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MCMC estimation for the p 2 network regression model with crossed random effects
Author(s) -
Zijlstra Bonne J. H.,
Duijn Marijtje A. J.,
Snijders Tom A. B.
Publication year - 2009
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1348/000711007x255336
Subject(s) - markov chain monte carlo , statistics , random walk , mathematics , covariate , gibbs sampling , variance (accounting) , econometrics , markov chain , random effects model , monte carlo method , bayesian probability , meta analysis , accounting , medicine , business
The p 2 model is a statistical model for the analysis of binary relational data with covariates, as occur in social network studies. It can be characterized as a multinomial regression model with crossed random effects that reflect actor heterogeneity and dependence between the ties from and to the same actor in the network. Three Markov chain Monte Carlo (MCMC) estimation methods for the p 2 model are presented to improve iterative generalized least squares (IGLS) estimation developed earlier, two of which use random walk proposals. The third method, an independence chain sampler, and one of the random walk algorithms use normal approximations of the binary network data to generate proposals in the MCMC algorithms. A large‐scale simulation study compares MCMC estimates with IGLS estimates for networks with 20 and 40 actors. It was found that the IGLS estimates have a smaller variance but are severely biased, while the MCMC estimates have a larger variance with a small bias. For networks with 20 actors, mean squared errors are generally comparable or smaller for the IGLS estimates. For networks with 40 actors, mean squared errors are the smallest for the MCMC estimates. Coverage rates of confidence intervals are good for the MCMC estimates but not for the IGLS estimates.