Multivariate Penalized-Complexity-Like Priors for Exploratory Factor Analysis

Abstract

Factor analysis is an important technique for modeling multivariate data. Researchers remain interested in developing Bayesian procedures to recover simpler structures to explain how observed variables relate to the underlying factors. We propose a new penalized-complexity-like prior to encourage sparse loading structures. We construct a prior by specifying a distribution on a function of the expected Kullback–Leibler divergence between a simpler base model with a sparse loading structure and a full model with a dense loading structure. We report simulation evidence that our new expected penalized complexity prior more accurately recovers sparse loading structures in many settings when compared to existing methods. We present an application using data on children’s mental ability test scores and demonstrate a strategy for selecting the number of factors.