Explains how the Gibbs sampler can be applied to obtain a sample from the posterior distribution over the parameters of a structural equation model. Presents statistics to use to summarize marginal posterior densities and model checks using posterior predictive p-values. (SLD)

Developed a Bayesian approach for a general multigroup nonlinear factor analysis model that simultaneously obtains joint Bayesian estimates of the factor scores and the structural parameters subjected to some constraints across different groups. (SLD)

Developed a Bayesian approach for structural equation models with ignorable missing continuous and polytomous data that obtains joint Bayesian estimates of thresholds, structural parameters, and latent factor scores simultaneously. Illustrated the approach through analysis of a real data set of 20 patterns of condom use in the Philippines. (SLD)

The question of how to analyze unbalanced hierarchical data generated from structural equation models has been a common problem for researchers and analysts. Among difficulties plaguing statistical modeling are estimation bias due to measurement error and the estimation of the effects of the individual's hierarchical social milieu. This paper…