Model comparison for factor models with Bayes factors through bridge sampling

Although factor analysis is popular, it remains controversial how to reduce dimensions or zero out loadings. Well-known procedures such as Kaiser rule, AIC, BIC, sAIC, and parallel analysis, may yield conflicting solutions. In this paper, we explore Bayes factor, a standard form of Bayesian model comparison, and explicitly compare competing models with varying covariance constraints. In the behavioral-data context, Bayes factors may be computed conveniently via bridge sampling with existing tools (Stan and the bridgesampling R package). We evaluate this approach using synthetic data sets with known structures and find that Bayes factors uncover the generating model. We apply it to two extant data sets and show that it provides a compact, parsimonious description. Finally, we discuss how sensitivity to prior settings should be interpreted as limitations of the data resolution, as well as extensions to larger scale data sets.