MEclustnet {MEclustnet}

MEclustnet: A package for model-based clustering of nodes in a network, accounting for covariates.

Description

The main function of interest is MEclustnet which will fit a mixture of experts latent position cluster model to a binary network.

MEclustnet will fit a mixture of experts latent position cluster model to a binary network.

Usage

MEclustnet(Y, covars, link.vars = c(1:ncol(covars)),
  mix.vars = c(1:ncol(covars)), G = 2, d = 2, itermax = 10000,
  uphill = 100, burnin = 1000, thin = 10, rho.input = 1,
  verbose = TRUE, ...)

Arguments

Y

An n x n binary matrix of links between n nodes, with 0 on the diagonal and 1 indicating a link.

covars

An n x p data frame of node specific covariates. Categorical variables should be factors. First column should be a column of 1s, and should always be passed in.

link.vars

A vector of the column numbers of the data frame covars to be included in link probability model. If none are to be included, this argument should be 1.

mix.vars

A vector of the column numbers of the data frame covars to be included in mixing proportions model. If none are to be included, argument should be 1.

G

The number of clusters in the model to be fitted.

d

The dimension of the latent space.

itermax

Maximum number of iterations in the MCMC chain.

uphill

Number of iterations for which uphill only steps in the MCMC chain should be run to find maximum a posteriori estimates.

burnin

Number of burnin iterations in the MCMC chain.

thin

The degree of thinning to be applied to the MCMC chain.

rho.input

Scaling factor to achieve desirable acceptance rates in Metropolis-Hastings steps.

verbose

Print progress updates to screen? Recommended as the models are slow to run.

...

Additional arguments.

Details

This function fits the mixture of experts latent position cluster model to a binary network via a Metropolis-within-Gibbs sampler. Covariates can influence either the link probabilities between nodes and/or the cluster memberships of nodes.

Value

An object of class MEclustnet, which is a list containing:

zstore

An n x d x store.dim array of sampled latent location matrices, where store.dim is the number of post burnin thinned iterations.

betastore

A store.dim x p matrix of sampled beta vectors, the logistic regression parameters of the link probabilities model.

Kstore

A store.dim x n matrix of sampled cluster membership vectors.

mustore

A G x d x store.dim array of sampled cluster mean latent location matrices.

sigma2store

A store.dim x G matrix of sampled cluster variances.

lambdastore

An n x G x store.dim array of sampled mixing proportion matrices.

taustore

A G x s x store.dim array of sampled tau vectors, the logistic regression parameters of the mixing proportions model, where s is the length of tau.

LLstore

A vector of length store.dim storing the loglikelihood from each stored iteration.

G

The number of clusters fitted

d

The dimension of the latent space

countbeta

Count of accepted beta values

counttau

Count of accepted tau values

MEclustnet functions

MEclustnet

References

Isobel Claire Gormley and Thomas Brendan Murphy. (2010) A Mixture of Experts Latent Position Cluster Model for Social Network Data. Statistical Methodology, 7 (3), pp.385-405.

See Also

MEclustnet

Examples

#################################################################
# An example from the Gormley and Murphy (2010) paper, using the Lazega lawyers friendship network.
#################################################################
# Number of iterations etc. are set to low values for illustrative purposes.
# Longer run times are likely to be required to achieve sufficient mixing.

library(latentnet)
data(lawyers.adjacency.friends)
data(lawyers.covariates)

link.vars = c(1)
mix.vars = c(1,4,5)

fit = MEclustnet(lawyers.adjacency.friends, lawyers.covariates,
link.vars, mix.vars, G=2, d=2, itermax = 500, burnin = 50, uphill = 1, thin=10)

# Plot the trace plot of the mean of dimension 1 for each cluster.
matplot(t(fit$mustore[,1,]), type="l", xlab="Iteration", ylab="Parameter")

# Compute posterior summaries
summ = summaryMEclustnet(fit, lawyers.adjacency.friends)
plot(summ$zmean, col=summ$Kmode, xlab="Dimension 1", ylab="Dimension 2", pch=summ$Kmode,
     main = "Posterior mean latent location for each node.")

# Plot the resulting latent space, with uncertainties
plotMEclustnet(fit, lawyers.adjacency.friends, link.vars, mix.vars)

#################################################################
# An example analysing a 2016 Twitter network of US politicians.
#################################################################
# Number of iterations etc. are set to low values for illustrative purposes.
# Longer run times are likely to be required to achieve sufficient mixing.

library(latentnet)
data(us.twitter.adjacency)
data(us.twitter.covariates)

link.vars = c(1)
mix.vars = c(1,5,7,8)

fit = MEclustnet(us.twitter.adjacency, us.twitter.covariates,
link.vars, mix.vars, G=4, d=2, itermax = 500, burnin = 50, uphill = 1, thin=10)

# Plot the trace plot of the mean of dimension 1 for each cluster.
matplot(t(fit$mustore[,1,]), type="l", xlab="Iteration", ylab="Parameter")

# Compute posterior summaries
summ = summaryMEclustnet(fit, us.twitter.adjacency)

plot(summ$zmean, col=summ$Kmode, xlab="Dimension 1", ylab="Dimension 2", pch=summ$Kmode,
     main = "Posterior mean latent location for each node.")

# Plot the resulting latent space, with uncertainties
plotMEclustnet(fit, us.twitter.adjacency, link.vars, mix.vars)

# Examine which politicians are in which clusters...
clusters = list()
for(g in 1:fit$G)
{
  clusters[[g]] = us.twitter.covariates[summ$Kmode==g,c("name", "party")]
}
clusters