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

Authors: Aditi Manoj Bhangale, Terrence D. Jorgensen

Abstract:
The social relations model (SRM) is a linear random-effects model applied to
examine multivariate dyadic data (e.g., round-robin data) within social
networks. Such data have a unique nesting structure in that dyads are
cross-classified within individuals who may be nested within different social
networks. The SRM decomposes perceptual measures into multiple
individual-level random effects (incoming and outgoing effects) and dyad-level
residuals (relationship effects), the associations among which are often of
theoretical interest. Nestler (2018) proposed maximum likelihood (ML)
estimation to estimate multivariate SRMs. However, Bayesian approaches, such
as Markov chain Monte Carlo (MCMC) estimators, may provide some practical
advantages to estimate complex or analytically intractable models. A previous
simulation showed that the accuracy of MCMC was greatly dependent on prior
information. In this study, we (1) explore the use of ANOVA-based
method-of-moments estimation of bivariate SRM relations to compute
hyperparameters for empirical Bayes prior distributions and (2) assess the
impact of manipulating the precision of these prior distributions when
estimating multivariate relations between SRM components with MCMC. We perform
a simulation to compare the accuracy and efficiency of ML and MCMC point (and
interval) estimates of a trivariate SRM on normally distributed, complete
round-robin data.

Keywords: Social-network data, social relations model, maximum likelihood
estimation, Markov chain Monte Carlo estimation, empirical Bayes priors