llStochBlock {StochBlock}

Function that computes criterion function used in stochastic one-mode and linked blockmodeling. If clu is a list, the method for linked/multilevel networks is applied

Description

Function that computes criterion function used in stochastic one-mode and linked blockmodeling. If clu is a list, the method for linked/multilevel networks is applied

Usage

llStochBlock(
  M,
  clu,
  weights = NULL,
  uWeights = NULL,
  diagonal = c("ignore", "seperate", "same"),
  limitType = c("none", "inside", "outside"),
  limits = NULL,
  weightClusterSize = 1,
  addOne = TRUE,
  eps = 0.001
)

Arguments

M

A matrix representing the (usually valued) network. For multi-relational networks, this should be an array with the third dimension representing the relation.

clu

A partition. Each unique value represents one cluster. If the network is one-mode, than this should be a vector, else a list of vectors, one for each mode. Similarly, if units are comprised of several sets, clu should be the list containing one vector for each set.

weights

The weights for each cell in the matrix/array. A matrix or an array with the same dimensions as M.

uWeights

The weights for each unit. A vector with the length equal to the number of units (in all sets).

diagonal

How should the diagonal values be treated. Possible values are:

• ignore - diagonal values are ignored

• seperate - diagonal values are treated separately

• same - diagonal values are treated the same as all other values

limitType

Type of limit to use. Forced to 'none' if limits is NULL. Otherwise, one of either outer or inner.

limits

If diagonal is "ignore" or "same", an array with dimensions equal to:

• number of clusters (of all types)

• number of clusters (of all types)

• number of relations

• 2 - the first is lower limit and the second is upper limit

If diagonal is "seperate", a list of two array. The first should be as described above, representing limits for off diagonal values. The second should be similar with only 3 dimensions, as one of the first two must be omitted.

weightClusterSize

The weight given to cluster sizes (log-probabilities) compared to ties in loglikelihood. Defaults to 1, which is "classical" stochastic blockmodeling.

addOne

Should one tie with the value of the tie equal to the density of the superBlock be added to each block to prevent block means equal to 0 or 1 and also "shrink" the block means toward the superBlock mean. Defaults to TRUE.

eps

If addOne = FALSE, the minimal deviation from 0 or 1 that the block mean/density can take.

Value

- the value of the log-likelihood criterion for the partition clu on the network represented by M for binary stochastic blockmodel.

Examples

# Create a synthetic network matrix
set.seed(2022)
library(blockmodeling)
k<-2 # number of blocks to generate
blockSizes<-rep(20,k)
IM<-matrix(c(0.8,.4,0.2,0.8), nrow=2)
clu<-rep(1:k, times=blockSizes)
n<-length(clu)
M<-matrix(rbinom(n*n,1,IM[clu,clu]),ncol=n, nrow=n)
clu<-sample(1:2,nrow(M),replace=TRUE)
plotMat(M,clu) # Have a look at this random partition
ll_pre<-llStochBlock(M,clu) # Calculate its loglikelihood
res<-stochBlockORP(M,k=2,rep=10) # Optimizing the partition
plot(res) # Have a look at the optimized partition
ll_post<-llStochBlock(M,clu(res)) # Calculate its loglikelihood
# We expect the loglikelihood pre-optimization to be smaller:
(-ll_pre)<(-ll_post)