Package 'NetMix'

Internal functions and generics for mmsbm package

Description

These are various utilities and generic methods used by the main package function.

Usage

approxB(y, d_id, pi_mat, directed = TRUE)

getZ(pi_mat)

alphaLBound(par, tot_nodes, c_t, x_t, s_mat, t_id, var_beta, mu_beta)

alphaGrad(par, tot_nodes, c_t, x_t, s_mat, t_id, var_beta, mu_beta)

.cbind.fill(...)

.scaleVars(x, keep_const = TRUE)

.transf_muvar(orig, is_var, is_array, des.mat, nblock = NULL, nstate = NULL)

.bar.legend(colPalette, range)

.mpower(mat, p)

.findPerm(block_list, target_mat = NULL, use_perms = TRUE)

.transf(mat)

.compute.alpha(X, beta)

.vcovBeta(
  all_phi,
  beta_coef,
  n.sim,
  n.blk,
  n.hmm,
  n.nodes,
  n.periods,
  mu.beta,
  var.beta,
  est_kappa,
  t_id_n,
  X
)

.e.pi(alpha_list, kappa, C_mat = NULL)

.initPi(
  soc_mats,
  dyads,
  edges,
  nodes_pp,
  dyads_pp,
  n.blocks,
  periods,
  directed,
  ctrl
)

Arguments

y, d_id, pi_mat, directed	Internal arguments for blockmodel approximation.
par	Vector of parameter values.
tot_nodes	Integer vector; total number of nodes each node interacts with.
c_t	Integer matrix; samples from Poisson-Binomial counts of a node instantiating a group.
x_t	Numeric matrix; transposed monadic design matrices.
s_mat	Integer matrix; Samples of HMM states by time period.
t_id	Integer vector; for each node, what time-period is it observed in? zero-indexed.
mu_beta, var_beta	Numeric arrays; prior mean and variances of monadic coefficients.
...	Numeric vectors; vectors of potentially different length to be cbind-ed.
x, keep_const	Internal arguments for matrix scaling.
orig	Object to be transformed.
is_var	Boolean. Is the object to be transformed a variance term?
is_array	Boolean. Is the object to be transformed an array?
des.mat	Numeric matrix. Design matrix corresponding to transformed object.
nblock	Number of groups in model, defaults to NULL.
nstate	Number of hidden Markov states in model, defaults to NULL.
colPalette	A function produced by colorRamp.
range	The range of values to label the legend.
mat	Numeric matrix.
p	Numeric scalar; power to raise matrix to.
block_list	List of matrices; each element is a square, numeric matrix that defines a blockmodel,
target_mat	Numeric matrix; reference blockmodel that those in block_list should be aligned to. Optional, defaults to NULL.
use_perms	Boolean; should all row/column permutations be explored when realigning matrices? defaults to TRUE.
X	Numeric matrix; design matrix of monadic predictors.
beta	Numeric array; array of coefficients associated with monadic predictors. It of dimensions Nr. Predictors by Nr. of Blocks by Nr. of HMM states.
all_phi, beta_coef, n.sim, n.blk, n.hmm, n.nodes, n.periods, mu.beta, var.beta, est_kappa, t_id_n	Additional internal arguments for covariance estimation.
alpha_list	List of mixed-membership parameter matrices.
kappa	Numeric matrix; matrix of marginal HMM state probabilities.
C_mat	Numeric matrix; matrix of posterior counts of block instantiations per node.
soc_mats, dyads, edges, nodes_pp, dyads_pp, n.blocks, periods, ctrl	Internal arguments for MM computation.

Details

These functions are meant for internal use only.

Value

See individual return section for each function:

.cbind.fill

Matrix of cbind'ed elements in ..., with missing values in each vector filled with NA.

.mpower

Matrix; the result of raising mat to the p power.

.findPerm

List of permuted blockmodel matrices.

.transf

Matrix with transformed mixed-membership vectors along its rows, s.t. no element is equal to 0.0 or 1.0.

.compute.alpha

List of predicted alpha matrices, one element per HMM state.

.e.pi

Matrix of predicted mixed-membership vectors along its rows, with expectation computed over marginal distribution over HMM states for each time period.

.missing

Transformed data.frame with missing values list-wise deleted, or expanded with missing indicator variables.

.createSocioB

List of sociomatrices.

.vertboot2

List of bootstrapped sociomatrices.

Author(s)

Santiago Olivella ([email protected]), Adeline Lo ([email protected]), Tyler Pratt ([email protected]), Kosuke Imai ([email protected])

---

Extract Regression Coefficients for a Fitted mmsbm Object

Description

Extract Regression Coefficients for a Fitted mmsbm Object

Usage

## S3 method for class 'mmsbm'
coef(object, param = "All", ...)

Arguments

object	An object of class mmsbm, a result of a call to mmsbm
param	Character string, which set of parameters should the vcov be extracted for? One of "MonadCoef", "DyadCoef" or "All" (the default).
...	Currently ignored

Value

For param="DyadCoef", a numeric vector. For param="MonadCoef", an array with HMM states along the third dimension. For param="All", named list of individual return components.

Author(s)

Santiago Olivella ([email protected]), Adeline Lo ([email protected]), Tyler Pratt ([email protected]), Kosuke Imai ([email protected])

Examples

library(NetMix)
## Load datasets
data("lazega_dyadic")
data("lazega_monadic")
## Estimate model with 2 groups
lazega_mmsbm <- mmsbm(SocializeWith ~ Coworkers,
                      ~  School,
                      senderID = "Lawyer1",
                      receiverID = "Lawyer2",
                      nodeID = "Lawyer",
                      data.dyad = lazega_dyadic,
                      data.monad = lazega_monadic,
                      n.blocks = 2,
                      mmsbm.control = list(seed = 123,
                                           conv_tol = 1e-2,
                                           hessian = FALSE))

coef(lazega_mmsbm, "MonadCoef")

---

Generate estimated monadic covariate effects for estimated mmsbm model

Description

The function estimates the effect of a shift in monadic covariate values on the probability of edge formation in the network.

Usage

covFX(fm, cov, shift, max.val = FALSE)

Arguments

fm	An object of class mmsbm, a result of a call to mmsbm.
cov	Character string identifying the monadic covariate to be shifted.
shift	Numeric value specifying the desired increase or decrease in the monadic covariate. The monadic predictor will be shifted by this value for all nodes and time periods.
max.val	An optional numeric value specifying the maximum possible value for the monadic covariate.

Value

List with named components:

Overall Avg. Effect

Overall average effect of the covariate shift on the predicted probability of edge formation.

Avg. Effect by Time

Vector of average effects of the covariate shift on the predicted probability of edge formation for each time period.

Avg. Effect by Node

Vector of average effects of the covariate shift on the predicted probability of edge formation for each node.

Avg. Effect by Dyad

Vector of average effects of the covariate shift on the predicted probability of edge formation for each node dyad.

Avg. Effect Dyad-Time

Vector of estimated effects of the covariate shift on the predicted probability of edge formation for each node dyad-time unit.

Author(s)

Santiago Olivella ([email protected]), Adeline Lo ([email protected]), Tyler Pratt ([email protected]), Kosuke Imai ([email protected])

Examples

library(NetMix)
## Load datasets
data("lazega_dyadic")
data("lazega_monadic")
## Estimate model with 2 groups
lazega_mmsbm <- mmsbm(SocializeWith ~ Coworkers,
                      ~  Age,
                      senderID = "Lawyer1",
                      receiverID = "Lawyer2",
                      nodeID = "Lawyer",
                      data.dyad = lazega_dyadic,
                      data.monad = lazega_monadic,
                      n.blocks = 2,
                      mmsbm.control = list(seed = 123, 
                                           conv_tol = 1e-2, 
                                           hessian = FALSE))

## Compute effect of decreasing every lawyers' age by 10 years
fx_list <- covFX(lazega_mmsbm, cov = "Age", shift = -10)
fx_list[["Overall Avg. Effect of Age"]]

---

Posterior predictive checks using structural network charactericts

Description

The function generates a variety of plots that serve as posterior predictive checks on the goodness of fit of a fitted mmsbm object.

Usage

gof(x, ...)

## S3 method for class 'mmsbm'
gof(
  x,
  gof_stat = c("Geodesics", "Degree"),
  level = 0.95,
  samples = 50,
  new.data.dyad = NULL,
  new.data.monad = NULL,
  seed = NULL,
  ...
)

Arguments

x	An object of class mmsbm, a result of a call to mmsbm.
...	Currently ignored.
gof_stat	Character vector. Accepts any subset from "Geodesics","Degree", "Indegree", "Outdegree", "3-Motifs", "Dyad Shared Partners", "Edge Shared Partners", and "Incoming K-stars". See details.
level	Double. Level of credible interval for posterior predictive distribution around structural quantities of interest.
samples	Integer. Number of sampled networks from model's posterior predictive using simulate.mmsbm.
new.data.dyad	See simulate.mmsbm. Enables out-of-sample checking.
new.data.monad	See simulate.mmsbm. Enables out-of-sample checking.
seed	See simulate.mmsbm.

Details

Goodness of fit of network models has typically been established by evaluating how the structural characteristics of predicted networks compare to those of the observed network. When estimated in a Bayesian framework, this approach is equivalent to conducting posterior preditive checks on these structural quantities of interest. When new.data.dyad and/or new.data.monad are passed that are different from those used in estimation, this is equivalent to conducting posterior predictive checks out-of-sample.

The set of structural features used to determine goodness of fit is somewhat arbitrary, and chosen mostly to incorporate various first order, second order, and (to the extent possible) third-order characteristics of the network. "Geodesics" focuses on the distribution over observed and predicted geodesic distances between nodes; "Indegree" and "Outdegree" focuses on the distribution over incoming and outgoing connections per node; "3-motifs" focus on a distribution over possible connectivity patterns between triads (i.e. the triadic census); "Dyad Shared Partners" focuses on the distribution over the number of shared partners between any two dayds; "Edge Shared Partners" is similarly defined, but w.r.t. edges, rather than dyads; and finally "Incoming K-stars" focuses on a frequency distribution over stars with k=1,... spokes.

Obtaining samples of the last three structural features can be very computationally expensive, and is discouraged on networks with more than 50 nodes.

Value

A ggplot object.

Author(s)

Santiago Olivella ([email protected]), Adeline Lo ([email protected]), Tyler Pratt ([email protected]), Kosuke Imai ([email protected])

Examples

library(NetMix)
## Load datasets
data("lazega_dyadic")
data("lazega_monadic")

## Estimate model with 2 groups
lazega_mmsbm <- mmsbm(SocializeWith ~ Coworkers,
                      senderID = "Lawyer1",
                      receiverID = "Lawyer2",
                      nodeID = "Lawyer",
                      data.dyad = lazega_dyadic,
                      data.monad = lazega_monadic,
                      n.blocks = 2,
                      mmsbm.control = list(seed = 123,
                                           conv_tol = 1e-2,
                                           hessian = FALSE))

## Plot observed (red) and simulated (gray) distributions over 
## indegrees
## (typically a larger number of samples would be taken) 
## (strictly requires ggplot2)


gof(lazega_mmsbm, gof_stat = "Indegree", samples = 2)

---

Identify nodes with most frequent membership in latent groups

Description

The function lists the nodes (optionally, node-time periods) that most frequently instantiate membership in each latent group.

Usage

## S3 method for class 'mmsbm'
head(x, n = 6, t = NULL, node = TRUE, t.correct = FALSE, ...)

Arguments

x	An object of class mmsbm, a result of a call to mmsbm.
n	Numeric or integer; specifies how many units will be identified for each group.
t	Optional vector of time periods to be used for assessing latent group membership.
node	Logical; indicates whether latent group memberships should be averaged at the node level. If FALSE, the function returns the node-time period units with highest estimated membership in each latent group.
t.correct	Logical; indicates whether latent group memberships should be corrected for temporal trends. If TRUE, the function returns the node-time period units with highest estimated membership in each latent group.
...	Currently ignored

Value

List of length n.blocks. Each entry contains a sorted vector of average latent membership probabilities of length n.

Author(s)

Santiago Olivella ([email protected]), Adeline Lo ([email protected]), Tyler Pratt ([email protected]), Kosuke Imai ([email protected])

Examples

library(NetMix)
## Load datasets
data("lazega_dyadic")
data("lazega_monadic")
## Estimate model with 2 groups
set.seed(123)
lazega_mmsbm <- mmsbm(SocializeWith ~ Coworkers,
                      ~  School + Practice + Status,
                      senderID = "Lawyer1",
                      receiverID = "Lawyer2",
                      nodeID = "Lawyer",
                      data.dyad = lazega_dyadic,
                      data.monad = lazega_monadic,
                      n.blocks = 2,
                      mmsbm.control = list(seed = 123,
                                           conv_tol = 1e-2,
                                           hessian = FALSE))

## Show top 6 lawyers in each estimated latent block
head(lazega_mmsbm)

---

Dyadic predictors in the Lazega friendship network (Lazega 2001).

Description

A dataset containing edges and dyad-level predictors in the network of friendships among lawyers in a New England law firm. More details are available in Lazega (2001).

Usage

data(lazega_dyadic)

Format

A data frame with 5041 rows and 4 variables:

Lawyer1, Lawyer2

lawyer ID, corresponding to identifiers common to those in lazega_monadic; numeric

SocializeWith

value of edge in network; binary

Coworkers

are the corresponding lawyers in the same office? boolean

Source

https://github.com/Z-co/networkdata/blob/master/networkdata/data/lazega.rda

References

Emmanuel Lazega, The Collegial Phenomenon: The Social Mechanisms of Cooperation Among Peers in a Corporate Law Partnership, Oxford University Press (2001).

---

Monadic predictors in the Lazega friendship network (Lazega 2001).

Description

A dataset containing vertex-level predictors in the network of sought-after advise among lawyers in a New England law firm. More details are available in Lazega (2001).

Usage

data(lazega_monadic)

Format

A data frame with 71 rows and 7 variables:

Lawyer

lawyer ID,corresponding to identifiers common to those in lazega_dyadic; numeric

Age

age, in years; numeric

Gender

1=man; 2=woman; factor

School

1=harvard, yale; 2=ucon; 3= other; factor

Practice

1=litigation; 2=corporate; factor

Seniority

time in the firm, in years; numeric

Status

1=partner; 2=associate; factor

Source

Emmanuel Lazega, The Collegial Phenomenon: The Social Mechanisms of Cooperation Among Peers in a Corporate Law Partnership, Oxford University Press (2001).

https://github.com/Z-co/networkdata/blob/master/networkdata/data/lazega.rda

---

Dynamic mixed-membership stochastic blockmodel with covariates

Description

The function estimates a dynamic mixed-membership stochastic blockmodel that incorporates covariates.

Usage

mmsbm(
  formula.dyad,
  formula.monad = ~1,
  senderID,
  receiverID,
  nodeID = NULL,
  timeID = NULL,
  data.dyad,
  data.monad = NULL,
  n.blocks,
  n.hmmstates = 1,
  directed = TRUE,
  mmsbm.control = list()
)

Arguments

formula.dyad	A formula object. The variable in data.dyad that contains binary edges should be used as a LHS, and any dyadic predictors can be included on the RHS (when no dyadic covariates are available, use y ~ 1). Same syntax as a glm formula.
formula.monad	An optional formula object. LHS is ignored. RHS contains names of nodal atrributes found in data.monad.
senderID	Character string. Quoted name of the variable in data.dyad identifying the sender node. For undirected networks, the variable simply contains name of first node in dyad. Cannot contain special charecter "'@'".
receiverID	Character string. Quoted name of the variable in data.dyad identifying the receiver node. For undirected networks, the variable simply contains name of second node in dyad. Cannot contain special charecter "'@'".
nodeID	Character string. Quoted name of the variable in data.monad identifying a node in either data.dyad[,senderID] or data.dyad[,senderID]. If not NULL, every node data.dyad[,senderID] or data.dyad[,senderID] must be present in data.monad[,nodeID]. Cannot contain special charecter "'@'".
timeID	Character string. Quoted name of the variable in both data.dyad and data.monad indicating the time in which network (and correspding nodal atrributes) were observed. The variable itself must be composed of integers. Cannot contain special charecter "'@'".
data.dyad	Data frame. Sociomatrix in “long” (i.e. dyadic) format. Must contain at least three variables: the sender identifier (or identifier of the first node in an undirected networks dyad), the receiver identifier (or identifier of the second node in an undirected network dyad), and the value of the edge between them. Currently, only edges between zero and one (inclusive) are supported.
data.monad	Data frame. Nodal atributes. Must contain a node identifier matching the names of nodes used in the data.dyad data frame.
n.blocks	Integer value. How many latent groups should be used to estimate the model?
n.hmmstates	Integer value. How many hidden Markov state should be used in the HMM? Defaults to 1 (i.e. no HMM).
directed	Boolean. Is the network directed? Defaults to TRUE.
mmsbm.control	A named list of optional algorithm control parameters. seed Integer. Seed the RNG. By default, a random seed is generated and returned for reproducibility purposes. nstart Integer. Number of random initialization trials. Defaults to 5. spectral Boolean. Type of initialization algorithm for mixed-membership vectors in static case. If TRUE (default), use spectral clustering with degree correction; otherwise, use kmeans algorithm. init_gibbs Boolean. Should a collapsed Gibbs sampler of non-regression mmsbm be used to initialize mixed-membership vectors, instead of a spectral or simple kmeans initialization? Setting to TRUE will result in slower initialization and faster model estimation. When TRUE, results are typically very sensitive to choice of alpha (see below). alpha Numeric positive value. Concentration parameter for collapsed Gibbs sampler to find initial mixed-membership values when init_gibbs=TRUE. Defaults to 1.0. missing Means of handling missing data. One of "indicator method" (default) or "listwise deletion". svi Boolean; should stochastic variational inference be used? Defaults to TRUE. vi_iter Number of maximum iterations in stochastic variational updates. Defaults to 5e2. batch_size When svi=TRUE, proportion of nodes sampled in each local. Defaults to 0.05 when svi=TRUE, and to 1.0 otherwise. forget_rate When svi=TRUE, value between (0.5,1], controlling speed of decay of weight of prior parameter values in global steps. Defaults to 0.75 when svi=TRUE, and to 0.0 otherwise. delay When svi=TRUE, non-negative value controlling weight of past iterations in global steps. Defaults to 1.0 when svi=TRUE, and ignored otherwise. opt_iter Number of maximum iterations of BFGS in global step. Defaults to 10e3. hessian Boolean indicating whether the Hessian matrix of regression coefficients should e returned. Defaults to TRUE. assortative Boolean indicating whether blockmodel should be assortative (i.e. stronger connections within groups) or disassortative (i.e. stronger connections between groups). Defaults to TRUE. mu_block Numeric vector with two elements: prior mean of blockmodel's main diagonal elements, and and prior mean of blockmodel's offdiagonal elements. Defaults to c(5.0, -5.0) if assortative=TRUE (default) and to c(-5.0, 5.0) otherwise. var_block Numeric vector with two positive elements: prior variance of blockmodel's main diagonal elements, and and prior variance of blockmodel's offdiagonal elements. Defaults to c(5.0, 5.0). mu_beta Either single numeric value, in which case the same prior mean is applied to all monadic coefficients, or an array that is npredictors by n.blocks by n.hmmstates, where npredictors is the number of monadic predictors for which a prior mean is being set (prior means need not be set for all) predictors). The rows in the array should be named to identify which variables a prior mean is being set for. Defaults to a common prior mean of 0.0 for all monadic coefficients. var_beta See mu_beta. Defaults to a single common prior variance of 5.0 for all (standardized) monadic coefficients. mu_gamma Either a single numeric value, in which case the same prior mean is applied to all dyadic coefficients, or a named vector of numeric values (with names corresponding to the name of the variable for which a prior mean is being set). Defaults to a common prior mean of 0.0 for all dyadic coefficients. var_gamma See mu_gamma. Defaults to a single common prior variance of 5.0 for all (standardized) dyadic coefficients. eta Numeric positive value. Concentration hyper-parameter for HMM. Defaults to 1.0. se_sim Number of samples from variational posterior of latent variables on which approximation to variance-covariance matrices are based. Defaults to 10. dyad_vcov_samp Maximum number of dyads to sample in computation of variance-covariance of dyadic and blockmodel parameters, when compared to ten percent of the observed dyads. Defaults to 1000. fixed_mm Optional character vector, with "nodeID@timeID" as elements, indicating which mixed-membership vectors should remain constant at their initial values throughout estimation. When only one year is observed, elements should be "nodeID@1". Typically used with mm_init_t. mm_init_t Matrix, n.blocks by nodes across years. Optional initial values for mixed-membership vectors. Although initial values need not be provided for all nodes, column names must have a nodeID@timeID format to avoid ambiguity. When only one year is observed, names should be "nodeID@1". kappa_init_t Matrix, n.hmmstates by number of years. Optional initial values for variational parameters for state probabilities. Columns must be named according to unique year values. b_init_t Matrix, n.blocks by n.blocks. Optional initial values for blockmodel. beta_init Array, predictors by n.blocks by n.hmmstates. Optional initial values for monadic coefficients. If gamma_init Vector. Optional initial values for dyadic coefficients. permute Boolean. Should all permutations be tested to realign initial block models in dynamic case? If FALSE, realignment is done via faster graph matching algorithm, but may not be exact. Defaults to TRUE. conv_tol Numeric value. Absolute tolerance for VI convergence. Defaults to 1e-3. verbose Boolean. Should extra information be printed as model iterates? Defaults to FALSE.

Value

Object of class mmsbm. List with named components:

MixedMembership

Matrix of variational posterior of mean of mixed-membership vectors. nodes by n.blocks.

BlockModel

n.blocks by n.blocks matrix of estimated tie log-odds between members of corresponding latent groups. The blockmodel.

vcov_blockmodel

If hessian=TRUE, variance-covariance matrix of parameters in blockmodel, ordered in column-major order.

MonadCoef

Array of estimated coefficient values for monadic covariates. Has n.blocks columns, and n.hmmstates slices.

vcov_monad

If hessian=TRUE, variance-covariance matrix of monadic coefficients.

DyadCoef

Vector estimated coefficient values for dyadic covariates.

vcov_dyad

If hessian=TRUE, variance-covariance matrix of dyadic coefficients.

TransitionKernel

Matrix of estimated HMM transition probabilities.

Kappa

Matrix of marginal probabilities of being in an HMM state at any given point in time. n.hmmstates by years (or whatever time interval networks are observed at).

LowerBound

Final LB value

lb

Vector of all LB across iterations, useful to check early convergence issues.

niter

Final number of VI iterations.

converged

Convergence indicator; zero indicates failure to converge.

NodeIndex

Order in which nodes are stored in all return objects.

monadic.data, dyadic.data

Model frames used during estimation (stripped of attributes).

forms

Values of selected formal arguments used by other methods.

seed

The value of RNG seed used during estimation.

call

Original (unevaluated) function call.

Author(s)

Santiago Olivella ([email protected]), Adeline Lo ([email protected]), Tyler Pratt ([email protected]), Kosuke Imai ([email protected])

Examples

library(NetMix)
## Load datasets
data("lazega_dyadic")
data("lazega_monadic")
## Estimate model with 2 groups
## Setting to `hessian=TRUE` increases computation time
## but is needed if standard errors are to be computed. 
lazega_mmsbm <- mmsbm(SocializeWith ~ Coworkers,
                      ~  School + Practice + Status,
                      senderID = "Lawyer1",
                      receiverID = "Lawyer2",
                      nodeID = "Lawyer",
                      data.dyad = lazega_dyadic,
                      data.monad = lazega_monadic,
                      n.blocks = 2,
                      mmsbm.control = list(seed = 123,
                                           conv_tol = 1e-2,
                                           hessian = FALSE))

---

Fitter Function for dynamic MMSBM Model

Description

This is the interface to the C++ fitter for the dynamic mixed-membership stochastic blockmodel for network regression.

Arguments

z_t	Numeric matrix; transpose of monadic design matrix. Should not include intercept row.
x_t	Numeric matrix; transpose of dyadic design matrix.
y	Numeric vector; vector of edge values. Must have same number of elements as ncol(x_t)
time_id_dyad	Integer vector; zero-based time-period identifier for each node.
nodes_per_period	Integer vector; total number of unique nodes observed in each time period.
node_id_dyad	Integer matrix; zero-based sender and receiver identifier per dyad.
mu_b	Numeric matrix; matrix of prior means for elements in blockmodel matrix.
var_b	Numeric matrix; matrix of prior variances for elements in blockmodel matrix.
pi_init	Numeric matrix; matrix of initial mixed-memberships. Nodes along columns.
kappa_init_t	Numeric matrix; matrix of initial marginal HMM state probabilities. Time-periods along columns.
b_init_t	Numeric matrix; square matrix of initial values of blockmodel.
beta_init	Numeric vector; flat array (column-major order) of initial values of monadic coefficients.
gamma_init	Numeric vector; vector of initial values of dyadic coefficients
control	List; see the mmsbm.control argument of mmsbm

Value

Unclassed list with named components; see Value of mmsbm

Warning

This function is for internal use only. End-users should always resort to mmsbm. In particular, that interface post-processes the return value of this internal in important ways.

Author(s)

Santiago Olivella ([email protected]), Adeline Lo ([email protected]), Tyler Pratt ([email protected]), Kosuke Imai ([email protected])

---

Various visualization tools for 'mmsbm' objects

Description

The function provides a variety of plotting options for a fitted mmsbm object.

Usage

## S3 method for class 'mmsbm'
plot(x, type = "groups", FX = NULL, node = NULL, ...)

Arguments

x	An object of class mmsbm, a result of a call to mmsbm.
type	character string denoting the type of plot. The default, "groups," plots the estimated matrix of group by group edge formation probabilities as a network plot, with nodes representing groups (sized proportional to relative membership) and edge colors encoding probability of between-group ties. "blockmodel" plots the same information, but using a tile plot instead of a network plot. "membership" plots average membership in each latent group by time period. "effect" provides a series of plots showing the estimated effect of a shfit in monadic covariate values.
FX	with type == "effect"; a list resulting from a call to covFX.
node	with type == "membership"; a character string specifying the node for which group membership should be plotted.
...	Currently ignored

Value

The requested plot object.

Author(s)

Santiago Olivella ([email protected]), Adeline Lo ([email protected]), Tyler Pratt ([email protected]), Kosuke Imai ([email protected])

Examples

library(NetMix)
## Load datasets
data("lazega_dyadic")
data("lazega_monadic")
## Estimate model with 2 groups
lazega_mmsbm <- mmsbm(SocializeWith ~ Coworkers,
                      ~  School + Practice + Status,
                      senderID = "Lawyer1",
                      receiverID = "Lawyer2",
                      nodeID = "Lawyer",
                      data.dyad = lazega_dyadic,
                      data.monad = lazega_monadic,
                      n.blocks = 2,
                      mmsbm.control = list(seed = 123,
                                           conv_tol = 1e-2,
                                           hessian = FALSE))

## Plot blockmodel as network
plot(lazega_mmsbm)

---

Predict edges based on estimated mmsbm model

Description

The function produces expected posterior edges based on estimated parameters and (optionally new) predictor data

Usage

## S3 method for class 'mmsbm'
predict(
  object,
  new.data.dyad = NULL,
  new.data.monad = NULL,
  forecast = FALSE,
  type = c("link", "response", "mm"),
  ...
)

Arguments

object	Object of class mmsbm.
new.data.dyad	An optional data.frame object.
new.data.monad	An optional data.frame object.
forecast	Boolean. Should prediction forcast one step into the future? Defaults to FALSE.
type	Character string. The default is to use the linear predictor of edges. The alternative "response" returns predicted probabilities. The alternative "mm" returns predicted mixed-membership vectors.
...	Currently ignored

Value

If new.data.dyad = NULL, vector of length nrow(object$dyadic.data). Else, vector of length nrow(new.data.dyad).

Author(s)

Santiago Olivella ([email protected]), Adeline Lo ([email protected]), Tyler Pratt ([email protected]), Kosuke Imai ([email protected])

Examples

library(NetMix)
## Load datasets
data("lazega_dyadic")
data("lazega_monadic")
## Estimate model with 2 groups
lazega_mmsbm <- mmsbm(SocializeWith ~ Coworkers,
                      ~  School + Practice + Status,
                      senderID = "Lawyer1",
                      receiverID = "Lawyer2",
                      nodeID = "Lawyer",
                      data.dyad = lazega_dyadic,
                      data.monad = lazega_monadic,
                      n.blocks = 2,
                      mmsbm.control = list(seed = 123,
                                           conv_tol = 1e-2, 
                                           hessian = FALSE))

## Get in-sample predicted edge probabilities
lazega_preds <- predict(lazega_mmsbm, type = "response")

---

Simulate a complete sociomatrix from an mmsbm object

Description

The function generates one sample network from the posterior predictive of the model represented by a fitted mmsbm object.

Usage

## S3 method for class 'mmsbm'
simulate(
  object,
  nsim = 1,
  seed = NULL,
  new.data.dyad = NULL,
  new.data.monad = NULL,
  ...
)

Arguments

object	An object of class mmsbm, a result of a call to mmsbm
nsim	Number of networks to simulate
seed	RNG seed.
new.data.dyad	An optional data.frame object. If not NULL, use these dyadic predictor values instead of those used to fit the original model.
new.data.monad	An optional data.frame object. See new.data.dyad.
...	Currently ignored

Value

List of length nsim of simulated networks. If new.data.dyad = NULL, each element is a vector of length nrow(object$dyadic.data). Else, vector of length nrow(new.data.dyad). If seed is not NULL, return object includes its value as attribute "seed".

Author(s)

Santiago Olivella ([email protected]), Adeline Lo ([email protected]), Tyler Pratt ([email protected]), Kosuke Imai ([email protected])

Examples

library(NetMix)
## Load datasets
data("lazega_dyadic")
data("lazega_monadic")
## Estimate model with 2 groups
lazega_mmsbm <- mmsbm(SocializeWith ~ Coworkers,
                      ~  School + Practice + Status,
                      senderID = "Lawyer1",
                      receiverID = "Lawyer2",
                      nodeID = "Lawyer",
                      data.dyad = lazega_dyadic,
                      data.monad = lazega_monadic,
                      n.blocks = 2,
                      mmsbm.control = list(seed = 123, 
                                           conv_tol = 1e-2,
                                           hessian = FALSE))

## Simulate 5 new networks
lazega_sim <- simulate(lazega_mmsbm, nsim = 5, seed = 123)

---

Summarize 'mmsbm' object

Description

The function summarizes the output of a dynMMSBM model object

Usage

## S3 method for class 'mmsbm'
summary(object, ...)

Arguments

object	An object of class mmsbm, a result of a call to mmsbm.
...	Currently ignored

Value

List with named components:

N

Total number of dyad-time period observations.

Number of Clusters

Number of latent groups included in the dynMMSBM model.

Percent of Observations in Each Cluster

Average membership in each latent group, across all node-time periods.

Edge Formation Probabilities

n.groups by n.groups matrix of estimated edge formation probabilities between latent groups.

Dyadic Coefficients

Vector of estimated coefficient values for dyadic covariates.

Monadic Coefficients

Array of estimated coefficient values for monadic covariates. Has n.groups columns, and n.hmmstates slices.

Markov State Probabilities

Average HMM state probabilities across all time periods.

Author(s)

Santiago Olivella ([email protected]), Adeline Lo ([email protected]), Tyler Pratt ([email protected]), Kosuke Imai ([email protected])

Examples

library(NetMix)
## Load datasets
data("lazega_dyadic")
data("lazega_monadic")
## Estimate model with 2 groups
lazega_mmsbm <- mmsbm(SocializeWith ~ Coworkers,
                      ~  School + Practice + Status,
                      senderID = "Lawyer1",
                      receiverID = "Lawyer2",
                      nodeID = "Lawyer",
                      data.dyad = lazega_dyadic,
                      data.monad = lazega_monadic,
                      n.blocks = 2,
                      mmsbm.control = list(seed = 123,
                                           conv_tol = 1e-2,
                                           hessian = TRUE))

## Summarize estimated model
summary(lazega_mmsbm)

---

Extract Variance-Covariance Matrix for a Fitted mmsbm Object

Description

Extract Variance-Covariance Matrix for a Fitted mmsbm Object

Usage

## S3 method for class 'mmsbm'
vcov(object, param = "All", ...)

Arguments

object	An object of class mmsbm, a result of a call to mmsbm
param	Character string, which set of parameters should the vcov be extracted for? One of "MonadCoef", "DyadCoef", "BlockModel" or "All" (the default).
...	Currently ignored

Value

For param="All", named list of individual return components. For all other values of param, a numeric covariance matrix.

Author(s)

Santiago Olivella ([email protected]), Adeline Lo ([email protected]), Tyler Pratt ([email protected]), Kosuke Imai ([email protected])

Examples

library(NetMix)
## Load datasets
data("lazega_dyadic")
data("lazega_monadic")
## Estimate model with 2 groups
lazega_mmsbm <- mmsbm(SocializeWith ~ Coworkers,
                      ~  School + Practice + Status,
                      senderID = "Lawyer1",
                      receiverID = "Lawyer2",
                      nodeID = "Lawyer",
                      data.dyad = lazega_dyadic,
                      data.monad = lazega_monadic,
                      n.blocks = 2,
                      mmsbm.control = list(seed = 123, 
                                           conv_tol = 1e-2,
                                           se_sim = 2)) # Usually requires more samples.

vcov(lazega_mmsbm, "MonadCoef")

---