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Estimation for Multiplex SBM

Source: R/estimate.R
estimateMultiplexSBM.Rd

Estimation for Multiplex SBM

Usage

estimateMultiplexSBM(listSBM, dependent = FALSE, estimOptions = list())

Arguments

listSBM

list of networks that were defined by the defineSBM function

dependent

logical parameter indicating whether the networks in the multiplex structure are dependent beyond the latent variables,

estimOptions

options for the inference procedure

Value

a MultiplexSBM_fit object with the estimated parameters and the blocks

Details

The list of parameters estimOptions essentially tunes the optimization process and the variational EM algorithm, with the following parameters

  • "nbCores" integer for number of cores used. Default is 2 (1 under Positron, which does not allow forking)

  • "verbosity" integer for verbosity (0, 1). Default is 1

  • "nbBlocksRange" List of length the number of functional groups, each element supplying the minimal and maximal number of blocks to be explored. The names of the list must be the names of the functional groups. Default value is from 1 to 10)

  • "initBM" Boolean. True if using simple and bipartite SBM as initialisations. Default value = TRUE

  • "maxiterVEM" Number of max. number of iterations in the VEM. Default value = 100

  • "maxiterVE" Number of max. number of iterations in the VE. Default value = 100

  • "plot" boolean, should the ICL be dynamically plotted or not. Default is TRUE, FALSE when "verbosity" is 0. For dependent networks

  • "exploreFactor" control the exploration of the number of groups. For dependent networks

  • "exploreMin" explore at least until exploreMin even if the exploration factor rule is achieved. Default 4. See the package blockmodels for details. For dependent networks

  • "exploreMax" Stop exploration at exploreMax even if the exploration factor rule is not achieved. Default Inf. See the package blockmodels for details. For dependent networks

  • "nbBlocksRange" minimal and maximal number or blocks explored. For dependent networks

  • "fast" logical: should approximation be used for Bernoulli model with covariates. Default to TRUE. For dependent networks

Missing values

The handling of missing values (NA) in the networks depends on dependent:

  • dependent = FALSE: the corresponding dyads are considered as not observed and are ignored in the inference (performed by the package GREMLINS), as for multipartite networks.

  • dependent = TRUE: missing values are not supported by the underlying models of blockmodels. They are replaced by 0, i.e. considered as observed absences of edges (or observed zero values for the Gaussian model), which biases the estimation. Remove or impute them beforehand, or use dependent = FALSE.

Examples

if (FALSE) { # \dontrun{
### =======================================
### MULTIPLEX SBM without dependence between layers
##
Nnodes <- 40
blockProp <- c(.4,.6)
nbLayers <- 2
connectParam <- list(list(mean=matrix(rbeta(4,.5,.5),2,2)),list(mean=matrix(rexp(4,.5),2,2)))
model <- c("bernoulli","poisson")
type <- "directed"
mySampleMultiplexSBM <-
   sampleMultiplexSBM(
   nbNodes = Nnodes,
    blockProp = blockProp,
   nbLayers = nbLayers,
   connectParam = connectParam,
   model=model,
   type=type)
listSBM <- mySampleMultiplexSBM$listSBM
estimOptions <- list(initBM = FALSE, nbCores  = 2)
myMultiplexSBM <- estimateMultiplexSBM(listSBM,estimOptions,dependent=FALSE)
### =======================================
### MULTIPLEX SBM Gaussian with dependence
##
Q <- 3
nbLayers <- 2
connectParam <- list()
connectParam$mu <- vector("list",nbLayers)
connectParam$mu[[1]] <-  matrix(.1,Q,Q) + diag(1:Q)
connectParam$mu[[2]] <- matrix(-2,Q,Q) + diag(rev(Q:1))
connectParam$Sigma <- matrix(c(2,1,1,4),nbLayers,nbLayers)
model <- rep("gaussian",2)
type <- "directed"
Nnodes <- 80
blockProp <- c(.3,.3,.4)
mySampleMultiplexSBM <-
  sampleMultiplexSBM(
     nbNodes = Nnodes,
     blockProp = blockProp,
     nbLayers = nbLayers,
     connectParam = connectParam,
     model=model,
     type="undirected",
     dependent=TRUE)
listSBM <- mySampleMultiplexSBM$listSBM
myMultiplexSBM <- estimateMultiplexSBM(listSBM,estimOptions,dependent=TRUE)
## MultiplexSBM Bernoulli with dependence
Q <- 2
P00<-matrix(runif(Q*Q),Q,Q)
P10<-matrix(runif(Q*Q),Q,Q)
P01<-matrix(runif(Q*Q),Q,Q)
P11<-matrix(runif(Q*Q),Q,Q)
SumP<-P00+P10+P01+P11
P00<-P00/SumP
P01<-P01/SumP
P10<-P10/SumP
P11<-P11/SumP
connectParam <- list()
connectParam$prob00 <- P00
connectParam$prob01 <- P01
connectParam$prob10 <- P10
connectParam$prob11 <- P11
model <- rep("bernoulli",2)
type <- "directed"
nbLayers <- 2
Nnodes <- 40
blockProp <- c(.6,.4)
mySampleMultiplexSBM <-
   sampleMultiplexSBM(
     nbNodes = Nnodes,
     blockProp = blockProp,
     nbLayers = nbLayers,
     connectParam = connectParam,
     model=model,
     type=type,
     dependent=TRUE)
listSBM <- mySampleMultiplexSBM$listSBM
myMultiplexSBM <- estimateMultiplexSBM(listSBM,estimOptions,dependent=TRUE)
} # }