Bayesian Inference for Finite Mixtures in Confirmatory Factor Analysis

The aim of this paper is to apply Baycsian methods via the Gibbs sampler to multivariate normal mixtures whose means and covariance matrices are structured as confirmatory factor analysis models. This estimation method uses the Gibbs sampling, and does not rely on the asymptotic theory nor on any other “sophisticated” MCMC methods. And yet, it can handle easily the cases where common parameterization between components is assumed and/or some parameters are linearly constrained (e.g., they are equal), which was impossible in previous studies. A simulation study showed that the proposed method is effective even for data in which the degree of separation is so small that the asymptotic theory could not apply. It is also shown that the proposed method applied to real data produced results capable of meaningful interpretation.