Latent position and cluster models for networks

Description

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 η_{i,j}=∑_{k=1}^p β_k X_{i,j,k}+d(Z_i,Z_j)+δ_i+γ_j, where X is an array of dyad covariates, β 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_icdot Z_j), and δ and γ 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.

Details

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.

Value

ergmm returns an object of class 'ergmm' that is a list.

References

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.

See Also

ergmm, terms.ergmm

Results