Bayesian factor analysis for multilevel binary observations

Multilevel covariance structure models have become increasingly popular in the psychometric literature in the past few years to account for population heterogeneity and complex study designs. We develop practical simulation b ased procedures for Bayesian inference of multilevel binary factor analysis models. We illustrate how Markov Chain Monte Carlo procedures such as Gibb s sampling and Metropolis-Hastings methods can be used to perform Bayesian inference, model checking and model comparison without the need for multidi mensional numerical integration. We illustrate the proposed estimation meth ods using three simulation studies and an application involving student's a chievement results in different areas of mathematics.