Expanding the Bayesian structural equation, multilevel and mixture models to logit, negative-binomial, and nominal variables

ABSTRACT

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.

KEYWORDS:

• Polya-Gamma distribution
• Bayesian estimation
• Negative-binomial SEM
• Nominal SEM

Notes

¹ http://statmodel.com/download/lcn.zip.

² If $T=2$, there is only one correlation $Corr(Y_{i1},Y_{i2})$ which cannot identify both $v_2$ and $\rho$. If $T=3$, the model implied correlation based on $v_2$ is only marginally different from the model implied correlation based on $\rho$ and to distinguish between the two a large sample size $N$ is needed.