Empirical Bayes Priors for MCMC Estimation of the Multivariate Social Relations Model

The social relations model (SRM) is a linear random-effects model applied to examine dyadic round-robin data within social networks. Such data have a unique multilevel structure in that dyads are cross-classified within individuals who may be nested within different social networks. The SRM decomposes perceptual or behavioral measures into multiple components: case-level random effects (in-coming and out-going effects) and dyad-level residuals (relationship effects), the associations among which are often of substantive interest. Multivariate SRM analyses are increasingly common, requiring more sophisticated estimation algorithms. This article evaluates Markov chain Monte Carlo (MCMC) estimation of multivariate-SRM parameters, compares MCMC to maximum-likelihood estimation, and introduces two methods to reduce bias in MCMC point estimates using empirical-Bayes priors. Four simulation studies are presented, two of which reveal dependency of small-group results on priors by manipulating location and precision hyperparameters, respectively. The third simulation study explores the impact of sampling more small groups on prior sensitivity. The fourth simulation study explores how Bayesian model averaging might compensate for underestimated variance due to empirical-Bayes priors. Finally, recommendations for future research are made and extensions of the SRM are discussed.