Bayesian Selection on the Number of Factors in a Factor Analysis Model

Abstract

This paper considers a Bayesian approach for selecting the number of factors in a factor analysis model with continuous and polvtomous variables. A procedure for computing the important statistic in model selection, namely the Bayes factor, is developed via path sampling. The main computation effort is on simulating observations from the appropriate posterior distribution. This task is done by a hybrid algorithm which combines the Gibbs sampler and the Metropolis-Hastings algorithm. Bayesian estimates of thresholds, factor loadings, unique variances, and latent factor scores as well as their standard errors can be produced as by-products. The empirical performance of the proposed procedure is illustrated by means of a simulation study and a real example.