The package latentnet is used to fit latent cluster random effect
models, where the probability of a network \(g\),
on a set of nodes is a product of dyad probabilities, each of which is
a GLM with linear component
\(\eta_{i,j}=\sum_{k=1}^p \beta_k X_{i,j,k}+d(Z_i,Z_j)+\delta_i+\gamma_j\),
where \(X\) is an array of dyad covariates, \(\beta\) is a vector
of covariate coefficients, \(Z_i\) is the latent space position of
node \(i\), \(d(\cdot,\cdot)\) is a function of the two positions:
either negative Euclidean (\(-||Z_i-Z_j||\)) or bilinear
(\(Z_i\cdot Z_j\)), and \(\delta\) and \(\gamma\) are vectors of sender
and receiver effects. (Note that these are different from the
eigenmodel of Hoff (2007) ``Modeling homophily and stochastic
equivalence in symmetric relational data'', fit by package eigenmodel.)
The ergmm specifies models via: g ~ <model terms>
where g is a network object For the list of possible
<model terms>, see terms.ergmm. For the list of
the possible dyad distribution families, see
families.ergmm.
ergmm returns an object of class 'ergmm' that is a list.
The arguments in the ergmm function specific to latent
variable models
are ergmm.control. See the help page for ergmm for the
details.
The result of a latent variable model fit is an ergmm object.
Hence the summary, print, and plot functions
apply to the fits.
The plot.ergmm function has many options specific to latent
variable models.
See the help page for plot.ergmm for the details.
Mark S. Handcock, Adrian E. Raftery and Jeremy Tantrum (2007). Model-Based Clustering for Social Networks. Journal of the Royal Statistical Society: Series A (Statistics in Society), 170(2), 301-354.
Peter D. Hoff (2005). Bilinear Mixed Effects Models for Dyadic Data. Journal of the American Statistical Association, 100(469), 286-295.
Peter D. Hoff, Adrian E. Raftery and Mark S. Handcock (2002). Latent space approaches to social network analysis. Journal of the American Statistical Association, 97(460), 1090-1098.
Pavel N. Krivitsky, Mark S. Handcock, Adrian E. Raftery, and Peter D. Hoff (2009). Representing degree distributions, clustering, and homophily in social networks with latent cluster random effects models. Social Networks, 31(3), 204-213.
Pavel N. Krivitsky and Mark S. Handcock (2008).
Fitting Position Latent Cluster Models for Social Networks with
latentnet. Journal of Statistical Software, 24(5).
Susan M. Shortreed, Mark S. Handcock, and Peter D. Hoff (2006). Positional Estimation within the Latent Space Model for Networks. Methodology, 2(1), 24-33.