Package 'missSBM' reference manual

Title:	Handling Missing Data in Stochastic Block Models
Description:	When a network is partially observed (here, NAs in the adjacency matrix rather than 1 or 0 due to missing information between node pairs), it is possible to account for the underlying process that generates those NAs. 'missSBM', presented in 'Barbillon, Chiquet and Tabouy' (2022) <doi:10.18637/jss.v101.i12>, adjusts the popular stochastic block model from network data sampled under various missing data conditions, as described in 'Tabouy, Barbillon and Chiquet' (2019) <doi:10.1080/01621459.2018.1562934>.
Authors:	Julien Chiquet [aut, cre] (ORCID: <https://orcid.org/0000-0002-3629-3429>), Pierre Barbillon [aut] (ORCID: <https://orcid.org/0000-0002-7766-7693>), Timothée Tabouy [aut], Jean-Benoist Léger [ctb] (provided C++ implementaion of K-means), François Gindraud [ctb] (provided C++ interface to NLopt), großBM team [ctb]
Maintainer:	Julien Chiquet <[email protected]>
License:	GPL-3
Version:	1.1.0
Built:	2026-07-22 01:12:58 UTC
Source:	https://github.com/cran/missSBM

Class for defining a block dyad sampler

Description

Class for defining a block dyad sampler

Super classes

networkSampling -> networkSampler -> dyadSampler -> blockDyadSampler

Active bindings

df: the number of parameters of this sampling

Methods

Inherited methods

networkSampling$print()
networkSampling$show()
networkSampler$rSamplingMatrix()

`blockDyadSampler$new()`

constructor for networkSampling

Usage

blockDyadSampler$new(
  parameters = NA,
  nbNodes = NA,
  directed = FALSE,
  clusters = NA
)

Arguments

parameters: the vector of parameters associated to the sampling at play
nbNodes: number of nodes in the network
directed: logical, directed network of not
clusters: a vector of class memberships

`blockDyadSampler$clone()`

The objects of this class are cloneable with this method.

Usage

blockDyadSampler$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Class for fitting a block-dyad sampling

Description

Class for fitting a block-dyad sampling

Super classes

networkSampling -> networkSamplingDyads_fit -> blockDyadSampling_fit

Active bindings

vExpec: variational expectation of the sampling
log_lambda: matrix, term for adjusting the imputation step which depends on the type of sampling

Methods

Public methods

blockDyadSampling_fit$new()
blockDyadSampling_fit$update_parameters()
blockDyadSampling_fit$clone()

Inherited methods

networkSampling$print()
networkSamplingDyads_fit$show()
networkSamplingDyads_fit$update_imputation()

`blockDyadSampling_fit$new()`

constructor

Usage

blockDyadSampling_fit$new(partlyObservedNetwork, blockInit)

Arguments

partlyObservedNetwork: a object with class partlyObservedNetwork representing the observed data with possibly missing entries
blockInit: n x Q matrix of initial block indicators

`blockDyadSampling_fit$update_parameters()`

a method to update the estimation of the parameters. By default, nothing to do (corresponds to MAR sampling)

Usage

blockDyadSampling_fit$update_parameters(nu, Z)

Arguments

nu: the matrix of (uncorrected) imputation for missing entries
Z: probabilities of block memberships

`blockDyadSampling_fit$clone()`

The objects of this class are cloneable with this method.

Usage

blockDyadSampling_fit$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Class for defining a block node sampler

Description

Class for defining a block node sampler

Super classes

networkSampling -> networkSampler -> nodeSampler -> blockNodeSampler

Methods

Public methods

blockNodeSampler$new()
blockNodeSampler$clone()

Inherited methods

networkSampling$print()
networkSampling$show()
networkSampler$rSamplingMatrix()

`blockNodeSampler$new()`

constructor for networkSampling

Usage

blockNodeSampler$new(
  parameters = NA,
  nbNodes = NA,
  directed = FALSE,
  clusters = NA
)

Arguments

parameters: the vector of parameters associated to the sampling at play
nbNodes: number of nodes in the network
directed: logical, directed network of not
clusters: a vector of class memberships

`blockNodeSampler$clone()`

The objects of this class are cloneable with this method.

Usage

blockNodeSampler$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Class for fitting a block-node sampling

Description

Class for fitting a block-node sampling

Super classes

networkSampling -> networkSamplingNodes_fit -> blockNodeSampling_fit

Active bindings

vExpec: variational expectation of the sampling
log_lambda: double, term for adjusting the imputation step which depends on the type of sampling

Methods

Public methods

blockNodeSampling_fit$new()
blockNodeSampling_fit$update_parameters()
blockNodeSampling_fit$clone()

Inherited methods

networkSampling$print()
networkSamplingNodes_fit$show()
networkSamplingNodes_fit$update_imputation()

`blockNodeSampling_fit$new()`

constructor

Usage

blockNodeSampling_fit$new(partlyObservedNetwork, blockInit)

Arguments

partlyObservedNetwork: a object with class partlyObservedNetwork representing the observed data with possibly missing entries
blockInit: n x Q matrix of initial block indicators

`blockNodeSampling_fit$update_parameters()`

a method to update the estimation of the parameters. By default, nothing to do (corresponds to MAR sampling)

Usage

blockNodeSampling_fit$update_parameters(imputedNet, Z)

Arguments

imputedNet: an adjacency matrix where missing values have been imputed
Z: indicator of blocks

`blockNodeSampling_fit$clone()`

The objects of this class are cloneable with this method.

Usage

blockNodeSampling_fit$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Extract model coefficients

Description

Extracts model coefficients from objects missSBM_fit returned by estimateMissSBM()

Usage

## S3 method for class 'missSBM_fit'
coef(
  object,
  type = c("mixture", "connectivity", "covariates", "sampling"),
  ...
)
## S3 method for class 'missSBM_fit'
coef(
  object,
  type = c("mixture", "connectivity", "covariates", "sampling"),
  ...
)

Arguments

object

an R6 object with class missSBM_fit

type

type of parameter that should be extracted. Either "mixture" (default), "connectivity", "covariates" or "sampling"

...

additional parameters for S3 compatibility. Not used

Value

A vector or matrix of coefficients extracted from the missSBM_fit model.

Class for fitting a dyad sampling with covariates

Description

Class for fitting a dyad sampling with covariates

Super classes

networkSampling -> networkSamplingDyads_fit -> covarDyadSampling_fit

Active bindings

vExpec: variational expectation of the sampling

Methods

Public methods

covarDyadSampling_fit$new()
covarDyadSampling_fit$clone()

Inherited methods

networkSampling$print()
networkSamplingDyads_fit$show()
networkSamplingDyads_fit$update_imputation()
networkSamplingDyads_fit$update_parameters()

`covarDyadSampling_fit$new()`

constructor

Usage

covarDyadSampling_fit$new(partialNet, ...)

Arguments

partialNet: a object with class partlyObservedNetwork representing the observed data with possibly missing entries
...: used for compatibility

`covarDyadSampling_fit$clone()`

The objects of this class are cloneable with this method.

Usage

covarDyadSampling_fit$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Class for fitting a node-centered sampling with covariate

Description

Class for fitting a node-centered sampling with covariate

Super classes

networkSampling -> networkSamplingNodes_fit -> covarNodeSampling_fit

Active bindings

vExpec: variational expectation of the sampling

Methods

Public methods

covarNodeSampling_fit$new()
covarNodeSampling_fit$clone()

Inherited methods

networkSampling$print()
networkSamplingNodes_fit$show()
networkSamplingNodes_fit$update_imputation()
networkSamplingNodes_fit$update_parameters()

`covarNodeSampling_fit$new()`

constructor

Usage

covarNodeSampling_fit$new(partlyObservedNetwork, ...)

Arguments

partlyObservedNetwork: a object with class partlyObservedNetwork representing the observed data with possibly missing entries
...: used for compatibility

`covarNodeSampling_fit$clone()`

The objects of this class are cloneable with this method.

Usage

covarNodeSampling_fit$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Class for defining a degree sampler

Description

Class for defining a degree sampler

Super classes

networkSampling -> networkSampler -> nodeSampler -> degreeSampler

Methods

Public methods

degreeSampler$new()
degreeSampler$clone()

Inherited methods

networkSampling$print()
networkSampling$show()
networkSampler$rSamplingMatrix()

`degreeSampler$new()`

constructor for networkSampling

Usage

degreeSampler$new(parameters = NA, degrees = NA, directed = FALSE)

Arguments

parameters: the vector of parameters associated to the sampling at play
degrees: vector of nodes' degrees
directed: logical, directed network of not

`degreeSampler$clone()`

The objects of this class are cloneable with this method.

Usage

degreeSampler$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Class for fitting a degree sampling

Description

Class for fitting a degree sampling

Super classes

networkSampling -> networkSamplingNodes_fit -> degreeSampling_fit

Active bindings

vExpec: variational expectation of the sampling

Methods

Public methods

degreeSampling_fit$new()
degreeSampling_fit$update_parameters()
degreeSampling_fit$update_imputation()
degreeSampling_fit$clone()

Inherited methods

networkSampling$print()
networkSamplingNodes_fit$show()

`degreeSampling_fit$new()`

constructor

Usage

degreeSampling_fit$new(partlyObservedNetwork, blockInit, connectInit)

Arguments

partlyObservedNetwork: a object with class partlyObservedNetwork representing the observed data with possibly missing entries
blockInit: n x Q matrix of initial block indicators
connectInit: Q x Q matrix of initial block probabilities of connection

`degreeSampling_fit$update_parameters()`

a method to update the estimation of the parameters. By default, nothing to do (corresponds to MAR sampling)

Usage

degreeSampling_fit$update_parameters(imputedNet, ...)

Arguments

imputedNet: an adjacency matrix where missing values have been imputed
...: used for compatibility

`degreeSampling_fit$update_imputation()`

a method to update the imputation of the missing entries.

Usage

degreeSampling_fit$update_imputation(PI, ...)

Arguments

PI: the matrix of inter/intra class probability of connection
...: use for compatibility

`degreeSampling_fit$clone()`

The objects of this class are cloneable with this method.

Usage

degreeSampling_fit$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Class for defining a double-standard sampler

Description

Class for defining a double-standard sampler

Super classes

networkSampling -> networkSampler -> dyadSampler -> doubleStandardSampler

Methods

Public methods

doubleStandardSampler$new()
doubleStandardSampler$clone()

Inherited methods

networkSampling$print()
networkSampling$show()
networkSampler$rSamplingMatrix()

`doubleStandardSampler$new()`

constructor for networkSampling

Usage

doubleStandardSampler$new(parameters = NA, adjMatrix = NA, directed = FALSE)

Arguments

parameters: the vector of parameters associated to the sampling at play
adjMatrix: matrix of adjacency
directed: logical, directed network of not

`doubleStandardSampler$clone()`

The objects of this class are cloneable with this method.

Usage

doubleStandardSampler$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Class for fitting a double-standard sampling

Description

Class for fitting a double-standard sampling

Super classes

networkSampling -> networkSamplingDyads_fit -> doubleStandardSampling_fit

Active bindings

vExpec: variational expectation of the sampling

Methods

Public methods

doubleStandardSampling_fit$new()
doubleStandardSampling_fit$update_parameters()
doubleStandardSampling_fit$update_imputation()
doubleStandardSampling_fit$clone()

Inherited methods

networkSampling$print()
networkSamplingDyads_fit$show()

`doubleStandardSampling_fit$new()`

constructor

Usage

doubleStandardSampling_fit$new(partlyObservedNetwork, ...)

Arguments

partlyObservedNetwork: a object with class partlyObservedNetwork representing the observed data with possibly missing entries
...: used for compatibility

`doubleStandardSampling_fit$update_parameters()`

a method to update the estimation of the parameters. By default, nothing to do (corresponds to MAR sampling)

Usage

doubleStandardSampling_fit$update_parameters(nu, ...)

Arguments

nu: an adjacency matrix with imputed values (only)
...: use for compatibility

`doubleStandardSampling_fit$update_imputation()`

a method to update the imputation of the missing entries.

Usage

doubleStandardSampling_fit$update_imputation(nu)

Arguments

nu: the matrix of (uncorrected) imputation for missing entries

`doubleStandardSampling_fit$clone()`

The objects of this class are cloneable with this method.

Usage

doubleStandardSampling_fit$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Virtual class for all dyad-centered samplers

Description

Virtual class for all dyad-centered samplers

Super classes

networkSampling -> networkSampler -> dyadSampler

Methods

Public methods

dyadSampler$new()
dyadSampler$clone()

Inherited methods

networkSampling$print()
networkSampling$show()
networkSampler$rSamplingMatrix()

`dyadSampler$new()`

constructor for networkSampling

Usage

dyadSampler$new(type = NA, parameters = NA, nbNodes = NA, directed = FALSE)

Arguments

type: character for the type of sampling. must be in ("dyad", "covar-dyad", "node", "covar-node", "block-node", "block-dyad", "double-standard", "degree")
parameters: the vector of parameters associated to the sampling at play
nbNodes: number of nodes in the network
directed: logical, directed network of not

`dyadSampler$clone()`

The objects of this class are cloneable with this method.

Usage

dyadSampler$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Class for fitting a dyad sampling

Description

Class for fitting a dyad sampling

Super classes

networkSampling -> networkSamplingDyads_fit -> dyadSampling_fit

Active bindings

vExpec: variational expectation of the sampling

Methods

Public methods

dyadSampling_fit$new()
dyadSampling_fit$clone()

Inherited methods

networkSampling$print()
networkSamplingDyads_fit$show()
networkSamplingDyads_fit$update_imputation()
networkSamplingDyads_fit$update_parameters()

`dyadSampling_fit$new()`

constructor

Usage

dyadSampling_fit$new(partlyObservedNetwork, ...)

Arguments

partlyObservedNetwork: a object with class partlyObservedNetwork representing the observed data with possibly missing entries
...: used for compatibility

`dyadSampling_fit$clone()`

The objects of this class are cloneable with this method.

Usage

dyadSampling_fit$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

ER ego centered network

Description

A dataset containing the weighted PPI network centered around the ESR1 (ER) protein

Usage

er_network
er_network

Format

A sparse symmetric matrix with 741 rows and 741 columns ESR1

Source

https://string-db.org/

Examples

data("er_network")
class(er_network)
data("er_network")
class(er_network)

Estimation of simple SBMs with missing data

Description

Variational EM inference of Stochastic Block Models indexed by block number from a partially observed network.

Usage

estimateMissSBM(
  adjacencyMatrix,
  vBlocks,
  sampling,
  covariates = list(),
  control = missSBM_param()
)
estimateMissSBM(
  adjacencyMatrix,
  vBlocks,
  sampling,
  covariates = list(),
  control = missSBM_param()
)

Arguments

adjacencyMatrix

The N x N adjacency matrix of the network data. If adjacencyMatrix is symmetric, we assume an undirected network with no loop; otherwise the network is assumed to be directed.

vBlocks

The vector of number of blocks considered in the collection.

sampling

The model used to described the process that originates the missing data: MAR designs ("dyad", "node","covar-dyad","covar-node","snowball") and MNAR designs ("double-standard", "block-dyad", "block-node" , "degree") are available. See details.

covariates

An optional list with M entries (the M covariates). If the covariates are node-centered, each entry of covariates must be a size-N vector; if the covariates are dyad-centered, each entry of covariates must be N x N matrix.

control

a list-like structure for controlling advanced features, with default generated by missSBM_param. See the associated documentation for details.

Details

Internal functions use future_lapply, so set your plan to 'multisession' or 'multicore' to use several cores/workers.

The different sampling designs are split into two families in which we find dyad-centered and node-centered samplings. See doi:10.1080/01621459.2018.1562934 for a complete description.

Missing at Random (MAR)
- dyad parameter = p = Prob(Dyad(i,j) is observed)
- node parameter = p = Prob(Node i is observed)
- covar-dyad": parameter = beta in R^M, such that Prob(Dyad (i,j) is observed) = logistic(parameter' covarArray (i,j, .))
- covar-node": parameter = nu in R^M such that Prob(Node i is observed) = logistic(parameter' covarMatrix (i,)
- snowball": parameter = number of waves with Prob(Node i is observed in the 1st wave)
Missing Not At Random (MNAR)
- double-standard parameter = (p0,p1) with p0 = Prob(Dyad (i,j) is observed | the dyad is equal to 0), p1 = Prob(Dyad (i,j) is observed | the dyad is equal to 1)
- block-node parameter = c(p(1),...,p(Q)) and p(q) = Prob(Node i is observed | node i is in cluster q)
- block-dyad parameter = c(p(1,1),...,p(Q,Q)) and p(q,l) = Prob(Edge (i,j) is observed | node i is in cluster q and node j is in cluster l)

Value

Returns an R6 object with class missSBM_collection.

Examples

## SBM parameters
N <- 100 # number of nodes
Q <- 3   # number of clusters
pi <- rep(1,Q)/Q     # block proportion
theta <- list(mean = diag(.45,Q) + .05 ) # connectivity matrix

## Sampling parameters
samplingParameters <- .75 # the sampling rate
sampling  <- "dyad"      # the sampling design

## generate a undirected binary SBM with no covariate
sbm <- sbm::sampleSimpleSBM(N, pi, theta)

## Uncomment to set parallel computing with future
## future::plan("multicore", workers = 2)

## Sample some dyads data + Infer SBM with missing data
collection <-
   observeNetwork(sbm$networkData, sampling, samplingParameters) %>%
   estimateMissSBM(vBlocks = 1:4, sampling = sampling)
plot(collection, "monitoring")
plot(collection, "icl")

collection$ICL
coef(collection$bestModel$fittedSBM, "connectivity")

myModel <- collection$bestModel
plot(myModel, "expected")
plot(myModel, "imputed")
plot(myModel, "meso")
coef(myModel, "sampling")
coef(myModel, "connectivity")
predict(myModel)[1:5, 1:5]

## SBM parameters
N <- 100 # number of nodes
Q <- 3   # number of clusters
pi <- rep(1,Q)/Q     # block proportion
theta <- list(mean = diag(.45,Q) + .05 ) # connectivity matrix

## Sampling parameters
samplingParameters <- .75 # the sampling rate
sampling  <- "dyad"      # the sampling design

## generate a undirected binary SBM with no covariate
sbm <- sbm::sampleSimpleSBM(N, pi, theta)

## Uncomment to set parallel computing with future
## future::plan("multicore", workers = 2)

## Sample some dyads data + Infer SBM with missing data
collection <-
   observeNetwork(sbm$networkData, sampling, samplingParameters) %>%
   estimateMissSBM(vBlocks = 1:4, sampling = sampling)
plot(collection, "monitoring")
plot(collection, "icl")

collection$ICL
coef(collection$bestModel$fittedSBM, "connectivity")

myModel <- collection$bestModel
plot(myModel, "expected")
plot(myModel, "imputed")
plot(myModel, "meso")
coef(myModel, "sampling")
coef(myModel, "connectivity")
predict(myModel)[1:5, 1:5]

Extract model fitted values from object `missSBM_fit`, return by `estimateMissSBM()`

Description

Extract model fitted values from object missSBM_fit, return by estimateMissSBM()

Usage

## S3 method for class 'missSBM_fit'
fitted(object, ...)
## S3 method for class 'missSBM_fit'
fitted(object, ...)

Arguments

object

an R6 object with class missSBM_fit

...

additional parameters for S3 compatibility.

Value

A matrix of estimated probabilities of connection

Political Blogosphere network prior to 2007 French presidential election

Description

French Political Blogosphere network dataset consists of a single day snapshot of over 200 political blogs automatically extracted the 14 October 2006 and manually classified by the "Observatoire Présidentielle" project. Originally part of the 'mixer' package

Usage

frenchblog2007
frenchblog2007

Format

An igraph object with 196 nodes. The vertex attribute "party" provides a possible clustering of the nodes.

Source

https://www.meltwater.com/en/suite/consumer-intelligence?utm_source=direct&utm_medium=linkfluence

Examples

data(frenchblog2007)
igraph::V(frenchblog2007)$party
igraph::plot.igraph(frenchblog2007,
  vertex.color = factor(igraph::V(frenchblog2007)$party),
  vertex.label = NA
 )
data(frenchblog2007)
igraph::V(frenchblog2007)$party
igraph::plot.igraph(frenchblog2007,
  vertex.color = factor(igraph::V(frenchblog2007)$party),
  vertex.label = NA
 )

L1-similarity

Description

Compute l1-similarity between two vectors

Usage

l1_similarity(x, y)
l1_similarity(x, y)

Arguments

x

a vector

y

a vector

Value

a vector equal to -abs(x-y)

Examples

l1_similarity(1:5, 5:1)
l1_similarity(1:5, 5:1)

An R6 class to represent a collection of SBM fits with missing data

Description

The function estimateMissSBM() fits a collection of SBM with missing data for a varying number of block. These models with class missSBM_fit are stored in an instance of an object with class missSBM_collection, described here.

Fields are accessed via active binding and cannot be changed by the user.

This class comes with a set of R6 methods, some of them being useful for the user and exported as S3 methods. See the documentation for show() and print()

Active bindings

models: a list of models
ICL: the vector of Integrated Classification Criterion (ICL) associated to the models in the collection (the smaller, the better)
bestModel: the best model according to the ICL, restricted to models without collapsed classes when at least one such model is available (see $degenerate)
vBlocks: a vector with the number of blocks
occupiedBlocks: a vector with the number of classes actually occupied in each model (see missSBM_fit's occupiedBlocks)
degenerate: logical vector, TRUE for models with collapsed classes (occupiedBlocks < vBlocks, see missSBM_fit's repair())
optimizationSettings: the control list used by estimate()/polish()/explore() when not overridden per call (set at construction by estimateMissSBM())
optimizationStatus: a data.frame summarizing the optimization process for all models

Methods

Public methods

missSBM_collection$new()
missSBM_collection$estimate()
missSBM_collection$estimate_chain()
missSBM_collection$polish()
missSBM_collection$explore()
missSBM_collection$plot()
missSBM_collection$show()
missSBM_collection$print()
missSBM_collection$clone()

`missSBM_collection$new()`

constructor for networkSampling

Usage

missSBM_collection$new(partlyObservedNet, sampling, clusterInit, control)

Arguments

partlyObservedNet: An object with class partlyObservedNetwork.
sampling: The sampling design for the modelling of missing data: MAR designs ("dyad", "node") and MNAR designs ("double-standard", "block-dyad", "block-node" ,"degree")
clusterInit: Initial clustering: a list of vectors, each with size ncol(adjacencyMatrix).
control: a list of parameters controlling advanced features. Only 'trace' and 'useCov' are relevant here. See estimateMissSBM() for details.

`missSBM_collection$estimate()`

method to launch the estimation of the collection of models

Usage

missSBM_collection$estimate(control = NULL)

Arguments

control: optional list of parameters overriding the collection's stored control (set at construction by estimateMissSBM(), see its details for the full list). Default NULL uses the stored control as-is.

`missSBM_collection$estimate_chain()`

alternative to estimate(): fits each model in increasing order of number of blocks, initializing vBlocks[k] by splitting (see missSBM_fit's split()/candidates_split()) the already-converged model at vBlocks[k-1] instead of an independent, cold spectral clustering. Meant to reduce VEM component collapse at higher numbers of blocks (see $degenerate), at the cost of being sequential in the number of blocks (unlike estimate(), which fits every model in parallel) – can be slower in wall-clock time with many workers available. Falls back to this slot's own cold-started clustering (built at construction, same as estimate() would use) whenever nothing is splittable along the chain.

Usage

missSBM_collection$estimate_chain(control = NULL)

Arguments

control: optional list of parameters overriding the collection's stored control (set at construction by estimateMissSBM(), see its details for the full list). Default NULL uses the stored control as-is.

`missSBM_collection$polish()`

method to node-swap-polish every model in the collection (see missSBM_fit's polish()); fixes individually misclassified nodes at each model's own number of blocks, unlike explore() which searches across blocks.

Usage

missSBM_collection$polish(control = NULL)

Arguments

control: optional list of parameters overriding the collection's stored control (set at construction by estimateMissSBM(), see its details for the full list). Default NULL uses the stored control as-is.

`missSBM_collection$explore()`

method for performing exploration of the ICL (split/merge search across numbers of blocks, see missSBM_fit's candidates_split()/candidates_merge()). Uses the collection's stored control by default; iterates lets the caller override it for this call only, without altering the stored control – handy to alternate explore()/polish() calls without having to reconstruct a full control list each time. iterates <= 0 is a no-op.

Usage

missSBM_collection$explore(control = NULL, iterates = NULL, direction = "both")

Arguments

control: optional list of parameters overriding the collection's stored control (set at construction by estimateMissSBM(), see its details for the full list). Default NULL uses the stored control as-is.
iterates: optional integer overriding control$iterates for this call only.
direction: character ("forward", "backward", "both" or "none") controlling which directions are searched. Default "both".

`missSBM_collection$plot()`

plot method for missSBM_collection

Usage

missSBM_collection$plot(type = c("icl", "elbo", "monitoring"))

Arguments

type: the type specifies the field to plot, either "icl", "elbo" or "monitoring". Default is "icl"

`missSBM_collection$show()`

show method for missSBM_collection

Usage

missSBM_collection$show()

`missSBM_collection$print()`

User friendly print method

Usage

missSBM_collection$print()

`missSBM_collection$clone()`

The objects of this class are cloneable with this method.

Usage

missSBM_collection$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

## Uncomment to set parallel computing with future
## future::plan("multicore", workers = 2)

## Sample 75% of dyads in  French political Blogosphere's network data
adjacencyMatrix <- missSBM::frenchblog2007 %>%
  igraph::delete.vertices(1:100) %>%
  igraph::as_adjacency_matrix() %>%
  missSBM::observeNetwork(sampling = "dyad", parameters = 0.75)
collection <- estimateMissSBM(adjacencyMatrix, 1:5, sampling = "dyad")
class(collection)

## Uncomment to set parallel computing with future
## future::plan("multicore", workers = 2)

## Sample 75% of dyads in  French political Blogosphere's network data
adjacencyMatrix <- missSBM::frenchblog2007 %>%
  igraph::delete.vertices(1:100) %>%
  igraph::as_adjacency_matrix() %>%
  missSBM::observeNetwork(sampling = "dyad", parameters = 0.75)
collection <- estimateMissSBM(adjacencyMatrix, 1:5, sampling = "dyad")
class(collection)

An R6 class to represent an SBM fit with missing data

Description

The function estimateMissSBM() fits a collection of SBM for varying number of block. Each fitted SBM is an instance of an R6 object with class missSBM_fit, described here.

Fields are accessed via active binding and cannot be changed by the user.

This class comes with a set of R6 methods, some of them being useful for the user and exported as S3 methods. See the documentation for show(), print(), fitted(), predict(), plot().

Active bindings

fittedSBM: the fitted SBM with class SimpleSBM_fit_noCov, SimpleSBM_fit_withCov or SimpleSBM_fit_MNAR inheriting from class sbm::SimpleSBM_fit
fittedSampling: the fitted sampling, inheriting from class networkSampling and corresponding fits
imputedNetwork: The network data as a matrix with NAs values imputed with the current model
monitoring: a list carrying information about the optimization process
occupiedBlocks: the number of classes actually occupied by at least one node; can be less than fittedSBM$nbBlocks for an over-specified fit whose VEM has collapsed one or more classes (see repair())
degenerate: TRUE if occupiedBlocks < fittedSBM$nbBlocks
entropyImputed: the entropy of the distribution of the imputed dyads
entropy: the entropy due to the distribution of the imputed dyads and of the clustering
vExpec: double: variational expectation of the complete log-likelihood
penalty: double, value of the penalty term in ICL
loglik: double: approximation of the log-likelihood (variational lower bound) reached
ICL: double: value of the integrated classification log-likelihood

Methods

Public methods

missSBM_fit$new()
missSBM_fit$doVEM()
missSBM_fit$split()
missSBM_fit$candidates_split()
missSBM_fit$merge()
missSBM_fit$candidates_merge()
missSBM_fit$repair()
missSBM_fit$polish()
missSBM_fit$show()
missSBM_fit$print()
missSBM_fit$clone()

`missSBM_fit$new()`

constructor for networkSampling

Usage

missSBM_fit$new(partlyObservedNet, netSampling, clusterInit, useCov = TRUE)

Arguments

partlyObservedNet: An object with class partlyObservedNetwork.
netSampling: The sampling design for the modelling of missing data: MAR designs ("dyad", "node") and MNAR designs ("double-standard", "block-dyad", "block-node" ,"degree")
clusterInit: Initial clustering: a vector with size ncol(adjacencyMatrix), providing a user-defined clustering. The number of blocks is deduced from the number of levels in with clusterInit.
useCov: logical. If covariates are present in partlyObservedNet, should they be used for the inference or of the network sampling design, or just for the SBM inference? default is TRUE.

`missSBM_fit$doVEM()`

a method to perform inference of the current missSBM fit with variational EM

Usage

missSBM_fit$doVEM(
  control = list(threshold = 0.01, maxIter = 100, fixPointIter = 3, trace = TRUE)
)

Arguments

control: a list of VEM control parameters (see estimateMissSBM())

`missSBM_fit$split()`

clone of the current fit after splitting cluster index in two, via a spectral bipartition of the sub-network it induces. Builds but does not fit the candidate (see candidates_split()).

Usage

missSBM_fit$split(index, in_place = FALSE, base_net = NULL)

Arguments

index: index (integer) of the cluster to split
in_place: replace self's own fit (TRUE) or return a new object (FALSE, the default)?
base_net: optional precomputed network to bipartition (as built internally at the top of this method); lets candidates_split() avoid recomputing it once per candidate.

Returns

a new missSBM_fit with one more block, or NULL if index cannot be split (its induced sub-network has zero variance)

`missSBM_fit$candidates_split()`

generate and cheaply trial-fit candidates obtained by splitting each splittable cluster in two (see split()). A cluster is splittable if it has at least 4 members and non-zero variance in its induced sub-network.

Usage

missSBM_fit$candidates_split(
  control = list(threshold = 0.01, maxIter = 100, fixPointIter = 3, trace = TRUE),
  trial_niter = 2
)

Arguments

control: a list of VEM control parameters (see estimateMissSBM()); maxIter is overridden by trial_niter
trial_niter: number of VEM iterations used for the trial fits. Default is 2.

Returns

a list of trial-fitted missSBM_fit candidates (one per splittable cluster)

`missSBM_fit$merge()`

clone of the current fit after merging clusters indices[1] and indices[2] into one. Builds but does not fit the candidate (see candidates_merge()).

Usage

missSBM_fit$merge(indices, in_place = FALSE)

Arguments

indices: indices (couple of integers) of the clusters to merge
in_place: replace self's own fit (TRUE) or return a new object (FALSE, the default)?

Returns

a new missSBM_fit with one fewer block

`missSBM_fit$candidates_merge()`

generate and cheaply trial-fit candidates obtained by merging pairs of clusters (see merge()). Beyond max_candidates pairs (quadratic in the number of blocks), only the most similar-connectivity pairs are tried.

Usage

missSBM_fit$candidates_merge(
  control = list(threshold = 0.01, maxIter = 100, fixPointIter = 3, trace = TRUE),
  max_candidates = 30,
  trial_niter = 2
)

Arguments

control: a list of VEM control parameters (see estimateMissSBM()); maxIter is overridden by trial_niter
max_candidates: cap on the number of pairs tried. Default is 30.
trial_niter: number of VEM iterations used for the trial fits. Default is 2.

Returns

a list of trial-fitted missSBM_fit candidates

`missSBM_fit$repair()`

recovers a degenerate fit (fewer occupied classes than its structural nbBlocks, e.g. after a VEM component collapse) by filling the empty classes (see repair_empty_classes()) and refitting the full VEM. Mutates self in place; a no-op if the fit is not degenerate.

Usage

missSBM_fit$repair(
  control = list(threshold = 0.01, maxIter = 100, fixPointIter = 3, trace = TRUE)
)

Arguments

control: a list of VEM control parameters (see estimateMissSBM())

Returns

invisibly, self

`missSBM_fit$polish()`

discrete node-swap polishing (Kernighan-Lin / greedy-ICL style): after VEM convergence, tau is near-hard and its fixed point cannot relocate a single misclassified node (only split()/merge() fix group-level mistakes). Each sweep computes, for every node, the closed-form complete-data log-likelihood gain of moving it to its best alternative class (theta/pi held fixed), applies the improving, non-class-emptying moves, then runs a full VEM to resettle. Stops as soon as a sweep fails to improve the ICL, mutates self in place, and never leaves the ICL worse than before the call.

Usage

missSBM_fit$polish(
  control = list(threshold = 0.01, maxIter = 100, fixPointIter = 3, trace = TRUE),
  max_sweeps = 10
)

Arguments

control: a list of VEM control parameters (see estimateMissSBM())
max_sweeps: maximum number of swap sweeps. Default is 10.

Returns

invisibly, self

`missSBM_fit$show()`

show method for missSBM_fit

Usage

missSBM_fit$show()

`missSBM_fit$print()`

User friendly print method

Usage

missSBM_fit$print()

`missSBM_fit$clone()`

The objects of this class are cloneable with this method.

Usage

missSBM_fit$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

## Sample 75% of dyads in  French political Blogosphere's network data
adjMatrix <- missSBM::frenchblog2007 %>%
  igraph::as_adjacency_matrix(sparse = FALSE) %>%
  missSBM::observeNetwork(sampling = "dyad", parameters = 0.75)
collection <- estimateMissSBM(adjMatrix, 3:5, sampling = "dyad")
my_missSBM_fit <- collection$bestModel
class(my_missSBM_fit)
plot(my_missSBM_fit, "imputed")

## Sample 75% of dyads in  French political Blogosphere's network data
adjMatrix <- missSBM::frenchblog2007 %>%
  igraph::as_adjacency_matrix(sparse = FALSE) %>%
  missSBM::observeNetwork(sampling = "dyad", parameters = 0.75)
collection <- estimateMissSBM(adjMatrix, 3:5, sampling = "dyad")
my_missSBM_fit <- collection$bestModel
class(my_missSBM_fit)
plot(my_missSBM_fit, "imputed")

Control of a missSBM fit

Description

Helper to define the list of parameters that controls estimateMissSBM(). All arguments have defaults.

Usage

missSBM_param(
  threshold = 0.01,
  maxIter = 50,
  fixPointIter = 3,
  imputation = c("median", "average", "zero"),
  similarity = l1_similarity,
  useCov = TRUE,
  clusterInit = NULL,
  polish = TRUE,
  iterates = 1,
  maxMergeCandidates = 30,
  stopOnDegenerate = TRUE,
  maxConsecutiveDegenerate = 2,
  warmChain = FALSE,
  trace = TRUE
)
missSBM_param(
  threshold = 0.01,
  maxIter = 50,
  fixPointIter = 3,
  imputation = c("median", "average", "zero"),
  similarity = l1_similarity,
  useCov = TRUE,
  clusterInit = NULL,
  polish = TRUE,
  iterates = 1,
  maxMergeCandidates = 30,
  stopOnDegenerate = TRUE,
  maxConsecutiveDegenerate = 2,
  warmChain = FALSE,
  trace = TRUE
)

Arguments

threshold

V-EM algorithm stops when an optimization step changes the objective function or the parameters by less than threshold. Default is 1e-2.

maxIter

V-EM algorithm stops when the number of iteration exceeds maxIter. Default is 50.

fixPointIter

number of fix-point iterations in the V-E step. Default is 3.

imputation

character, the imputation strategy used to build the initial clustering (see partlyObservedNetwork's imputation()). Either "median" (default), "average" or "zero".

similarity

an R x R -> R function to compute similarities between node covariates. Default is l1_similarity, that is, -abs(x - y). Only relevant when the covariates are node-centered (i.e. covariates is a list of size-N vectors).

useCov

logical. If covariates is not empty, should they be used for the SBM inference (or just for the sampling)? Default is TRUE.

clusterInit

initial clustering: NULL (default) for a cold spectral clustering, or a list with length(vBlocks) vectors, each with size ncol(adjacencyMatrix), providing a user-defined clustering.

polish

logical, should each model be node-swap-polished (see missSBM_fit's polish()) after the initial VEM fit, fixing individually misclassified nodes at that model's own number of blocks? Cheap relative to exploration (iterates), since it does not search across numbers of blocks. Default is TRUE.

iterates

integer, the number of forward/backward exploration passes searching for a better number of blocks by splitting/merging clusters (unlike polish, which only refines each model at its own number of blocks): more expensive than polish. 0 disables exploration entirely (only the initial VEM fit, plus polish if enabled, is returned). Default is 1.

maxMergeCandidates

integer, caps the number of cluster-pair merge candidates tried during backward exploration (quadratic in the number of blocks otherwise). Beyond this cap, only the pairs with the most similar fitted connectivity profiles are tried, since merging two blocks with very different connectivity is rarely competitive anyway. Default is 30.

stopOnDegenerate

logical. A requested number of blocks can be higher than what the network actually supports: VEM then collapses one or more classes (see missSBM_fit's repair()), and even a fair recovery attempt (repair(), then a full exploration pass letting explore_forward() try to split a healthy neighbor into that range) can still collapse right back down. When this persists over maxConsecutiveDegenerate consecutive (increasing) values of vBlocks after a pass, forward (split) exploration stops growing further into that range on subsequent passes (only relevant when iterates > 1); the affected models stay as fitted, flagged via $degenerate, and a warning is issued. Default is TRUE.

maxConsecutiveDegenerate

integer, the run length that triggers stopOnDegenerate. Default is 2.

warmChain

logical (work in progress). If TRUE, each model is initialized by splitting (see missSBM_fit's split()) the already-converged, smaller neighbor in vBlocks instead of an independent cold spectral clustering (see missSBM_collection's estimate_chain()) – meant to reduce VEM component collapse at higher numbers of blocks. Sequential in the number of blocks, unlike the default (FALSE), which fits every model in parallel: can be slower in wall-clock time when several workers are available. Default is FALSE.

trace

logical for verbosity. Default is TRUE.

Value

a list of parameters configuring the fit, with class missSBM_param.

Examples

my_control <- missSBM_param(iterates = 2, polish = FALSE)
my_control$iterates
my_control <- missSBM_param(iterates = 2, polish = FALSE)
my_control$iterates

Definition of R6 Class 'networkSampling_sampler'

Description

This class is use to define a sampling model for a network. Inherits from 'networkSampling'. Owns a rSampling method which takes an adjacency matrix as an input and send back an object with class partlyObservedNetwork.

Super class

networkSampling -> networkSampler

Active bindings

samplingMatrix: a matrix of logical indicating observed entries

Methods

Public methods

networkSampler$new()
networkSampler$rSamplingMatrix()
networkSampler$clone()

Inherited methods

networkSampling$print()
networkSampling$show()

`networkSampler$new()`

constructor for networkSampling

Usage

networkSampler$new(type = NA, parameters = NA, nbNodes = NA, directed = FALSE)

Arguments

type: character for the type of sampling. must be in ("dyad", "covar-dyad", "node", "covar-node", "block-node", "block-dyad", "double-standard", "degree")
parameters: the vector of parameters associated to the sampling at play
nbNodes: number of nodes in the network
directed: logical, directed network of not

`networkSampler$rSamplingMatrix()`

a method for drawing a sampling matrix according to the current sampling design

Usage

networkSampler$rSamplingMatrix()

`networkSampler$clone()`

The objects of this class are cloneable with this method.

Usage

networkSampler$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Definition of R6 Class 'networkSampling'

Description

this virtual class is the mother of all subtypes of networkSampling (either sampler or fit) It is used to define a sampling model for a network. It has a rSampling method which takes an adjacency matrix as an input and send back an object with class partlyObservedNetwork.

Active bindings

type: a character for the type of sampling
parameters: the vector of parameters associated with the sampling at play
df: the number of entries in the vector of parameters

Methods

Public methods

networkSampling$new()
networkSampling$show()
networkSampling$print()
networkSampling$clone()

`networkSampling$new()`

constructor for networkSampling

Usage

networkSampling$new(type = NA, parameters = NA)

Arguments

type: character for the type of sampling. must be in ("dyad", "covar-dyad", "node", "covar-node", "block-node", "block-dyad", "double-standard", "degree")
parameters: the vector of parameters associated to the sampling at play

`networkSampling$show()`

show method

Usage

networkSampling$show(
  type = paste0(private$name, "-model for network sampling\n")
)

Arguments

type: character used to specify the type of sampling

`networkSampling$print()`

User friendly print method

Usage

networkSampling$print()

`networkSampling$clone()`

The objects of this class are cloneable with this method.

Usage

networkSampling$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Virtual class used to define a family of networkSamplingDyads_fit

Description

Virtual class used to define a family of networkSamplingDyads_fit

Super class

networkSampling -> networkSamplingDyads_fit

Active bindings

penalty: double, value of the penalty term in ICL
log_lambda: double, term for adjusting the imputation step which depends on the type of sampling

Methods

Public methods

networkSamplingDyads_fit$new()
networkSamplingDyads_fit$show()
networkSamplingDyads_fit$update_parameters()
networkSamplingDyads_fit$update_imputation()
networkSamplingDyads_fit$clone()

Inherited methods

networkSampling$print()

`networkSamplingDyads_fit$new()`

constructor for networkSampling_fit

Usage

networkSamplingDyads_fit$new(partlyObservedNetwork, name)

Arguments

partlyObservedNetwork: a object with class partlyObservedNetwork representing the observed data with possibly missing entries
name: a character for the name of sampling to fit on the partlyObservedNetwork

`networkSamplingDyads_fit$show()`

show method

Usage

networkSamplingDyads_fit$show()

`networkSamplingDyads_fit$update_parameters()`

a method to update the estimation of the parameters. By default, nothing to do (corresponds to MAR sampling)

Usage

networkSamplingDyads_fit$update_parameters(...)

Arguments

...: use for compatibility

`networkSamplingDyads_fit$update_imputation()`

a method to update the imputation of the missing entries.

Usage

networkSamplingDyads_fit$update_imputation(nu)

Arguments

nu: the matrix of (uncorrected) imputation for missing entries

`networkSamplingDyads_fit$clone()`

The objects of this class are cloneable with this method.

Usage

networkSamplingDyads_fit$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Virtual class used to define a family of networkSamplingNodes_fit

Description

Virtual class used to define a family of networkSamplingNodes_fit

Super class

networkSampling -> networkSamplingNodes_fit

Active bindings

penalty: double, value of the penalty term in ICL
log_lambda: double, term for adjusting the imputation step which depends on the type of sampling

Methods

Public methods

networkSamplingNodes_fit$new()
networkSamplingNodes_fit$show()
networkSamplingNodes_fit$update_parameters()
networkSamplingNodes_fit$update_imputation()
networkSamplingNodes_fit$clone()

Inherited methods

networkSampling$print()

`networkSamplingNodes_fit$new()`

constructor

Usage

networkSamplingNodes_fit$new(partlyObservedNetwork, name)

Arguments

partlyObservedNetwork: a object with class partlyObservedNetwork representing the observed data with possibly missing entries
name: a character for the name of sampling to fit on the partlyObservedNetwork

`networkSamplingNodes_fit$show()`

show method

Usage

networkSamplingNodes_fit$show()

`networkSamplingNodes_fit$update_parameters()`

a method to update the estimation of the parameters. By default, nothing to do (corresponds to MAR sampling)

Usage

networkSamplingNodes_fit$update_parameters(...)

Arguments

...: use for compatibility

`networkSamplingNodes_fit$update_imputation()`

a method to update the imputation of the missing entries.

Usage

networkSamplingNodes_fit$update_imputation(nu)

Arguments

nu: the matrix of (uncorrected) imputation for missing entries

`networkSamplingNodes_fit$clone()`

The objects of this class are cloneable with this method.

Usage

networkSamplingNodes_fit$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Virtual class for all node-centered samplers

Description

Virtual class for all node-centered samplers

Super classes

networkSampling -> networkSampler -> nodeSampler

Methods

Public methods

nodeSampler$clone()

Inherited methods

networkSampling$print()
networkSampling$show()
networkSampler$initialize()
networkSampler$rSamplingMatrix()

`nodeSampler$clone()`

The objects of this class are cloneable with this method.

Usage

nodeSampler$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Class for fitting a node sampling

Description

Class for fitting a node sampling

Super classes

networkSampling -> networkSamplingNodes_fit -> nodeSampling_fit

Active bindings

vExpec: variational expectation of the sampling

Methods

Public methods

nodeSampling_fit$new()
nodeSampling_fit$clone()

Inherited methods

networkSampling$print()
networkSamplingNodes_fit$show()
networkSamplingNodes_fit$update_imputation()
networkSamplingNodes_fit$update_parameters()

`nodeSampling_fit$new()`

constructor

Usage

nodeSampling_fit$new(partlyObservedNetwork, ...)

Arguments

partlyObservedNetwork: a object with class partlyObservedNetwork representing the observed data with possibly missing entries
...: used for compatibility

`nodeSampling_fit$clone()`

The objects of this class are cloneable with this method.

Usage

nodeSampling_fit$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Observe a network partially according to a given sampling design

Description

This function draws observations in an adjacency matrix according to a given network sampling design.

Usage

observeNetwork(
  adjacencyMatrix,
  sampling,
  parameters,
  clusters = NULL,
  covariates = list(),
  similarity = l1_similarity,
  intercept = 0
)
observeNetwork(
  adjacencyMatrix,
  sampling,
  parameters,
  clusters = NULL,
  covariates = list(),
  similarity = l1_similarity,
  intercept = 0
)

Arguments

adjacencyMatrix

The N x N adjacency matrix of the network to sample. The diagonal is expected to be NA (no self-loops); any other pre-existing NA entry is treated as an absent edge (coded 0) before sampling is applied on top of it, with a warning.

sampling

The sampling design used to observe the adjacency matrix, see details.

parameters

The sampling parameters (adapted to each sampling, see details).

clusters

An optional clustering membership vector of the nodes. Only necessary for block samplings.

covariates

An optional list with M entries (the M covariates). If the covariates are node-centered, each entry of covariates. must be a size-N vector; if the covariates are dyad-centered, each entry of covariates must be N x N matrix.

similarity

An optional function to compute similarities between node covariates. Default is l1_similarity, that is, -abs(x-y). Only relevant when the covariates are node-centered.

intercept

An optional intercept term to be added in case of the presence of covariates. Default is 0.

Details

Internal functions use future_lapply, so set your plan to 'multisession' or 'multicore' to use several cores/workers.

The different sampling designs are split into two families in which we find dyad-centered and node-centered samplings. See doi:10.1080/01621459.2018.1562934 for a complete description.

Missing at Random (MAR)
- dyad parameter = p = Prob(Dyad(i,j) is observed)
- node parameter = p = Prob(Node i is observed)
- covar-dyad": parameter = beta in R^M, such that Prob(Dyad (i,j) is observed) = logistic(parameter' covarArray (i,j, .))
- covar-node": parameter = nu in R^M such that Prob(Node i is observed) = logistic(parameter' covarMatrix (i,)
- snowball": parameter = number of waves with Prob(Node i is observed in the 1st wave)
Missing Not At Random (MNAR)
- double-standard parameter = (p0,p1) with p0 = Prob(Dyad (i,j) is observed | the dyad is equal to 0), p1 = Prob(Dyad (i,j) is observed | the dyad is equal to 1)
- block-node parameter = c(p(1),...,p(Q)) and p(q) = Prob(Node i is observed | node i is in cluster q)
- block-dyad parameter = c(p(1,1),...,p(Q,Q)) and p(q,l) = Prob(Edge (i,j) is observed | node i is in cluster q and node j is in cluster l)

Value

an adjacency matrix with the same dimension as the input, yet with additional NAs.

Examples

## SBM parameters
N <- 300 # number of nodes
Q <- 3   # number of clusters
pi <- rep(1,Q)/Q     # block proportion
theta <- list(mean = diag(.45,Q) + .05 ) # connectivity matrix

## simulate an unidrected binary SBM without covariate
sbm <- sbm::sampleSimpleSBM(N, pi, theta)

## Sample network data

# some sampling design and their associated parameters
sampling_parameters <- list(
   "dyad" = .3,
   "node" = .3,
   "double-standard" = c(0.4, 0.8),
   "block-node" = c(.3, .8, .5),
   "block-dyad" = theta$mean,
   "degree" = c(.01, .01),
   "snowball" = c(2,.1)
 )

observed_networks <- list()

for (sampling in names(sampling_parameters)) {
  observed_networks[[sampling]] <-
     missSBM::observeNetwork(
       adjacencyMatrix = sbm$networkData,
       sampling        = sampling,
       parameters      = sampling_parameters[[sampling]],
       clusters        = sbm$memberships
     )
}
## SBM parameters
N <- 300 # number of nodes
Q <- 3   # number of clusters
pi <- rep(1,Q)/Q     # block proportion
theta <- list(mean = diag(.45,Q) + .05 ) # connectivity matrix

## simulate an unidrected binary SBM without covariate
sbm <- sbm::sampleSimpleSBM(N, pi, theta)

## Sample network data

# some sampling design and their associated parameters
sampling_parameters <- list(
   "dyad" = .3,
   "node" = .3,
   "double-standard" = c(0.4, 0.8),
   "block-node" = c(.3, .8, .5),
   "block-dyad" = theta$mean,
   "degree" = c(.01, .01),
   "snowball" = c(2,.1)
 )

observed_networks <- list()

for (sampling in names(sampling_parameters)) {
  observed_networks[[sampling]] <-
     missSBM::observeNetwork(
       adjacencyMatrix = sbm$networkData,
       sampling        = sampling,
       parameters      = sampling_parameters[[sampling]],
       clusters        = sbm$memberships
     )
}

An R6 Class used for internal representation of a partially observed network

Description

This class is not exported to the user

Active bindings

samplingRate: The percentage of observed dyads
nbNodes: The number of nodes
nbDyads: The number of dyads
is_directed: logical indicating if the network is directed or not
networkData: The adjacency matrix of the network
covarArray: the array of covariates
covarMatrix: the matrix of covariates
samplingMatrix: matrix of observed and non-observed edges
samplingMatrixBar: matrix of observed and non-observed edges
observedNodes: a vector of observed and non-observed nodes (observed means at least one non NA value)

Methods

Public methods

partlyObservedNetwork$new()
partlyObservedNetwork$clustering()
partlyObservedNetwork$imputation()
partlyObservedNetwork$clone()

`partlyObservedNetwork$new()`

constructor

Usage

partlyObservedNetwork$new(
  adjacencyMatrix,
  covariates = list(),
  similarity = l1_similarity
)

Arguments

adjacencyMatrix: The adjacency matrix of the network
covariates: A list with M entries (the M covariates), each of whom being either a size-N vector or N x N matrix.
similarity: An R x R -> R function to compute similarities between node covariates. Default is l1_similarity, that is, -abs(x-y).

`partlyObservedNetwork$clustering()`

method to cluster network data with missing value

Usage

partlyObservedNetwork$clustering(
  vBlocks,
  imputation = ifelse(is.null(private$phi), "median", "average")
)

Arguments

vBlocks: The vector of number of blocks considered in the collection.
imputation: character indicating the type of imputation among "median", "average"

`partlyObservedNetwork$imputation()`

basic imputation from existing clustering

Usage

partlyObservedNetwork$imputation(type = c("median", "average", "zero"))

Arguments

type: a character, the type of imputation. Either "median" or "average"

`partlyObservedNetwork$clone()`

The objects of this class are cloneable with this method.

Usage

partlyObservedNetwork$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Visualization for an object `missSBM_fit`

Description

Plot function for the various fields of a missSBM_fit: the fitted SBM (network or connectivity), and a plot monitoring the optimization.

Usage

## S3 method for class 'missSBM_fit'
plot(
  x,
  type = c("imputed", "expected", "meso", "monitoring"),
  dimLabels = list(row = "node", col = "node"),
  ...
)
## S3 method for class 'missSBM_fit'
plot(
  x,
  type = c("imputed", "expected", "meso", "monitoring"),
  dimLabels = list(row = "node", col = "node"),
  ...
)

Arguments

x

an object with class missSBM_fit

type

the type specifies the field to plot, either "imputed", "expected", "meso", or "monitoring"

dimLabels

: a list of two characters specifying the labels of the nodes. Default to list(row= 'node',col = 'node'))

...

additional parameters for S3 compatibility. Not used

Value

a ggplot object

Prediction of a `missSBM_fit` (i.e. network with imputed missing dyads)

Description

Prediction of a missSBM_fit (i.e. network with imputed missing dyads)

Usage

## S3 method for class 'missSBM_fit'
predict(object, ...)
## S3 method for class 'missSBM_fit'
predict(object, ...)

Arguments

object

an R6 object with class missSBM_fit

...

additional parameters for S3 compatibility.

Value

an adjacency matrix between pairs of nodes. Missing dyads are imputed with their expected values, i.e. by there estimated probabilities of connection under the missing SBM.

Class for defining a simple dyad sampler

Description

Class for defining a simple dyad sampler

Super classes

networkSampling -> networkSampler -> dyadSampler -> simpleDyadSampler

Methods

Public methods

simpleDyadSampler$new()
simpleDyadSampler$clone()

Inherited methods

networkSampling$print()
networkSampling$show()
networkSampler$rSamplingMatrix()

`simpleDyadSampler$new()`

constructor for networkSampling

Usage

simpleDyadSampler$new(
  parameters = NA,
  nbNodes = NA,
  directed = FALSE,
  covarArray = NULL,
  intercept = 0
)

Arguments

parameters: the vector of parameters associated to the sampling at play
nbNodes: number of nodes in the network
directed: logical, directed network of not
covarArray: an array of covariates used
intercept: double, intercept term used to compute the probability of sampling in the presence of covariates. Default 0.

`simpleDyadSampler$clone()`

The objects of this class are cloneable with this method.

Usage

simpleDyadSampler$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Class for defining a simple node sampler

Description

Class for defining a simple node sampler

Super classes

networkSampling -> networkSampler -> nodeSampler -> simpleNodeSampler

Methods

Public methods

simpleNodeSampler$new()
simpleNodeSampler$clone()

Inherited methods

networkSampling$print()
networkSampling$show()
networkSampler$rSamplingMatrix()

`simpleNodeSampler$new()`

constructor for networkSampling

Usage

simpleNodeSampler$new(
  parameters = NA,
  nbNodes = NA,
  directed = FALSE,
  covarMatrix = NULL,
  intercept = 0
)

Arguments

parameters: the vector of parameters associated to the sampling at play
nbNodes: number of nodes in the network
directed: logical, directed network of not
covarMatrix: a matrix of covariates used
intercept: double, intercept term used to compute the probability of sampling in the presence of covariates. Default 0.

`simpleNodeSampler$clone()`

The objects of this class are cloneable with this method.

Usage

simpleNodeSampler$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Base internal class for adjusting a binary Stochastic Block Model in the context of missSBM.

Description

It is not designed to be called directly by the user; see the concrete variants SimpleSBM_fit_noCov, SimpleSBM_fit_withCov and SimpleSBM_fit_MNAR.

Super classes

sbm::SBM -> sbm::SimpleSBM -> SimpleSBM_fit

Active bindings

type: the type of SBM (distribution of edges values, network type, presence of covariates)
penalty: double, value of the penalty term in ICL
entropy: double, value of the entropy due to the clustering distribution
loglik: double: approximation of the log-likelihood (variational lower bound) reached
ICL: double: value of the integrated classification log-likelihood

Methods

Public methods

SimpleSBM_fit$new()
SimpleSBM_fit$doVEM()
SimpleSBM_fit$reorder()
SimpleSBM_fit$get_state()
SimpleSBM_fit$set_state()
SimpleSBM_fit$clone()

Inherited methods

`SimpleSBM_fit$new()`

constructor for simpleSBM_fit for missSBM purpose

Usage

SimpleSBM_fit$new(networkData, clusterInit, covarList = list())

Arguments

networkData: a structure to store network under missing data condition: either a matrix possibly with NA, or a missSBM:::partlyObservedNetwork
clusterInit: Initial clustering: a vector with size ncol(adjacencyMatrix), providing a user-defined clustering with nbBlocks levels.
covarList: An optional list with M entries (the M covariates).

`SimpleSBM_fit$doVEM()`

method to perform estimation via variational EM

Usage

SimpleSBM_fit$doVEM(
  threshold = 0.01,
  maxIter = 100,
  fixPointIter = 3,
  trace = FALSE
)

Arguments

threshold: stop when an optimization step changes the objective function by less than threshold. Default is 1e-4.
maxIter: V-EM algorithm stops when the number of iteration exceeds maxIter. Default is 10
fixPointIter: number of fix-point iterations in the Variational E step. Default is 5.
trace: logical for verbosity. Default is FALSE.

`SimpleSBM_fit$reorder()`

permute group labels by order of decreasing probability

Usage

SimpleSBM_fit$reorder()

`SimpleSBM_fit$get_state()`

a lightweight snapshot of the mutable VEM state (as opposed to clone(), which duplicates the whole object, including the – possibly large – network data)

Usage

SimpleSBM_fit$get_state()

`SimpleSBM_fit$set_state()`

restore a state previously returned by get_state()

Usage

SimpleSBM_fit$set_state(state)

Arguments

state: a state, as returned by get_state()

`SimpleSBM_fit$clone()`

The objects of this class are cloneable with this method.

Usage

SimpleSBM_fit$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Internal class for a binary SBM fit under MNAR sampling designs (double-standard, block-node, block-dyad).

Description

It is not designed to be called directly by the user.

Super classes

sbm::SBM -> sbm::SimpleSBM -> SimpleSBM_fit -> SimpleSBM_fit_noCov -> SimpleSBM_MNAR_noCov

Active bindings

vExpec: double: variational approximation of the expectation complete log-likelihood

Methods

Public methods

SimpleSBM_MNAR_noCov$new()
SimpleSBM_MNAR_noCov$update_parameters()
SimpleSBM_MNAR_noCov$update_blocks()
SimpleSBM_MNAR_noCov$polish_log_tau()
SimpleSBM_MNAR_noCov$clone()

Inherited methods

`SimpleSBM_MNAR_noCov$new()`

constructor for simpleSBM_fit for missSBM purpose

Usage

SimpleSBM_MNAR_noCov$new(networkData, clusterInit)

Arguments

networkData: a structure to store network under missing data condition: either a matrix possibly with NA, or a missSBM:::partlyObservedNetwork
clusterInit: Initial clustering: a vector with size ncol(adjacencyMatrix), providing a user-defined clustering with nbBlocks levels.

`SimpleSBM_MNAR_noCov$update_parameters()`

update parameters estimation (M-step)

Usage

SimpleSBM_MNAR_noCov$update_parameters(nu = NULL)

Arguments

nu: currently imputed values

`SimpleSBM_MNAR_noCov$update_blocks()`

update variational estimation of blocks (VE-step)

Usage

SimpleSBM_MNAR_noCov$update_blocks(log_lambda = 0)

Arguments

log_lambda: additional term sampling dependent used to de-bias estimation of tau

`SimpleSBM_MNAR_noCov$polish_log_tau()`

for each node, the complete-data log-likelihood it would contribute to each class if hard-assigned there (theta/pi held fixed), used to decide node-swap moves in missSBM_fit$polish(). Unlike update_blocks()'s tau update (which combines the observed- and imputed-part E-steps as-is), this subtracts one copy of log(pi): both E-step calls add it, so summing them double-counts it relative to vExpec's convention – verified numerically to matter (see git history).

Usage

SimpleSBM_MNAR_noCov$polish_log_tau(log_lambda = 0)

Arguments

log_lambda: additional sampling-design-dependent term, added as-is

Returns

an N x Q matrix

`SimpleSBM_MNAR_noCov$clone()`

The objects of this class are cloneable with this method.

Usage

SimpleSBM_MNAR_noCov$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Internal class for a binary SBM fit under MAR sampling designs without covariates.

Description

It is not designed to be called directly by the user.

Super classes

sbm::SBM -> sbm::SimpleSBM -> SimpleSBM_fit -> SimpleSBM_fit_noCov

Active bindings

imputation: the matrix of imputed values
vExpec: double: variational approximation of the expectation complete log-likelihood
vExpec_corrected: double: variational approximation of the expectation complete log-likelihood with correction to be comparable with MNAR criteria

Methods

Public methods

SimpleSBM_fit_noCov$update_parameters()
SimpleSBM_fit_noCov$update_blocks()
SimpleSBM_fit_noCov$polish_log_tau()
SimpleSBM_fit_noCov$clone()

Inherited methods

`SimpleSBM_fit_noCov$update_parameters()`

update parameters estimation (M-step)

Usage

SimpleSBM_fit_noCov$update_parameters(...)

Arguments

...: additional arguments, only required for MNAR cases

`SimpleSBM_fit_noCov$update_blocks()`

update variational estimation of blocks (VE-step)

Usage

SimpleSBM_fit_noCov$update_blocks(...)

Arguments

...: additional arguments, only required for MNAR cases

`SimpleSBM_fit_noCov$polish_log_tau()`

for each node, the complete-data log-likelihood it would contribute to each class if hard-assigned there (theta/pi held fixed), used to decide node-swap moves in missSBM_fit$polish().

Usage

SimpleSBM_fit_noCov$polish_log_tau(log_lambda = 0)

Arguments

log_lambda: additional sampling-design-dependent term, added as-is

Returns

an N x Q matrix

`SimpleSBM_fit_noCov$clone()`

The objects of this class are cloneable with this method.

Usage

SimpleSBM_fit_noCov$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Internal class for a binary SBM fit under MAR sampling designs with covariates.

Description

It is not designed to be called directly by the user.

Super classes

sbm::SBM -> sbm::SimpleSBM -> SimpleSBM_fit -> SimpleSBM_fit_withCov

Active bindings

imputation: the matrix of imputed values
vExpec: double: variational approximation of the expectation complete log-likelihood
vExpec_corrected: double: variational approximation of the expectation complete log-likelihood with correction to be comparable with MNAR criteria

Methods

Public methods

SimpleSBM_fit_withCov$update_parameters()
SimpleSBM_fit_withCov$update_blocks()
SimpleSBM_fit_withCov$polish_log_tau()
SimpleSBM_fit_withCov$clone()

Inherited methods

`SimpleSBM_fit_withCov$update_parameters()`

update parameters estimation (M-step) via Newton-Raphson: the M-step objective is a weighted logistic regression (concave), so Newton converges in a handful of iterations – no external optimizer is required.

Usage

SimpleSBM_fit_withCov$update_parameters(...)

Arguments

...: use for compatibility

`SimpleSBM_fit_withCov$update_blocks()`

update variational estimation of blocks (VE-step)

Usage

SimpleSBM_fit_withCov$update_blocks(...)

Arguments

...: use for compatibility

`SimpleSBM_fit_withCov$polish_log_tau()`

for each node, the complete-data log-likelihood it would contribute to each class if hard-assigned there (theta/beta/pi held fixed), used to decide node-swap moves in missSBM_fit$polish().

Usage

SimpleSBM_fit_withCov$polish_log_tau(log_lambda = 0)

Arguments

log_lambda: additional sampling-design-dependent term, added as-is

Returns

an N x Q matrix

`SimpleSBM_fit_withCov$clone()`

The objects of this class are cloneable with this method.

Usage

SimpleSBM_fit_withCov$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Class for defining a snowball sampler

Description

Class for defining a snowball sampler

Super classes

networkSampling -> networkSampler -> nodeSampler -> snowballSampler

Methods

Public methods

snowballSampler$new()
snowballSampler$clone()

Inherited methods

networkSampling$print()
networkSampling$show()
networkSampler$rSamplingMatrix()

`snowballSampler$new()`

constructor for networkSampling

Usage

snowballSampler$new(parameters = NA, adjacencyMatrix = NA, directed = FALSE)

Arguments

parameters: the vector of parameters associated to the sampling at play
adjacencyMatrix: the adjacency matrix of the network
directed: logical, directed network of not

`snowballSampler$clone()`

The objects of this class are cloneable with this method.

Usage

snowballSampler$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Summary method for a `missSBM_fit`

Description

Summary method for a missSBM_fit

Usage

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

Arguments

object

an R6 object with class missSBM_fit

...

additional parameters for S3 compatibility.

Value

a basic printing output

War data set

Description

This dataset contains two networks where the nodes are countries and an edge in network "belligerent" means that the two countries have been at least once at war between years 1816 to 2007 while an edge in network "alliance" means that the two countries have had a formal alliance between years 1816 to 2012. The network belligerent have less nodes since countries which have not been at war are not considered.

Usage

war
war

Format

A list with 2 two igraph objects, alliance and belligerent. Each graph have three attributes: 'name' (the country name), 'power' (a score related to military power: the higher, the better) and 'trade' (a score related to the trade effort between pairs of countries).

Source

networks were extracted from https://correlatesofwar.org/

References

Sarkees, Meredith Reid and Frank Wayman (2010). Resort to War: 1816 - 2007. Washington DC: CQ Press.

Gibler, Douglas M. 2009. International military alliances, 1648-2008. CQ Press

Examples

data(war)
class(war$belligerent)
igraph::gorder(war$alliance)
igraph::gorder(war$belligerent)
igraph::edges(war$alliance)
igraph::get.graph.attribute(war$alliance)
data(war)
class(war$belligerent)
igraph::gorder(war$alliance)
igraph::gorder(war$belligerent)
igraph::edges(war$alliance)
igraph::get.graph.attribute(war$alliance)

Package 'missSBM'

Help Index

Class for defining a block dyad sampler

Description

Super classes

Active bindings

Methods

Public methods

blockDyadSampler$new()

Usage

Arguments

blockDyadSampler$clone()

Usage

Arguments

Class for fitting a block-dyad sampling

Description

Super classes

Active bindings

Methods

Public methods

blockDyadSampling_fit$new()

Usage

Arguments

blockDyadSampling_fit$update_parameters()

Usage

Arguments

blockDyadSampling_fit$clone()

Usage

Arguments

Class for defining a block node sampler

Description

Super classes

Methods

Public methods

blockNodeSampler$new()

Usage

Arguments

blockNodeSampler$clone()

Usage

Arguments

Class for fitting a block-node sampling

Description

Super classes

Active bindings

Methods

Public methods

blockNodeSampling_fit$new()

Usage

Arguments

blockNodeSampling_fit$update_parameters()

Usage

Arguments

blockNodeSampling_fit$clone()

Usage

Arguments

Extract model coefficients

Description

Usage

Arguments

Value

Class for fitting a dyad sampling with covariates

Description

Super classes

Active bindings

Methods

Public methods

covarDyadSampling_fit$new()

Usage

Arguments

covarDyadSampling_fit$clone()

Usage

Arguments

Class for fitting a node-centered sampling with covariate

Description

Super classes

Active bindings

Methods

Public methods

covarNodeSampling_fit$new()

Usage

`blockDyadSampler$new()`

`blockDyadSampler$clone()`

`blockDyadSampling_fit$new()`

`blockDyadSampling_fit$update_parameters()`

`blockDyadSampling_fit$clone()`

`blockNodeSampler$new()`

`blockNodeSampler$clone()`

`blockNodeSampling_fit$new()`

`blockNodeSampling_fit$update_parameters()`

`blockNodeSampling_fit$clone()`

`covarDyadSampling_fit$new()`

`covarDyadSampling_fit$clone()`

`covarNodeSampling_fit$new()`

`covarNodeSampling_fit$clone()`

`degreeSampler$new()`

`degreeSampler$clone()`

`degreeSampling_fit$new()`

`degreeSampling_fit$update_parameters()`

`degreeSampling_fit$update_imputation()`

`degreeSampling_fit$clone()`

`doubleStandardSampler$new()`

`doubleStandardSampler$clone()`

`doubleStandardSampling_fit$new()`

`doubleStandardSampling_fit$update_parameters()`

`doubleStandardSampling_fit$update_imputation()`

`doubleStandardSampling_fit$clone()`

`dyadSampler$new()`