Statistical analysis of nonlinear factor analysis models

Abstract

This paper presents a Bayesian analysis of a general nonlinear factor analysis model. Both the non‐informative and conjugate prior distributions are considered. A hybrid algorithm that combines the Metropolis‐Hastings algorithm and the Gibbs sampler is implemented to produce direct estimates of the latent factor scores and the structural parameters. Standard errors estimates as well as a goodness‐of‐fit statistic for assessing the posited model are presented. To illustrate the methodology, results from a simulation study and a real example are reported.