Comparing maximum likelihood to Markov chain Monte Carlo estimation of the multivariate social relations model

The social relations model (SRM) is a linear random-effects model applied to dyadic data within social networks (i.e., round-robin data). Such data have a unique nesting structure in that dyads (pairs) are cross-classified within individuals, who can also be nested in different networks. The SRM is used to examine basic multivariate relations between components of dyadic variables at two levels: individual-level random effects and dyad-level residuals. The current “gold standard” for estimating multivariate SRMs is the maximum likelihood (ML) estimation. However, Bayesian approaches, such as Markov chain Monte Carlo (MCMC) estimators, may provide some practical advantages to estimate complex or computationally intensive models. In this chapter, we report a small simulation study to compare the accuracy and efficiency of ML and MCMC point (and interval) estimates of a trivariate SRM on the ideal scenario: normally distributed, complete round-robin data. We found that MLE outperformed MCMC at both levels. MCMC greatly underestimated parameters and displayed poor coverage rates at the individual level but was relatively accurate at the dyad level.