llStochBlock function

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

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.

Returns

• 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)