Expanding The Bayesian Structural Equation, Multilevel And Mixture Models To Logit, Negative-Binomial, And Nominal Variables

Recent work on the Polya-Gamma distribution provides a breakthrough for the Bayesian modeling of logit, count, and nominal variables. We describe how the methodology is incorporated in the Mplus modeling framework and illustrate it with several examples: logistic latent growth models, multilevel IRT, multilevel time-series models for count data, multilevel nominal regression, and nominal factor analysis.