Title: Bayesian Inference for Multivariate Social Relations Models via (r)Stan

Authors: Terrence D. Jorgensen, Aditi Manoj Bhangale

Abstract:
It is becoming increasingly common for researchers to study psychological
phenomena from an interpersonal perspective, using data gathered from a
round-robin design, in which each member of a group (e.g., a nuclear family,
classroom, or team of employees) provides data about every other member. For
example, each student in a classroom can indicate how much they like each
other student. Dyadic data from this design have a complex underlying
structure because each dyad is cross-nested within both members, given that
each of N members provides information about N - 1 members, as well as having
information provided about them by N - 1 members. The social relations model
(SRM) was designed to decompose interpersonal perceptions (or behaviors) into
random effects associated with perceivers (or actors), targets (or partners),
and the uniqueness of particular relationships. The primary outcomes of an SRM
analysis involve the estimated covariance matrices at the personal level
(individual differences in actor and partner effects, and how they are
correlated within persons) and the dyad level (e.g., how relationship-specific
behaviors differ across dyads, given person-level effects), but it is also
often interesting to estimate correlations of those effects with other
variables, particularly person-level covariates. This presentation will
showcase an in-progress R package that facilitates estimating a multivariate
SRM (including covariances with person-level covariates) using the Bayesian
modeling software Stan, via its R interface rstan.  An application to real
data will demonstrate various methods to summarize the posterior distribution
of (functions of) parameters of interest, and some possibilities will be
highlighted for subsequent analyses of SRM results.