresponding network data sets are named samplk1, samplk2, and samplk3, respectively.

See also the data set sampson containing the time-aggregated graph samplike.

samplk3 is a data set of Hoff, Raftery and Handcock (2002).

The data sets are stored as network objects with three vertex attributes:

group

Groups of novices as classified by Sampson, that is, "Loyal", "Outcasts", and "Turks", but with a fourth group called the "Waverers" by White et al. (1975) that comprises two of the original Loyal opposition and one of the original Outcasts. See the samplike data set for the original classifications of these three waverers.

cloisterville

An indicator of attendance in the minor seminary of "Cloisterville" before coming to the monastery.

vertex.names

The given names of the novices. NB: These names have been corrected as of ergm version 3.6.1.

This data set is standard in the social network analysis literature, having been modeled by Holland and Leinhardt (1981), Reitz (1982), Holland, Laskey and Leinhardt (1983), Fienberg, Meyer, and Wasserman (1981), and Hoff, Raftery, and Handcock (2002), among others. This is only a small piece of the data collected by Sampson.

This data set was updated for version 2.5 (March 2012) to add the cloisterville variable and refine the names. This information is from de Nooy, Mrvar, and Batagelj (2005). The original vertex names were: Romul_10, Bonaven_5, Ambrose_9, Berth_6, Peter_4, Louis_11, Victor_8, Winf_12, John_1, Greg_2, Hugh_14, Boni_15, Mark_7, Albert_16, Amand_13, Basil_3, Elias_17, Simp_18. The numbers indicate the ordering used in the original dissertation of Sampson (1969).

Mislabeling in Versions Prior to 3.6.1

In ergm versions 3.6.0 and earlier, The adjacency matrices of the samplike, samplk1, samplk2, and samplk3 networks reflected the original Sampson (1969) ordering of the names even though the vertex labels used the name order of de Nooy, Mrvar, and Batagelj (2005). That is, in ergm version 3.6.0 and earlier, the vertices were mislabeled. The correct order is the same one given in Tables D5, D9, and D13 of Sampson (1969): John Bosco, Gregory, Basil, Peter, Bonaventure, Berthold, Mark, Victor, Ambrose, Romauld (Sampson uses both spellings "Romauld" and "Ramauld" in the dissertation), Louis, Winfrid, Amand, Hugh, Boniface, Albert, Elias, Simplicius. By contrast, the order given in ergm version 3.6.0 and earlier is: Ramuald, Bonaventure, Ambrose, Berthold, Peter, Louis, Victor, Winfrid, John Bosco, Gregory, Hugh, Boniface, Mark, Albert, Amand, Basil, Elias, Simplicius.

Source

Sampson, S.~F. (1968), A novitiate in a period of change: An experimental and case study of relationships, Unpublished Ph.D. dissertation, Department of Sociology, Cornell University.

http://vlado.fmf.uni-lj.si/pub/networks/data/esna/sampson.htm

References

White, H.C., Boorman, S.A. and Breiger, R.L. (1976). Social structure from multiple networks. I. Blockmodels of roles and positions. American Journal of Sociology, 81(4), 730-780.

Wouter de Nooy, Andrej Mrvar, Vladimir Batagelj (2005) Exploratory Social Network Analysis with Pajek, Cambridge: Cambridge University Press

See Also

sampson, florentine, network, plot.network, ergm

Cumulative network of positive affection within a monastery as a "network" object

Description

A network object containing the cumulative "liking" nominations of Sampson's (1969) monks over the three time points.

Usage

data(sampson)

Details

Sampson (1969) recorded the social interactions among a group of monks while he was a resident as an experimenter at the cloister. During his stay, a political "crisis in the cloister" resulted in the expulsion of four monks– namely, the three "outcasts," Brothers Elias, Simplicius, Basil, and the leader of the "young Turks," Brother Gregory. Not long after Brother Gregory departed, all but one of the "young Turks" left voluntarily: Brothers John Bosco, Albert, Boniface, Hugh, and Mark. Then, all three of the "waverers" also left: First, Brothers Amand and Victor, then later Brother Romuald. Eventually, Brother Peter and Brother Winfrid also left, leaving only four of the original group.

Of particular interest are the data on positive affect relations ("liking," using the terminology later adopted by White et al. (1976)), in which each monk was asked if he had positive relations to each of the other monks. Each monk ranked only his top three choices (or four, in the case of ties) on "liking". Here, we consider a directed edge from monk A to monk B to exist if A nominated B among these top choices.

The data were gathered at three times to capture changes in group sentiment over time. They represent three time points in the period during which a new cohort had entered the monastery near the end of the study but before the major conflict began. These three time points are labeled T2, T3, and T4 in Tables D5 through D16 in the appendices of Sampson's 1969 dissertation. The samplike data set is the time-aggregated network. Thus, a tie from monk A to monk B exists if A nominated B as one of his three (or four, in case of ties) best friends at any of the three time points.

See also the data sets samplk1, samplk2, and samplk3, containing the networks at each of the three individual time points.

The data set is stored as a network object with three vertex attributes:

group

Groups of novices as classified by Sampson: "Loyal", "Outcasts", and "Turks".

cloisterville

An indicator of attendance in the minor seminary of "Cloisterville" before coming to the monastery.

vertex.names

The given names of the novices. NB: These names have been corrected as of ergm version 3.6.1; see details below.

In addition, the data set has an edge attribute, nominations, giving the number of times (out of 3) that monk A nominated monk B.

This data set is standard in the social network analysis literature, having been modeled by Holland and Leinhardt (1981), Reitz (1982), Holland, Laskey and Leinhardt (1983), Fienberg, Meyer, and Wasserman (1981), and Hoff, Raftery, and Handcock (2002), among others. This is only a small piece of the data collected by Sampson.

This data set was updated for version 2.5 (March 2012) to add the cloisterville variable and refine the names. This information is from de Nooy, Mrvar, and Batagelj (2005). The original vertex names were: Romul_10, Bonaven_5, Ambrose_9, Berth_6, Peter_4, Louis_11, Victor_8, Winf_12, John_1, Greg_2, Hugh_14, Boni_15, Mark_7, Albert_16, Amand_13, Basil_3, Elias_17, Simp_18. The numbers indicate the ordering used in the original dissertation of Sampson (1969).

Mislabeling in Versions Prior to 3.6.1

In ergm version 3.6.0 and earlier, The adjacency matrices of the samplike, samplk1, samplk2, and samplk3 networks reflected the original Sampson (1969) ordering of the names even though the vertex labels used the name order of de Nooy, Mrvar, and Batagelj (2005). That is, in ergm version 3.6.0 and earlier, the vertices were mislabeled. The correct order is the same one given in Tables D5, D9, and D13 of Sampson (1969): John Bosco, Gregory, Basil, Peter, Bonaventure, Berthold, Mark, Victor, Ambrose, Romauld (Sampson uses both spellings "Romauld" and "Ramauld" in the dissertation), Louis, Winfrid, Amand, Hugh, Boniface, Albert, Elias, Simplicius. By contrast, the order given in ergm version 3.6.0 and earlier is: Ramuald, Bonaventure, Ambrose, Berthold, Peter, Louis, Victor, Winfrid, John Bosco, Gregory, Hugh, Boniface, Mark, Albert, Amand, Basil, Elias, Simplicius.

Source

Sampson, S.~F. (1968), A novitiate in a period of change: An experimental and case study of relationships, Unpublished Ph.D. dissertation, Department of Sociology, Cornell University.

http://vlado.fmf.uni-lj.si/pub/networks/data/esna/sampson.htm

References

White, H.C., Boorman, S.A. and Breiger, R.L. (1976). Social structure from multiple networks. I. Blockmodels of roles and positions. American Journal of Sociology, 81(4), 730-780.

Wouter de Nooy, Andrej Mrvar, Vladimir Batagelj (2005) Exploratory Social Network Analysis with Pajek, Cambridge: Cambridge University Press

See Also

florentine, network, plot.network, ergm

Generate networks with a given set of network statistics

Description

This function attempts to find a network or networks whose statistics match those passed in via the target.stats vector.

Usage

san(object, ...)

## S3 method for class 'formula'
san(
  object,
  response = NULL,
  reference = ~Bernoulli,
  constraints = ~.,
  target.stats = NULL,
  nsim = NULL,
  basis = NULL,
  output = c("network", "edgelist", "ergm_state"),
  only.last = TRUE,
  control = control.san(),
  verbose = FALSE,
  offset.coef = NULL,
  ...
)

## S3 method for class 'ergm_model'
san(
  object,
  reference = ~Bernoulli,
  constraints = ~.,
  target.stats = NULL,
  nsim = NULL,
  basis = NULL,
  output = c("network", "edgelist", "ergm_state"),
  only.last = TRUE,
  control = control.san(),
  verbose = FALSE,
  offset.coef = NULL,
  ...
)

Arguments

object

Either a formula or some other supported representation of an ERGM, such as an ergm_model object. formula should be of the form y ~ <model terms>, where y is a network object or a matrix that can be coerced to a network object. For the details on the possible <model terms>, see ergmTerm. To create a network object in , use the network() function, then add nodal attributes to it using the %v% operator if necessary.
...

Further arguments passed to other functions.
response

Either a character string, a formula, or NULL (the default), to specify the response attributes and whether the ERGM is binary or valued. Interpreted as follows:

NULL

Model simple presence or absence, via a binary ERGM.

character string

The name of the edge attribute whose value is to be modeled. Type of ERGM will be determined by whether the attribute is logical (TRUE/FALSE) for binary or numeric for valued.

a formula

must be of the form NAME~EXPR|TYPE (with | being literal). EXPR is evaluated in the formula's environment with the network's edge attributes accessible as variables. The optional NAME specifies the name of the edge attribute into which the results should be stored, with the default being a concise version of EXPR. Normally, the type of ERGM is determined by whether the result of evaluating EXPR is logical or numeric, but the optional TYPE can be used to override by specifying a scalar of the type involved (e.g., TRUE for binary and 1 for valued).
reference

A one-sided formula specifying the reference measure (h(y)h(y)) to be used. See help for ERGM reference measures implemented in the ergm package.
constraints

A formula specifying one or more constraints on the support of the distribution of the networks being modeled. Multiple constraints may be given, separated by “+” and “-” operators. See ergmConstraint for the detailed explanation of their semantics and also for an indexed list of the constraints visible to the ergm package.

The default is to have no constraints except those provided through the ergmlhs API.

Together with the model terms in the formula and the reference measure, the constraints define the distribution of networks being modeled.

It is also possible to specify a proposal function directly either by passing a string with the function's name (in which case, arguments to the proposal should be specified through the MCMC.prop.args argument to the relevant control function, or by giving it on the LHS of the hints formula to MCMC.prop argument to the control function. This will override the one chosen automatically.

Note that not all possible combinations of constraints and reference measures are supported. However, for relatively simple constraints (i.e., those that simply permit or forbid specific dyads or sets of dyads from changing), arbitrary combinations should be possible.
target.stats

A vector of the same length as the number of non-offset statistics implied by the formula.
nsim

Number of networks to generate. Deprecated: just use replicate().
basis

If not NULL, a network object used to start the Markov chain. If NULL, this is taken to be the network named in the formula.
output

Character, one of "network" (default), "edgelist", or "ergm_state": determines the output format. Partial matching is performed.
only.last

if TRUE, only return the last network generated; otherwise, return a network.list with nsim networks.
control

A list of control parameters for algorithm tuning, typically constructed with control.san(). Its documentation gives the the list of recognized control parameters and their meaning. The more generic utility snctrl() (StatNet ConTRoL) also provides argument completion for the available control functions and limited argument name checking.
verbose

A logical or an integer to control the amount of progress and diagnostic information to be printed. FALSE/0 produces minimal output, with higher values producing more detail. Note that very high values (5+) may significantly slow down processing.
offset.coef

A vector of offset coefficients; these must be passed in by the user. Note that these should be the same set of coefficients one would pass to ergm via its offset.coef argument.
formula

(By default, the formula is taken from the ergm object. If a different formula object is wanted, specify it here.

Details

The following description is an exegesis of section 4 of Krivitsky et al. (2022).

Let g\mathbf{g} be a vector of target statistics for the network we wish to construct. That is, we are given an arbitrary network y0∈Y\mathbf{y}^0 \in \mathcal{Y}, and we seek a network y∈Y\mathbf{y} \in \mathcal{Y} such that g(y)≈g\mathbf{g}(\mathbf{y}) \approx \mathbf{g} – ideally equality is achieved, but in practice we may have to settle for a close approximation. The variant of simulated annealing is as follows.

The energy function is defined

EW(y)=(g(y)−g)TW(g(y)−g),E_W (\mathbf{y}) = (\mathbf{g}(\mathbf{y}) - \mathbf{g})^\mathsf{T} W (\mathbf{g}(\mathbf{y}) - \mathbf{g}),

with WW a symmetric positive (barring multicollinearity in statistics) definite matrix of weights. This function achieves 0 only if the target is reached. A good choice of this matrix yields a more efficient search.

A standard simulated annealing loop is used, as described below, with some modifications. In particular, we allow the user to specify a vector of offsets η\eta to bias the annealing, with ηk=0\eta_k = 0 denoting no offset. Offsets can be used with SAN to forbid certain statistics from ever increasing or decreasing. As with ergm(), offset terms are specified using the offset() decorator and their coefficients specified with the offset.coef argument. By default, finite offsets are ignored by, but this can be overridden by setting the control.san() argument SAN.ignore.finite.offsets = FALSE.

The number of simulated annealing runs is specified by the SAN.maxit control parameter and the initial value of the temperature TT is set to SAN.tau. The value of TT decreases linearly until T=0T = 0 at the last run, which implies that all proposals that increase EW(y)E_W (\mathbf{y}) are rejected. The weight matrix WW is initially set to Ip/pI_p / p, where IpI_p is the identity matrix of an appropriate dimension. For weight WW and temperature TT, the simulated annealing iteration proceeds as follows:

  1. Test if EW(y)=0E_W(\mathbf{y}) = 0. If so, then exit.

  2. Generate a perturbed network y∗\mathbf{y^*} from a proposal that respects the model constraints. (This is typically the same proposal as that used for MCMC.)

  3. Store the quantity g(y∗)−g(y)\mathbf{g}(\mathbf{y^*}) - \mathbf{g}(\mathbf{y}) for later use.

  4. Calculate acceptance probability

    α=exp⁡[−(EW(y∗)−EW(y))/T+ηT(g(y∗)−g(y))]\alpha = \exp[ - (E_W (\mathbf{y^*}) - E_W (\mathbf{y})) / T + \eta^\mathsf{T} (\mathbf{g}(\mathbf{y^*}) - \mathbf{g}(\mathbf{y}))]

    (If ∣ηk∣=∞|\eta_k| = \infty and gk(y∗)−gk(y)=0g_k (\mathbf{y^*}) - g_k (\mathbf{y}) = 0, their product is defined to be 0.)

  5. Replace y\mathbf{y} with y∗\mathbf{y^*} with probability min⁡(1,α)\min(1, \alpha).

After the specified number of iterations, TT is updated as described above, and WW is recalculated by first computing a matrix SS, the sample covariance matrix of the proposed differences stored in Step 3 (i.e., whether or not they were rejected), then W=S+/tr(S+)W = S^+ / tr(S^+), where S+S^+ is the Moore–Penrose pseudoinverse of SS and tr(S+)tr(S^+) is the trace of S+S^+. The differences in Step 3 closely reflect the relative variances and correlations among the network statistics.

In Step 2, the many options for MCMC proposals can provide for effective means of speeding the SAN algorithm's search for a viable network.

Value

A network or list of networks that hopefully have network statistics close to the target.stats vector. No guarantees are provided about their probability distribution. Additionally, attr()-style attributes formula and stats are included.

Methods (by class)

  • san(formula): Sufficient statistics are specified by a formula.

  • san(ergm_model): A lower-level function that expects a pre-initialized ergm_model.

References

Krivitsky, P. N., Hunter, D. R., Morris, M., & Klumb, C. (2022). ergm 4: Computational Improvements. arXiv preprint arXiv:2203.08198.

Examples

# initialize x to a random undirected network with 50 nodes and a density of 0.1
x <- network(50, density = 0.05, directed = FALSE)
 
# try to find a network on 50 nodes with 300 edges, 150 triangles,
# and 1250 4-cycles, starting from the network x
y <- san(x ~ edges + triangles + cycle(4), target.stats = c(300, 150, 1250))

# check results
summary(y ~ edges + triangles + cycle(4))

# initialize x to a random directed network with 50 nodes
x <- network(50)

# add vertex attributes
x %v% 'give' <- runif(50, 0, 1)
x %v% 'take' <- runif(50, 0, 1)

# try to find a set of 100 directed edges making the outward sum of
# 'give' and the inward sum of 'take' both equal to 62.5, so in
# edges (i,j) the node i tends to have above average 'give' and j
# tends to have above average 'take'
y <- san(x ~ edges + nodeocov('give') + nodeicov('take'), target.stats = c(100, 62.5, 62.5))

# check results
summary(y ~ edges + nodeocov('give') + nodeicov('take'))


# initialize x to a random undirected network with 50 nodes
x <- network(50, directed = FALSE)

# add a vertex attribute
x %v% 'popularity' <- runif(50, 0, 1)

# try to find a set of 100 edges making the total sum of
# popularity(i) and popularity(j) over all edges (i,j) equal to
# 125, so nodes with higher popularity are more likely to be
# connected to other nodes
y <- san(x ~ edges + nodecov('popularity'), target.stats = c(100, 125))
 
# check results
summary(y ~ edges + nodecov('popularity'))

# creates a network with denser "core" spreading out to sparser
# "periphery"
plot(y)

Search ERGM terms, constraints, references, hints, and proposals

Description

Searches through the database of ergmTerms, ergmConstraints, ergmReferences, ergmHints, and ergmProposals and prints out a list of terms and term-alikes appropriate for the specified network's structural constraints, optionally restricting by additional keywords and search term matches.

Usage

search.ergmTerms(search, net, keywords, name, packages)

search.ergmConstraints(search, keywords, name, packages)

search.ergmReferences(search, keywords, name, packages)

search.ergmHints(search, keywords, name, packages)

search.ergmProposals(search, name, reference, constraints, packages)

Arguments

search

optional character search term to search for in the text of the term descriptions. Only matching terms will be returned. Matching is case insensitive.
net

a network object that the term would be applied to, used as template to determine directedness, bipartite, etc
keywords

optional character vector of keyword tags to use to restrict the results (i.e. 'curved', 'triad-related')
name

optional character name of a specific term to return
packages

optional character vector indicating the subset of packages in which to search
reference, constraints

optional names of references and constraints to narrow down the proposal

Details

Uses grep() internally to match the search terms against the term description, so search is currently matched as a single phrase. Keyword tags will only return a match if all of the specified tags are included in the term.

Value

prints out the name and short description of matching terms, and invisibly returns them as a list. If name is specified, prints out the full definition for the named term.

Author(s)

[email protected]

See Also

See also ergmTerm, ergmConstraint, ergmReference, ergmHint, and ergmProposal, for lists of terms and term-alikes visible to ergm.

Examples

# find all of the terms that mention triangles
search.ergmTerms('triangle')

# two ways to search for bipartite terms:

# search using a bipartite net as a template
myNet<-network.initialize(5,bipartite=3)
search.ergmTerms(net=myNet)

# or request the bipartite keyword
search.ergmTerms(keywords='bipartite')

# search on multiple keywords
search.ergmTerms(keywords=c('bipartite','dyad-independent'))

# print out the content for a specific term
search.ergmTerms(name='b2factor')

# request the bipartite keyword in the ergm package
search.ergmTerms(keywords='bipartite', packages='ergm')


# find all of the constraint that mention degrees
search.ergmConstraints('degree')

# search for hints only
search.ergmConstraints(keywords='hint')

# search on multiple keywords
search.ergmConstraints(keywords=c('directed','dyad-independent'))

# print out the content for a specific constraint
search.ergmConstraints(name='b1degrees')

# request the bipartite keyword in the ergm package
search.ergmConstraints(keywords='directed', packages='ergm')


# find all discrete references
search.ergmReferences(keywords='discrete')


# find all of the hints
search.ergmHints('degree')


# find all of the proposals that mention triangles
search.ergmProposals('MH algorithm')

# print out the content for a specific proposals
search.ergmProposals(name='randomtoggle')

# find all proposals with required or optional constraints
search.ergmProposals(constraints='.dyads')

# find all proposals with references
search.ergmProposals(reference='Bernoulli')

# request proposals that mention triangle in the ergm package
search.ergmProposals('MH algorithm', packages='ergm')

Sender effect

Description

This term adds one network statistic for each node equal to the number of out-ties for that node. This measures the activity of the node. The term for the first node is omitted by default because of linear dependence that arises if this term is used together with edges , but its coefficient can be computed as the negative of the sum of the coefficients of all the other actors. That is, the average coefficient is zero, following the Holland-Leinhardt parametrization of the $p_1$ model (Holland and Leinhardt, 1981).

For undirected networks, see sociality .

Usage

# binary: sender(base=1, nodes=-1)

# valued: sender(base=1, nodes=-1, form="sum")

Arguments

base

deprecated
nodes

specify which nodes' statistics should be included or excluded (see Specifying Vertex attributes and Levels (?nodal_attributes) for details)
form

character how to aggregate tie values in a valued ERGM

Note

The argument base is retained for backwards compatibility and may be removed in a future version. When both base and nodes are passed, nodes overrides base.

This term can only be used with directed networks.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

directed, dyad-independent, binary, valued

Simmelian triads

Description

This term adds one statistic to the model equal to the number of Simmelian triads, as defined by Krackhardt and Handcock (2007). This is a complete sub-graph of size three.

Usage

# binary: simmelian

Note

This term can only be used with directed networks.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

directed, triad-related, binary

Ties in simmelian triads

Description

This term adds one statistic to the model equal to the number of ties in the network that are associated with Simmelian triads, as defined by Krackhardt and Handcock (2007). Each Simmelian has six ties in it but, because Simmelians can overlap in terms of nodes (and associated ties), the total number of ties in these Simmelians is less than six times the number of Simmelians. Hence this is a measure of the clustering of Simmelians (given the number of Simmelians).

Usage

# binary: simmelianties

Note

This term can only be used with directed networks.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

directed, triad-related, binary

Draw from the distribution of an Exponential Family Random Graph Model

Description

simulate is used to draw from exponential family random network models. See ergm() for more information on these models.

The method for ergm objects inherits the model, the coefficients, the response attribute, the reference, the constraints, and most simulation parameters from the model fit, unless overridden by passing them explicitly. Unless overridden, the simulation is initialized with either a random draw from near the fitted model saved by ergm() or, if unavailable, the network to which the ERGM was fit.

Usage

## S3 method for class 'formula_lhs_network'
simulate(object, nsim = 1, seed = NULL, ...)

simulate_formula(object, ..., basis = eval_lhs.formula(object))

## S3 method for class 'network'
simulate_formula(
  object,
  nsim = 1,
  seed = NULL,
  coef,
  response = NULL,
  reference = ~Bernoulli,
  constraints = ~.,
  observational = FALSE,
  monitor = NULL,
  statsonly = FALSE,
  esteq = FALSE,
  output = c("network", "stats", "edgelist", "ergm_state"),
  simplify = TRUE,
  sequential = TRUE,
  control = control.simulate.formula(),
  verbose = FALSE,
  ...,
  basis = ergm.getnetwork(object),
  do.sim = NULL,
  return.args = NULL
)

## S3 method for class 'ergm_state'
simulate_formula(
  object,
  nsim = 1,
  seed = NULL,
  coef,
  response = NULL,
  reference = ~Bernoulli,
  constraints = ~.,
  observational = FALSE,
  monitor = NULL,
  statsonly = FALSE,
  esteq = FALSE,
  output = c("network", "stats", "edgelist", "ergm_state"),
  simplify = TRUE,
  sequential = TRUE,
  control = control.simulate.formula(),
  verbose = FALSE,
  ...,
  basis = ergm.getnetwork(object),
  do.sim = NULL,
  return.args = NULL
)

## S3 method for class 'ergm_model'
simulate(
  object,
  nsim = 1,
  seed = NULL,
  coef,
  reference = if (is(constraints, "ergm_proposal")) NULL else trim_env(~Bernoulli),
  constraints = trim_env(~.),
  observational = FALSE,
  monitor = NULL,
  basis = NULL,
  esteq = FALSE,
  output = c("network", "stats", "edgelist", "ergm_state"),
  simplify = TRUE,
  sequential = TRUE,
  control = control.simulate.formula(),
  verbose = FALSE,
  ...,
  do.sim = NULL,
  return.args = NULL
)

## S3 method for class 'ergm_state_full'
simulate(
  object,
  nsim = 1,
  seed = NULL,
  coef,
  esteq = FALSE,
  output = c("network", "stats", "edgelist", "ergm_state"),
  simplify = TRUE,
  sequential = TRUE,
  control = control.simulate.formula(),
  verbose = FALSE,
  ...,
  return.args = NULL
)

## S3 method for class 'ergm'
simulate(
  object,
  nsim = 1,
  seed = NULL,
  coef = coefficients(object),
  response = object$network %ergmlhs% "response",
  reference = object$reference,
  constraints = list(object$constraints, object$obs.constraints),
  observational = FALSE,
  monitor = NULL,
  basis = if (observational) object$network else NVL(object$newnetwork, object$network),
  statsonly = FALSE,
  esteq = FALSE,
  output = c("network", "stats", "edgelist", "ergm_state"),
  simplify = TRUE,
  sequential = TRUE,
  control = control.simulate.ergm(),
  verbose = FALSE,
  ...,
  return.args = NULL
)

Arguments

object

Either a formula or an ergm object. The formula should be of the form y ~ <model terms>, where y is a network object or a matrix that can be coerced to a network object. For the details on the possible <model terms>, see ergmTerm. To create a network object in , use the network() function, then add nodal attributes to it using the %v% operator if necessary.
nsim

Number of networks to be randomly drawn from the given distribution on the set of all networks, returned by the Metropolis-Hastings algorithm.
seed

Seed value (integer) for the random number generator. See set.seed().
...

Further arguments passed to or used by methods.
basis

a value (usually a network) to override the LHS of the formula.
coef

Vector of parameter values for the model from which the sample is to be drawn. If object is of class ergm, the default value is the vector of estimated coefficients. Can be set to NULL to bypass, but only if return.args below is used.
response

Either a character string, a formula, or NULL (the default), to specify the response attributes and whether the ERGM is binary or valued. Interpreted as follows:

NULL

Model simple presence or absence, via a binary ERGM.

character string

The name of the edge attribute whose value is to be modeled. Type of ERGM will be determined by whether the attribute is logical (TRUE/FALSE) for binary or numeric for valued.

a formula

must be of the form NAME~EXPR|TYPE (with | being literal). EXPR is evaluated in the formula's environment with the network's edge attributes accessible as variables. The optional NAME specifies the name of the edge attribute into which the results should be stored, with the default being a concise version of EXPR. Normally, the type of ERGM is determined by whether the result of evaluating EXPR is logical or numeric, but the optional TYPE can be used to override by specifying a scalar of the type involved (e.g., TRUE for binary and 1 for valued).
reference

A one-sided formula specifying the reference measure (h(y)h(y)) to be used. See help for ERGM reference measures implemented in the ergm package.
constraints

A formula specifying one or more constraints on the support of the distribution of the networks being modeled. Multiple constraints may be given, separated by “+” and “-” operators. See ergmConstraint for the detailed explanation of their semantics and also for an indexed list of the constraints visible to the ergm package.

The default is to have no constraints except those provided through the ergmlhs API.

Together with the model terms in the formula and the reference measure, the constraints define the distribution of networks being modeled.

It is also possible to specify a proposal function directly either by passing a string with the function's name (in which case, arguments to the proposal should be specified through the MCMC.prop.args argument to the relevant control function, or by giving it on the LHS of the hints formula to MCMC.prop argument to the control function. This will override the one chosen automatically.

Note that not all possible combinations of constraints and reference measures are supported. However, for relatively simple constraints (i.e., those that simply permit or forbid specific dyads or sets of dyads from changing), arbitrary combinations should be possible.
observational

Inherit observational constraints rather than model constraints.
monitor

A one-sided formula specifying one or more terms whose value is to be monitored. These terms are appended to the model, along with a coefficient of 0, so their statistics are returned. An ergm_model objectcan be passed as well.
statsonly

Logical: If TRUE, return only the network statistics, not the network(s) themselves. Deprecated in favor of ⁠output=⁠.
esteq

Logical: If TRUE, compute the sample estimating equations of an ERGM: if the model is non-curved, all non-offset statistics are returned either way, but if the model is curved, the score estimating function values (3.1) by Hunter and Handcock (2006) are returned instead.
output

Normally character, one of "network" (default), "stats", "edgelist", or "ergm_state": determines the output format. Partial matching is performed.

Alternatively, a function with prototype ⁠function(ergm_state, chain, iter, ...)⁠ that is called for each returned network, and its return value, rather than the network itself, is stored. This can be used to, for example, store the simulated networks to disk without storing them in memory or compute network statistics not implemented using the ERGM API, without having to store the networks themselves.
simplify

Logical: If TRUE the output is "simplified": sampled networks are returned in a single list, statistics from multiple parallel chains are stacked, etc.. This makes it consistent with behavior prior to ergm 3.10.
sequential

Logical: If FALSE, each of the nsim simulated Markov chains begins at the initial network. If TRUE, the end of one simulation is used as the start of the next. Irrelevant when nsim=1.
control

A list of control parameters for algorithm tuning, typically constructed with control.simulate.ergm() or control.simulate.formula(), which have different defaults. Their documentation gives the the list of recognized control parameters and their meaning. The more generic utility snctrl() (StatNet ConTRoL) also provides argument completion for the available control functions and limited argument name checking.
verbose

A logical or an integer to control the amount of progress and diagnostic information to be printed. FALSE/0 produces minimal output, with higher values producing more detail. Note that very high values (5+) may significantly slow down processing.
do.sim

Logical; a deprecated interface superseded by return.args, that saves the inputs to the next level of the function.
return.args

Character; if not NULL, the simulate method for that particular class will, instead of proceeding for simulation, instead return its arguments as a list that can be passed as a second argument to do.call() or a lower-level function such as ergm_MCMC_sample(). This can be useful if, for example, one wants to run several simulations with varying coefficients and does not want to reinitialize the model and the proposal every time. Valid inputs at this time are "formula", "ergm_model", and one of the "ergm_state" classes, for the three respective stopping points.

Details

A sample of networks is randomly drawn from the specified model. The model is specified by the first argument of the function. If the first argument is a formula then this defines the model. If the first argument is the output of a call to ergm() then the model used for that call is the one fit – and unless coef is specified, the sample is from the MLE of the parameters. If neither of those are given as the first argument then a Bernoulli network is generated with the probability of ties defined by prob or coef.

Note that the first network is sampled after burnin steps, and any subsequent networks are sampled each interval steps after the first.

More information can be found by looking at the documentation of ergm().

Value

If output=="stats" an mcmc object containing the simulated network statistics. If control$parallel>0, an mcmc.list object. If simplify=TRUE (the default), these would then be "stacked" and converted to a standard matrix. A logical vector indicating whether or not the term had come from the ⁠monitor=⁠ formula is stored in attr()-style attribute "monitored".

Otherwise, a representation of the simulated network is returned, in the form specified by output. In addition to a network representation or a list thereof, they have the following attr()-style attributes:

formula

The formula used to generate the sample.

stats

An mcmc or mcmc.list object as above.

control

Control parameters used to generate the sample.

constraints

Constraints used to generate the sample.

reference

The reference measure for the sample.

monitor

The monitoring formula.

response

The edge attribute used as a response.

The following are the permitted network formats:

"network"

If nsim==1, an object of class network. If nsim>1, it returns an object of class network.list (a list of networks) with the above-listed additional attributes.

"edgelist"

An edgelist representation of the network, or a list thereof, depending on nsim.

"ergm_state"

A semi-internal representation of a network consisting of a network object emptied of edges, with an attached edgelist matrix, or a list thereof, depending on nsim.

If simplify==FALSE, the networks are returned as a nested list, with outer list being the parallel chain (including 1 for no parallelism) and inner list being the samples within that chains (including 1, if one network per chain). If TRUE, they are concatenated, and if a total of one network had been simulated, the network itself will be returned.

Functions

  • simulate(ergm_state_full): a low-level function to simulate from an ergm_state object.

Note

The actual network method for simulate_formula() is actually called .simulate_formula.network() and is also exported as an object. This allows it to be overridden by extension packages, such as tergm, but also accessed directly when needed.

simulate.ergm_model() is a lower-level interface, providing a simulate() method for the ergm_model class. The basis argument is required; monitor, if passed, must be an ergm_model as well; and constraints can be an ergm_proposal object instead.

See Also

ergm(), network, ergm_MCMC_sample() for a demonstration of ⁠return.args=⁠.

Examples

#
# Let's draw from a Bernoulli model with 16 nodes
# and density 0.5 (i.e., coef = c(0,0))
#
g.sim <- simulate(network(16) ~ edges + mutual, coef=c(0, 0))
#
# What are the statistics like?
#
summary(g.sim ~ edges + mutual)
#
# Now simulate a network with higher mutuality
#
g.sim <- simulate(network(16) ~ edges + mutual, coef=c(0,2))
#
# How do the statistics look?
#
summary(g.sim ~ edges + mutual)
#
# Let's draw from a Bernoulli model with 16 nodes
# and tie probability 0.1
#
g.use <- network(16,density=0.1,directed=FALSE)
#
# Starting from this network let's draw 3 realizations
# of a edges and 2-star network
#
g.sim <- simulate(~edges+kstar(2), nsim=3, coef=c(-1.8,0.03),
               basis=g.use, control=control.simulate(
                 MCMC.burnin=1000,
                 MCMC.interval=100))
g.sim
summary(g.sim)
#
# attach the Florentine Marriage data
#
data(florentine)
#
# fit an edges and 2-star model using the ergm function
#
gest <- ergm(flomarriage ~ edges + kstar(2))
summary(gest)
#
# Draw from the fitted model (statistics only), and observe the number
# of triangles as well.
#
g.sim <- simulate(gest, nsim=10, 
            monitor=~triangles, output="stats",
            control=control.simulate.ergm(MCMC.burnin=1000, MCMC.interval=100))
g.sim

# Custom output: store the edgecount (computed in R), iteration index, and chain index.
output.f <- function(x, iter, chain, ...){
  list(nedges = network.edgecount(as.network(x)),
       chain = chain, iter = iter)
}
g.sim <- simulate(gest, nsim=3,
            output=output.f, simplify=FALSE,
            control=control.simulate.ergm(MCMC.burnin=1000, MCMC.interval=100))
unclass(g.sim)

A simulate Method for formula objects that dispatches based on the Left-Hand Side

Description

This method evaluates the left-hand side (LHS) of the given formula and dispatches it to an appropriate method based on the result by setting an nonce class name on the formula.

Usage

## S3 method for class 'formula'
simulate(object, nsim = 1, seed = NULL, ..., basis, newdata, data)

## S3 method for class 'formula_lhs'
simulate(object, nsim = 1, seed = NULL, ...)

Arguments

object

a one- or two-sided formula.
nsim, seed

number of realisations to simulate and the random seed to use; see simulate().
...

additional arguments to methods.
basis

if given, overrides the LHS of the formula for the purposes of dispatching.
newdata, data

if passed, the object's LHS is evaluated in this environment; at most one of the two may be passed.

The dispatching works as follows:

  1. If basis is not passed, and the formula has an LHS the expression on the LHS of the formula in the object is evaluated in the environment newdata or data (if given), in any case enclosed by the environment of object. Otherwise, basis is used.

  2. The result is set as an attribute ".Basis" on object. If there is no basis or LHS, it is not set.

  3. The class vector of object has c("formula_lhs_CLASS", "formula_lhs") prepended to it, where CLASS is the class of the LHS value or basis. If LHS or basis has multiple classes, they are all prepended; if there is no LHS or basis, c("formula_lhs_", "formula_lhs") is.

  4. simulate() generic is evaluated on the new object, with all arguments passed on, excluding basis; if newdata or data are missing, they too are not passed on. The evaluation takes place in the parent's environment.

A "method" to receive a formula whose LHS evaluates to CLASS can therefore be implemented by a function ⁠simulate.formula_lhs_\var{CLASS}()⁠. This function can expect a formula object, with additional attribute .Basis giving the evaluated LHS (so that it does not need to be evaluated again).

Functions

  • simulate(formula_lhs): A function to catch the situation when there is no method implemented for the class to which the LHS evaluates.

See Also

simulate.ergm() family of functions, which uses this interface.

Number of ties between actors with similar attribute values

Description

This term adds one statistic, having as its value the number of edges in the network for which the incident actors' attribute values differ less than cutoff ; that is, number of edges between i to j such that abs(attr[i]-attr[j])<cutoff .

Usage

# binary: smalldiff(attr, cutoff)

Arguments

attr

a vertex attribute specification (see Specifying Vertex attributes and Levels (?nodal_attributes) for details.)
maximum

difference in attribute values for ties to be considered

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

directed, dyad-independent, quantitative nodal attribute, undirected, binary

Number of dyads with values strictly smaller than a threshold

Description

Adds the number of statistics equal to the length of threshold equaling to the number of dyads whose values are exceeded by the corresponding element of threshold .

Usage

# valued: smallerthan(threshold=0)

Arguments

threshold

vector of numerical values

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

directed, dyad-independent, undirected, valued

Statnet Control

Description

A utility to facilitate argument completion of control lists, reexported from statnet.common.

Currently recognised control parameters

This list is updated as packages are loaded and unloaded.

Package ergm

control.ergm

drop, init, init.method, main.method, force.main, main.hessian, checkpoint, resume, MPLE.samplesize, init.MPLE.samplesize, MPLE.type, MPLE.maxit, MPLE.nonvar, MPLE.nonident, MPLE.nonident.tol, MPLE.covariance.samplesize, MPLE.covariance.method, MPLE.covariance.sim.burnin, MPLE.covariance.sim.interval, MPLE.check, MPLE.constraints.ignore, MCMC.prop, MCMC.prop.weights, MCMC.prop.args, MCMC.interval, MCMC.burnin, MCMC.samplesize, MCMC.effectiveSize, MCMC.effectiveSize.damp, MCMC.effectiveSize.maxruns, MCMC.effectiveSize.burnin.pval, MCMC.effectiveSize.burnin.min, MCMC.effectiveSize.burnin.max, MCMC.effectiveSize.burnin.nmin, MCMC.effectiveSize.burnin.nmax, MCMC.effectiveSize.burnin.PC, MCMC.effectiveSize.burnin.scl, MCMC.effectiveSize.order.max, MCMC.return.stats, MCMC.runtime.traceplot, MCMC.maxedges, MCMC.addto.se, MCMC.packagenames, SAN.maxit, SAN.nsteps.times, SAN, MCMLE.termination, MCMLE.maxit, MCMLE.conv.min.pval, MCMLE.confidence, MCMLE.confidence.boost, MCMLE.confidence.boost.threshold, MCMLE.confidence.boost.lag, MCMLE.NR.maxit, MCMLE.NR.reltol, obs.MCMC.mul, obs.MCMC.samplesize.mul, obs.MCMC.samplesize, obs.MCMC.effectiveSize, obs.MCMC.interval.mul, obs.MCMC.interval, obs.MCMC.burnin.mul, obs.MCMC.burnin, obs.MCMC.prop, obs.MCMC.prop.weights, obs.MCMC.prop.args, obs.MCMC.impute.min_informative, obs.MCMC.impute.default_density, MCMLE.min.depfac, MCMLE.sampsize.boost.pow, MCMLE.MCMC.precision, MCMLE.MCMC.max.ESS.frac, MCMLE.metric, MCMLE.method, MCMLE.dampening, MCMLE.dampening.min.ess, MCMLE.dampening.level, MCMLE.steplength.margin, MCMLE.steplength, MCMLE.steplength.parallel, MCMLE.sequential, MCMLE.density.guard.min, MCMLE.density.guard, MCMLE.effectiveSize, obs.MCMLE.effectiveSize, MCMLE.interval, MCMLE.burnin, MCMLE.samplesize.per_theta, MCMLE.samplesize.min, MCMLE.samplesize, obs.MCMLE.samplesize.per_theta, obs.MCMLE.samplesize.min, obs.MCMLE.samplesize, obs.MCMLE.interval, obs.MCMLE.burnin, MCMLE.steplength.solver, MCMLE.last.boost, MCMLE.steplength.esteq, MCMLE.steplength.miss.sample, MCMLE.steplength.min, MCMLE.effectiveSize.interval_drop, MCMLE.save_intermediates, MCMLE.nonvar, MCMLE.nonident, MCMLE.nonident.tol, SA.phase1_n, SA.initial_gain, SA.nsubphases, SA.min_iterations, SA.max_iterations, SA.phase3_n, SA.interval, SA.burnin, SA.samplesize, CD.samplesize.per_theta, obs.CD.samplesize.per_theta, CD.nsteps, CD.multiplicity, CD.nsteps.obs, CD.multiplicity.obs, CD.maxit, CD.conv.min.pval, CD.NR.maxit, CD.NR.reltol, CD.metric, CD.method, CD.dampening, CD.dampening.min.ess, CD.dampening.level, CD.steplength.margin, CD.steplength, CD.adaptive.epsilon, CD.steplength.esteq, CD.steplength.miss.sample, CD.steplength.min, CD.steplength.parallel, CD.steplength.solver, loglik, term.options, seed, parallel, parallel.type, parallel.version.check, parallel.inherit.MT, ...

control.ergm.bridge

bridge.nsteps, bridge.target.se, bridge.bidirectional, drop, MCMC.burnin, MCMC.burnin.between, MCMC.interval, MCMC.samplesize, obs.MCMC.burnin, obs.MCMC.burnin.between, obs.MCMC.interval, obs.MCMC.samplesize, MCMC.prop, MCMC.prop.weights, MCMC.prop.args, obs.MCMC.prop, obs.MCMC.prop.weights, obs.MCMC.prop.args, MCMC.maxedges, MCMC.packagenames, term.options, seed, parallel, parallel.type, parallel.version.check, parallel.inherit.MT, ...

control.ergm.godfather

term.options

control.gof.ergm

nsim, MCMC.burnin, MCMC.interval, MCMC.batch, MCMC.prop, MCMC.prop.weights, MCMC.prop.args, MCMC.maxedges, MCMC.packagenames, MCMC.runtime.traceplot, network.output, seed, parallel, parallel.type, parallel.version.check, parallel.inherit.MT

control.gof.formula

nsim, MCMC.burnin, MCMC.interval, MCMC.batch, MCMC.prop, MCMC.prop.weights, MCMC.prop.args, MCMC.maxedges, MCMC.packagenames, MCMC.runtime.traceplot, network.output, seed, parallel, parallel.type, parallel.version.check, parallel.inherit.MT

control.logLik.ergm

bridge.nsteps, bridge.target.se, bridge.bidirectional, drop, MCMC.burnin, MCMC.interval, MCMC.samplesize, obs.MCMC.samplesize, obs.MCMC.interval, obs.MCMC.burnin, MCMC.prop, MCMC.prop.weights, MCMC.prop.args, obs.MCMC.prop, obs.MCMC.prop.weights, obs.MCMC.prop.args, MCMC.maxedges, MCMC.packagenames, term.options, seed, parallel, parallel.type, parallel.version.check, parallel.inherit.MT, ...

control.san

SAN.maxit, SAN.tau, SAN.invcov, SAN.invcov.diag, SAN.nsteps.alloc, SAN.nsteps, SAN.samplesize, SAN.prop, SAN.prop.weights, SAN.prop.args, SAN.packagenames, SAN.ignore.finite.offsets, term.options, seed, parallel, parallel.type, parallel.version.check, parallel.inherit.MT

control.simulate

MCMC.burnin, MCMC.interval, MCMC.prop, MCMC.prop.weights, MCMC.prop.args, MCMC.batch, MCMC.effectiveSize, MCMC.effectiveSize.damp, MCMC.effectiveSize.maxruns, MCMC.effectiveSize.burnin.pval, MCMC.effectiveSize.burnin.min, MCMC.effectiveSize.burnin.max, MCMC.effectiveSize.burnin.nmin, MCMC.effectiveSize.burnin.nmax, MCMC.effectiveSize.burnin.PC, MCMC.effectiveSize.burnin.scl, MCMC.effectiveSize.order.max, MCMC.maxedges, MCMC.packagenames, MCMC.runtime.traceplot, network.output, term.options, parallel, parallel.type, parallel.version.check, parallel.inherit.MT, ...

control.simulate.ergm

MCMC.burnin, MCMC.interval, MCMC.scale, MCMC.prop, MCMC.prop.weights, MCMC.prop.args, MCMC.batch, MCMC.effectiveSize, MCMC.effectiveSize.damp, MCMC.effectiveSize.maxruns, MCMC.effectiveSize.burnin.pval, MCMC.effectiveSize.burnin.min, MCMC.effectiveSize.burnin.max, MCMC.effectiveSize.burnin.nmin, MCMC.effectiveSize.burnin.nmax, MCMC.effectiveSize.burnin.PC, MCMC.effectiveSize.burnin.scl, MCMC.effectiveSize.order.max, MCMC.maxedges, MCMC.packagenames, MCMC.runtime.traceplot, network.output, term.options, parallel, parallel.type, parallel.version.check, parallel.inherit.MT, ...

control.simulate.formula

MCMC.burnin, MCMC.interval, MCMC.prop, MCMC.prop.weights, MCMC.prop.args, MCMC.batch, MCMC.effectiveSize, MCMC.effectiveSize.damp, MCMC.effectiveSize.maxruns, MCMC.effectiveSize.burnin.pval, MCMC.effectiveSize.burnin.min, MCMC.effectiveSize.burnin.max, MCMC.effectiveSize.burnin.nmin, MCMC.effectiveSize.burnin.nmax, MCMC.effectiveSize.burnin.PC, MCMC.effectiveSize.burnin.scl, MCMC.effectiveSize.order.max, MCMC.maxedges, MCMC.packagenames, MCMC.runtime.traceplot, network.output, term.options, parallel, parallel.type, parallel.version.check, parallel.inherit.MT, ...

control.simulate.formula.ergm

MCMC.burnin, MCMC.interval, MCMC.prop, MCMC.prop.weights, MCMC.prop.args, MCMC.batch, MCMC.effectiveSize, MCMC.effectiveSize.damp, MCMC.effectiveSize.maxruns, MCMC.effectiveSize.burnin.pval, MCMC.effectiveSize.burnin.min, MCMC.effectiveSize.burnin.max, MCMC.effectiveSize.burnin.nmin, MCMC.effectiveSize.burnin.nmax, MCMC.effectiveSize.burnin.PC, MCMC.effectiveSize.burnin.scl, MCMC.effectiveSize.order.max, MCMC.maxedges, MCMC.packagenames, MCMC.runtime.traceplot, network.output, term.options, parallel, parallel.type, parallel.version.check, parallel.inherit.MT, ...

See Also

statnet.common::snctrl()

Undirected degree

Description

This term adds one network statistic for each node equal to the number of ties of that node. For directed networks, see sender and receiver .

Usage

# binary: sociality(attr=NULL, base=1, levels=NULL, nodes=-1)

# valued: sociality(attr=NULL, base=1, levels=NULL, nodes=-1, form="sum")

Arguments

attr, levels

this optional argument is deprecated and will be replaced with a more elegant implementation in a future release. In the meantime, it specifies a categorical vertex attribute (see Specifying Vertex attributes and Levels (?nodal_attributes) for details). If provided, this term only counts ties between nodes with the same value of the attribute (an actor-specific version of the nodematch term), restricted to be one of the values specified by (also deprecated) levels if levels is not NULL .
base

deprecated
nodes

By default, nodes=-1 means that the statistic for the first node will be omitted, but this argument may be changed to control which statistics are included just as for the nodes argument of sender and receiver terms.
form

character how to aggregate tie values in a valued ERGM

Note

The argument base is retained for backwards compatibility and may be removed in a future version. When both base and levels are passed, levels overrides base.

The argument base is retained for backwards compatibility and may be removed in a future version. When both base and nodes are passed, nodes overrides base.

This term can only be used with undirected networks.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

categorical nodal attribute, dyad-independent, undirected, binary, valued

Sparse network

Description

The network is sparse. This typically results in a Tie-Non-Tie (TNT) proposal regime.

Usage

# sparse

See Also

ergmHint for index of constraints and hints currently visible to the package.

Keywords

dyad-independent

Multivariate version of coda's spectrum0.ar().

Description

Its return value, divided by nrow(cbind(x)), is the estimated variance-covariance matrix of the sampling distribution of the mean of x if x is a multivatriate time series with AR(pp) structure, with pp determined by AIC.

Usage

spectrum0.mvar(
  x,
  order.max = NULL,
  aic = is.null(order.max),
  tol = .Machine$double.eps^0.5,
  ...
)

Arguments

x

a matrix with observations in rows and variables in columns.
order.max

maximum (or fixed) order for the AR model.
aic

use AIC to select the order (up to order.max).
tol

tolerance used in detecting multicollinearity. See Note below.
...

additional arguments to ar().

Value

A square matrix with dimension equalling to the number of columns of x, with an additional attribute "infl" giving the factor by which the effective sample size is reduced due to autocorrelation, according to the Vats, Flegal, and Jones (2015) estimate for ESS.

Note

ar() fails if crossprod(x) is singular. This is is remedied as follows:

  1. Standardize the variables.

  2. Use the eigenvectors to map the variables onto their principal components.

  3. Use the eigenvalues to standardize the principal components.

  4. Drop those components whose standard deviation differs from 1 by more than tol. This should filter out redundant components or those too numerically unstable.

  5. Call ar() and calculate the variance.

  6. Reverse the mapping in steps 1-4 to obtain the variance of the original data.

Standard Normal reference

Description

Specifies each dyad's baseline distribution to be the normal distribution with mean 0 and variance 1.

Usage

# StdNormal

See Also

ergmReference for index of reference distributions currently visible to the package.

Keywords

continuous

Stratify Proposed Toggles by Mixing Type on a Vertex Attribute

Description

Proposed toggles are stratified according to mixing type on a vertex attribute.

Usage

# strat(attr=NULL, pmat=NULL, empirical=FALSE)

Details

The user may pass a vertex attribute attr as an argument (the default for attr gives every vertex the same attribute value), and may also pass a matrix of weights pmat (the default for pmat gives equal weight to each mixing type). See Specifying Vertex Attributes and Levels for details on specifying vertex attributes. The matrix pmat, if specified, must have the same dimensions as a mixing matrix for the network and vertex attribute under consideration, and the correspondence between rows and columns of pmat and values of attr is the same as for a mixing matrix.

The interpretation is that pmat[i,j]/sum(pmat) is the probability of proposing a toggle for mixing type ⁠(i,j)⁠. (For undirected, unipartite networks, pmat is first symmetrized, and then entries below the diagonal are set to zero. Only entries on or above the diagonal of the symmetrized pmat are considered when making proposals. This accounts for the convention that mixing is undirected in an undirected, unipartite network: a tail of type i and a head of type j has the same mixing type as a tail of type j and a head of type i.)

As an alternative way of specifying pmat, the user may pass empirical = TRUE to use the mixing matrix of the network beginning the MCMC chain as pmat. In order for this to work, that network should have a reasonable (in particular, nonempty) edge set.

While some mixing types may be assigned zero proposal probability (either with a direct specification of pmat or with empirical = TRUE), this will not be recognized as a constraint by all components of ergm, and should be used with caution.

See Also

ergmHint for index of constraints and hints currently visible to the package.

Keywords

dyad-independent

Sum of dyad values (optionally taken to a power)

Description

This term adds one statistic equal to the sum of dyad values taken to the power pow.

Usage

# valued: sum(pow=1)

Arguments

pow

power of dyad values. Defaults to 1.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

directed, undirected, valued

A sum (or an arbitrary linear combination) of one or more formulas

Description

This operator sums up the RHS statistics of the input formulas elementwise.

Usage

# binary: Sum(formulas, label)

# valued: Sum(formulas, label)

Arguments

formulas

a list (constructed using list() or c()) of ergm()-style formulas whose RHS gives the statistics to be evaluated, or a single formula.

If a formula in the list has an LHS, it is interpreted as follows:

  • a numeric scalar: Network statistics of this formula will be multiplied by this.

  • a numeric vector: Corresponding network statistics of this formula will be multiplied by this.

  • a numeric matrix: Vector of network statistics will be pre-multiplied by this.

  • a character string: One of several predefined linear combinations. Currently supported presets are as follows:

    • "sum" Network statistics of this formula will be summed up; equivalent to matrix(1,1,p) , where p is the length of the network statistic vector.

    • "mean" Network statistics of this formula will be averaged; equivalent to matrix(1/p,1,p) , where p is the length of the network statistic vector.

label

used to specify the names of the elements of the resulting term sum vector. If label is a character vector of length 1, it will be recycled with indices appended. If a function is specified, formulas parameter names are extracted and their list of character vectors is passed label.

Details

Note that each formula must either produce the same number of statistics or be mapped through a matrix to produce the same number of statistics.

A single formula is also permitted. This can be useful if one wishes to, say, scale or sum up the statistics returned by a formula.

Offsets are ignored unless there is only one formula and the transformation only scales the statistics (i.e., the effective transformation matrix is diagonal).

Curved models are supported, subject to some limitations. In particular, the first model's etamap will be used, overwriting the others. If label is not of length 1, it should have an attr -style attribute "curved" specifying the names for the curved parameters.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

operator, binary, valued

Summarizing ERGM Model Fits

Description

base::summary() method for ergm() fits.

Usage

## S3 method for class 'ergm'
summary(
  object,
  ...,
  correlation = FALSE,
  covariance = FALSE,
  total.variation = TRUE
)

## S3 method for class 'summary.ergm'
print(
  x,
  digits = max(3, getOption("digits") - 3),
  correlation = x$correlation,
  covariance = x$covariance,
  signif.stars = getOption("show.signif.stars"),
  eps.Pvalue = 1e-04,
  print.formula = FALSE,
  print.fitinfo = TRUE,
  print.coefmat = TRUE,
  print.message = TRUE,
  print.deviances = TRUE,
  print.drop = TRUE,
  print.offset = TRUE,
  print.call = TRUE,
  ...
)

Arguments

object

an object of class ergm, usually, a result of a call to ergm().
...

For summary.ergm() additional arguments are passed to logLik.ergm(). For print.summary.ergm(), to stats::printCoefmat().
correlation

logical; if TRUE, the correlation matrix of the estimated parameters is returned and printed.
covariance

logical; if TRUE, the covariance matrix of the estimated parameters is returned and printed.
total.variation

logical; if TRUE, the standard errors reported in the ⁠Std. Error⁠ column are based on the sum of the likelihood variation and the MCMC variation. If FALSE only the likelihood variation is used. The pp-values are based on this source of variation.
x

object of class summary.ergm returned by summary.ergm().
digits

significant digits for coefficients
signif.stars

whether to print dots and stars to signify statistical significance. See print.summary.lm().
eps.Pvalue

pp-values below this level will be printed as "<eps.Pvalue".
print.formula, print.fitinfo, print.coefmat, print.message, print.deviances, print.drop, print.offset, print.call

which components of the fit summary to print.

Details

summary.ergm() tries to be smart about formatting the coefficients, standard errors, etc.

The default printout of the summary object contains the call, number of iterations used, null and residual deviances, and the values of AIC and BIC (and their MCMC standard errors, if applicable). The coefficient table contains the following columns:

  • Estimate, ⁠Std. Error⁠ - parameter estimates and their standard errors

  • ⁠MCMC %⁠ - if total.variation=TRUE (default) the percentage of standard error attributable to MCMC estimation process rounded to an integer. See also vcov.ergm() and its sources argument.

  • ⁠z value⁠, ⁠Pr(>|z|)⁠ - z-test and p-values

Value

The returned object is a list of class "ergm.summary" with the following elements:

formula

ERGM model formula
call

R call used to fit the model
correlation, covariance

whether to print correlation/covariance matrices of the estimated parameters
pseudolikelihood

was the model estimated with MPLE
independence

is the model dyad-independent
control

the control.ergm() object used
samplesize

MCMC sample size
message

optional message on the validity of the standard error estimates
null.lik.0

It is TRUE of the null model likelihood has not been calculated. See logLikNull()
devtext, devtable

Deviance type and table
aic, bic

values of AIC and BIC
coefficients

matrices with model parameters and associated statistics
asycov

asymptotic covariance matrix
asyse

asymptotic standard error matrix
offset, drop, estimate, iterations, mle.lik, null.lik

see documentation of the object returned by ergm()

See Also

The model fitting function ergm(), print.ergm(), and base::summary(). Function stats::coef() will extract the matrix of coefficients with standard errors, t-statistics and p-values.

Examples

data(florentine)

 x <- ergm(flomarriage ~ density)
 summary(x)

Calculation of network or graph statistics or other attributes specified on a formula

Description

Most generally, this function computes those summaries of the object on the LHS of the formula that are specified by its RHS. In particular, if given a network as its LHS and ergmTerm on its RHS, it computes the sufficient statistics associated with those terms.

Usage

## S3 method for class 'formula'
summary(object, ...)

Arguments

object

A formula having as its LHS a network object or a matrix that can be coerced to a network object, a network.list, or other types to be summarized using a formula. (See ‘methods(’summary_formula') for the possible LHS types.
...

further arguments passed to or used by methods.

Details

In practice, summary.formula() is a thin wrapper around the summary_formula() generic, which dispatches methods based on the class of the LHS of the formula.

Value

A vector of statistics specified in RHS of the formula.

See Also

ergm(), network(), ergmTerm

Examples

#
# Lets look at the Florentine marriage data
#
data(florentine)
#
# test the summary_formula function
#
summary(flomarriage ~ edges + kstar(2))
m <- as.matrix(flomarriage)
summary(m ~ edges)  # twice as large as it should be
summary(m ~ edges, directed=FALSE) # Now it's correct

Evaluation on symmetrized (undirected) network

Description

Evaluates the terms in formula on an undirected network constructed by symmetrizing the LHS network using one of four rules:

  1. "weak" A tie (i,j)(i,j) is present in the constructed network if the LHS network has either tie (i,j)(i,j) or (j,i)(j,i) (or both).

  2. "strong" A tie (i,j)(i,j) is present in the constructed network if the LHS network has both tie (i,j)(i,j) and tie (j,i)(j,i) .

  3. "upper" A tie (i,j)(i,j) is present in the constructed network if the LHS network has tie (min⁡(i,j),max⁡(i,j))(\min(i,j),\max(i,j)) : the upper triangle of the LHS network.

  4. "lower" A tie (i,j)(i,j) is present in the constructed network if the LHS network has tie (max⁡(i,j),min⁡(i,j))(\max(i,j),\min(i,j)) : the lower triangle of the LHS network.

Usage

# binary: Symmetrize(formula, rule="weak")

Arguments

formula

a one-sided ergm()-style formula with the terms to be evaluated
rule

one of "weak", "strong", "upper", "lower"

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

directed, operator, binary

Three-trails

Description

For an undirected network, this term adds one statistic equal to the number of 3-trails, where a 3-trail is defined as a trail of length three that traverses three distinct edges. Note that a 3-trail need not include four distinct nodes; in particular, a triangle counts as three 3-trails. For a directed network, this term adds four statistics (or some subset of these four), one for each of the four distinct types of directed three-paths. If the nodes of the path are written from left to right such that the middle edge points to the right (R), then the four types are RRR, RRL, LRR, and LRL. That is, an RRR 3-trail is of the form i→j→k→li\rightarrow j\rightarrow k\rightarrow l , and RRL 3-trail is of the form i→j→k←li\rightarrow j\rightarrow k\leftarrow l , etc. Like in the undirected case, there is no requirement that the nodes be distinct in a directed 3-trail. However, the three edges must all be distinct. Thus, a mutual tie i↔ji\leftrightarrow j does not count as a 3-trail of the form i→j→i←ji\rightarrow j\rightarrow i\leftarrow j ; however, in the subnetwork i↔j→ki\leftrightarrow j \rightarrow k , there are two directed 3-trails, one LRR ( k←j→i←jk\leftarrow j\rightarrow i\leftarrow j ) and one RRR ( j→i→j←kj\rightarrow i\rightarrow j\leftarrow k ).

Usage

# binary: threetrail(keep=NULL, levels=NULL)

# binary: threepath(keep=NULL, levels=NULL)

Arguments

keep

deprecated
levels

specify a subset of the four statistics for directed networks. (See Specifying Vertex attributes and Levels (?nodal_attributes) for details.)

Note

The argument keep is retained for backwards compatibility and may be removed in a future version. When both keep and levels are passed, levels overrides keep.

This term used to be (inaccurately) called threepath . That name has been deprecated and may be removed in a future version.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

directed, triad-related, undirected, binary

Transitive triads

Description

This term adds one statistic to the model, equal to the number of triads in the network that are transitive. The transitive triads are those of type ⁠120D⁠ , ⁠030T⁠ , ⁠120U⁠ , or 300 in the categorization of Davis and Leinhardt (1972). For details on the 16 possible triad types, see ?triad.classify in the sna package. Note the distinction from the ttriple term. This term can only be used with directed networks.

Usage

# binary: transitive

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

directed, triad-related, binary

Transitive ties

Description

This term adds one statistic, equal to the number of ties i→ji\rightarrow j such that there exists a two-path from ii to jj . (Related to the ttriple term.)

Usage

# binary: transitiveties(attr=NULL, levels=NULL)

Arguments

attr

quantitative attribute (see Specifying Vertex attributes and Levels (?nodal_attributes) for details.) If set, all three nodes involved ( ii , jj , and the node on the two-path) must match on this attribute in order for i→ji\rightarrow j to be counted.
levels

TODO (See Specifying Vertex attributes and Levels (?nodal_attributes) for details.)

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

categorical nodal attribute, directed, triad-related, undirected, binary

Transitive weights

Description

This statistic implements the transitive weights statistic defined by Krivitsky (2012), Equation 13. For each of these options, the first (and the default) is more stable but also more conservative, while the second is more sensitive but more likely to induce a multimodal distribution of networks.

Usage

# valued: transitiveweights(twopath="min", combine="max", affect="min")

Arguments

twopath

the minimum of the constituent dyads ( "min" ) or their geometric mean ( "geomean" )
combine

the maximum of the 2-path strengths ( "max" ) or their sum ( "sum" )
affect

the minimum of the focus dyad and the combined strength of the two paths ( "min" ) or their geometric mean ( "geomean" )

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

directed, nonnegative, triad-related, undirected, valued

Triad census

Description

For a directed network, this term adds one network statistic for each of an arbitrary subset of the 16 possible types of triads categorized by Davis and Leinhardt (1972) as ⁠003, 012, 102, 021D, 021U, 021C, 111D, ⁠ ⁠ 111U, 030T, 030C, 201, 120D, 120U, 120C, 210,⁠ and 300 . Note that at least one category should be dropped; otherwise a linear dependency will exist among the 16 statistics, since they must sum to the total number of three-node sets. By default, the category 003 , which is the category of completely empty three-node sets, is dropped. This is considered category zero, and the others are numbered 1 through 15 in the order given above. Each statistic is the count of the corresponding triad type in the network. For details on the 16 types, see ?triad.classify in the sna package, on which this code is based. For an undirected network, the triad census is over the four types defined by the number of ties (i.e., 0, 1, 2, and 3).

Usage

# binary: triadcensus(levels)

Arguments

levels

For directed networks, specify a set of terms to add other than the default value of 1:15. attributes and Levels (?nodal_attributes) for details.)

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

directed, triad-related, undirected, binary

Network with strong clustering (triad-closure) effects

Description

The network has a high clustering coefficient. This typically results in alternating between the Tie-Non-Tie (TNT) proposal and a triad-focused proposal along the lines of that of Wang and Atchadé (2013).

Usage

# triadic(triFocus = 0.25, type="OTP")

# .triadic(triFocus = 0.25, type = "OTP")

Arguments

triFocus

A number between 0 and 1, indicating how often triad-focused proposals should be made relative to the standard proposals.
type

A string indicating the type of shared partner or path to be considered for directed networks: "OTP" (default for directed), "ITP", "RTP", "OSP", and "ISP"; has no effect for undirected. See the section below on Shared partner types for details.

Shared partner types

While there is only one shared partner configuration in the undirected case, nine distinct configurations are possible for directed graphs, selected using the type argument. Currently, terms may be defined with respect to five of these configurations; they are defined here as follows (using terminology from Butts (2008) and the relevent package):

  • Outgoing Two-path ("OTP"): vertex kk is an OTP shared partner of ordered pair (i,j)(i,j) iff i→k→ji \to k \to j. Also known as "transitive shared partner".

  • Incoming Two-path ("ITP"): vertex kk is an ITP shared partner of ordered pair (i,j)(i,j) iff j→k→ij \to k \to i. Also known as "cyclical shared partner"

  • Reciprocated Two-path ("RTP"): vertex kk is an RTP shared partner of ordered pair (i,j)(i,j) iff i↔k↔ji \leftrightarrow k \leftrightarrow j.

  • Outgoing Shared Partner ("OSP"): vertex kk is an OSP shared partner of ordered pair (i,j)(i,j) iff i→k,j→ki \to k, j \to k.

  • Incoming Shared Partner ("ISP"): vertex kk is an ISP shared partner of ordered pair (i,j)(i,j) iff k→i,k→jk \to i, k \to j.

By default, outgoing two-paths ("OTP") are calculated. Note that Robins et al. (2009) define closely related statistics to several of the above, using slightly different terminology.

.triadic() versus triadic()

If given a bipartite network, the dotted form will skip silently, whereas the plain form will raise an error, since triadic effects are not possible in bipartite networks. The dotted form is thus suitable as a default argument when the bipartitedness of the network is not known a priori.

References

Wang J, Atchadé YF (2013). “Approximate Bayesian Computation for Exponential Random Graph Models for Large Social Networks.” Communications in Statistics - Simulation and Computation, 43(2), 359–377. ISSN 1532-4141, doi:10.1080/03610918.2012.703359.

See Also

ergmHint for index of constraints and hints currently visible to the package.

Keywords

dyad-dependent

Triangles

Description

By default, this term adds one statistic to the model equal to the number of triangles in the network. For an undirected network, a triangle is defined to be any set {(i,j),(j,k),(k,i)}\{(i,j), (j,k), (k,i)\} of three edges. For a directed network, a triangle is defined as any set of three edges (i→j)(i{\rightarrow}j) and (j→k)(j{\rightarrow}k) and either (k→i)(k{\rightarrow}i) or (k←i)(k{\leftarrow}i) . The former case is called a "transitive triple" and the latter is called a "cyclic triple", so in the case of a directed network, triangle equals ttriple plus ctriple — thus at most two of these three terms can be in a model.

Usage

# binary: triangle(attr=NULL, diff=FALSE, levels=NULL)

# binary: triangles(attr=NULL, diff=FALSE, levels=NULL)

Arguments

attr, diff

quantitative attribute (see Specifying Vertex attributes and Levels (?nodal_attributes) for details.) If attr is specified and diff is FALSE , then the count is restricted to those triples of nodes with equal values of the vertex attribute specified by attr . If attr is specified and diff is TRUE , then one statistic is added for each value of attr , equal to the number of triangles where all three nodes have that value of the attribute.
levels

add one statistic for each value specified if diff is TRUE. (See Specifying Vertex attributes and Levels (?nodal_attributes) for details.)

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

categorical nodal attribute, directed, frequently-used, triad-related, undirected, binary

Triangle percentage

Description

By default, this term adds one statistic to the model equal to 100 times the ratio of the number of triangles in the network to the sum of the number of triangles and the number of 2-stars not in triangles (the latter is considered a potential but incomplete triangle). In case the denominator equals zero, the statistic is defined to be zero. For the definition of triangle, see triangle . This is often called the mean correlation coefficient. This term can only be used with undirected networks; for directed networks, it is difficult to define the numerator and denominator in a consistent and meaningful way.

Usage

# binary: tripercent(attr=NULL, diff=FALSE, levels=NULL)

Arguments

attr, diff

quantitative attribute (see Specifying Vertex attributes and Levels (?nodal_attributes) for details.) If attr is specified and diff is FALSE , then the counts are restricted to those triples of nodes with equal values of the vertex attribute specified by attr . If attr is specified and diff is TRUE , then one statistic is added for each value of attr , equal to the number of triangles where all three nodes have that value of the attribute.
levels

add one statistic for each value specified if diff is TRUE attributes and Levels (?nodal_attributes) for details.)

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

categorical nodal attribute, triad-related, undirected, binary

Transitive triples

Description

By default, this term adds one statistic to the model, equal to the number of transitive triples in the network, defined as a set of edges {(i→j),j→k),(i→k)}\{(i{\rightarrow}j), j{\rightarrow}k), (i{\rightarrow}k)\} . Note that triangle equals ttriple+ctriple for a directed network, so at most two of the three terms can be in a model.

Usage

# binary: ttriple(attr=NULL, diff=FALSE, levels=NULL)

# binary: ttriad

Arguments

attr

a vertex attribute specification (see Specifying Vertex attributes and Levels (?nodal_attributes) for details.)
diff

If attr is specified and diff is FALSE , then the count is over the number of transitive triples where all three nodes have the same value of the attribute. If attr is specified and diff is TRUE , then one statistic is added for each value of attr , equal to the number of triangles where all three nodes have that value of the attribute.
levels

add one statistic for each value specified if diff is TRUE. (See Specifying Vertex attributes and Levels (?nodal_attributes) for details.)

Note

This term can only be used with directed networks.

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

categorical nodal attribute, directed, triad-related, binary

2-Paths

Description

This term adds one statistic to the model, equal to the number of 2-paths in the network. For a directed network this is defined as a pair of edges (i→j),(j→k)(i{\rightarrow}j), (j{\rightarrow}k) , where ii and jj must be distinct. That is, it is a directed path of length 2 from ii to kk via jj . For directed networks a 2-path is also a mixed 2-star but the interpretation is usually different; see m2star . For undirected networks a twopath is defined as a pair of edges {i,j},{j,k}\{i,j\}, \{j,k\} . That is, it is an undirected path of length 2 from ii to kk via jj , also known as a 2-star.

Usage

# binary: twopath

See Also

ergmTerm for index of model terms currently visible to the package.

Keywords

directed, undirected, binary

Continuous Uniform reference

Description

Specifies each dyad's baseline distribution to be continuous uniform between a and b: h(y)=1h(y)=1 , with the support being ⁠[a, b]⁠.

Usage

# Unif(a,b)

Arguments

a, b

minimum and maximum to the baseline discrete uniform distribution, both inclusive. Both values must be finite.

See Also

ergmReference for index of reference distributions currently visible to the package.

Keywords

continuous

Update the edges in a network based on a matrix

Description

Replaces the edges in a network object with the edges corresponding to the sociomatrix or edge list specified by new.

Usage

## S3 method for class 'network'
update(object, ...)

update_network(object, new, ...)

## S3 method for class 'matrix_edgelist'
update_network(object, new, attrname = if (ncol(new) > 2) names(new)[3], ...)

## S3 method for class 'data.frame'
update_network(object, new, attrname = if (ncol(new) > 2) names(new)[3], ...)

## S3 method for class 'matrix'
update_network(object, new, matrix.type = NULL, attrname = NULL, ...)

## S3 method for class 'ergm_state'
update_network(object, new, ...)

Arguments

object

a network object.
...

Additional arguments; currently unused.
new

Either an adjacency matrix (a matrix of values indicating the presence and/or the value of a tie from i to j) or an edge list (a two-column matrix listing origin and destination node numbers for each edge, with an optional third column for the value of the edge).
attrname

For a network with edge weights gives the name of the edge attribute whose names to set.
matrix.type

One of "adjacency" or "edgelist" telling which type of matrix new is. Default is to use the which.matrix.type() function.

Value

A new network object with the edges specified by new and network and vertex attributes copied from the input network object. Input network is not modified.

Functions

  • update_network(): dispatcher for network update based on the type of updating information.

  • update_network(matrix_edgelist): a method for updating a network based on a matrix-form edgelist

  • update_network(data.frame): a method for updating a network based on an edgelist

  • update_network(matrix): a method for updating a network based on a matrix

  • update_network(ergm_state): a method for updating a network based on an ergm_state object.

See Also

ergm(), network

Examples

#
data(florentine)
#
# test the network.update function
#
# Create a Bernoulli network
rand.net <- network(network.size(flomarriage))
# store the sociomatrix 
rand.mat <- rand.net[,]
# Update the network
update(flomarriage, rand.mat, matrix.type="adjacency")
# Try this with an edgelist
rand.mat <- as.matrix.network.edgelist(flomarriage)[1:5,]
update(flomarriage, rand.mat, matrix.type="edgelist")

Weighted Median

Description

Compute weighted median.

Usage

wtd.median(x, na.rm = FALSE, weight = FALSE)

Arguments

x

Vector of data, same length as weight
na.rm

Logical: Should NAs be stripped before computation proceeds?
weight

Vector of weights

Details

Uses a simple algorithm based on sorting.

Value

Returns an empirical .5 quantile from a weighted sample.