Bayesian estimation and test for factor analysis model with continuous and polytomous data in several populations

The main purpose of this paper is to develop a Bayesian approach for the multisample factor analysis model with continuous and polytomous variables. Joint Bayesian estimates of the thresholds, the factor scores and the structural parameters subjected to some simple constraints across groups are obtained simultaneously. The Gibbs sampler is used to produce the joint Bayesian estimates. It is shown that the conditional distributions involved in the implementation are the familiar uniform, gamma, normal, univariate truncated normal and Wishart distributions. The Bayes factor is introduced to test hypotheses involving constraints among the structural parameters of the factor analysis models across groups. Two procedures for computing the test statistics are developed, one based on the Schwarz criterion (or Bayesian information criterion), while the other computes the posterior densities and likelihood ratios by means of draws from the appropriate conditional distributions via the Gibbs sampler. The empirical performance of the proposed Bayesian procedure and its sensitivity to prior distributions are illustrated by some simulation results and two real-life examples.