Bayesian Analysis of Multiple Group Nonlinear Structural Equation Models with Ordered Categorical and Dichotomous Variables: A Survey

This paper is designed to give a complete overview of the literature that is available, as it relates to application of the Bayesian analysis model to investigate multiple group nonlinear structural equation models, also known as SEMs, including those having ordered categorical, dichotomous and categorical-dichotomous mixed variables. It will also work to summarize Bayesian multiple group nonlinear SEMs with nonlinear covariate variables, and latent variables in the structural model and both linear covariant and latent variable sin the measurement models. More specifically, it will be suggested that using hidden continuous normal distribution, including both right and left censoring and truncation, and interval censoring and truncation, can improve the Bayesian approach to multiple group nonlinear structural equation models when solving problems using ordered categorical and dichotomous data.