Abstract: The main purpose of this article is to investigate a nonlinear structural equation model with covariates and mixed continuous and ordered categorical outcomes, in the presence of missing observations and missing covariates that are missing with a nonignorable mechanism. The nonignorable missingness mechanism is specified by a logistic regression model. A Bayesian approach is proposed for obtaining the joint Bayesian estimates of structural parameters, latent variables and parameters in the logistic regression model. An algorithm that combines the Gibbs sampler and the Metropolis-Hastings algorithm is developed for sampling observations from the posterior distributions, and for obtaining the Bayesian solution. A procedure for computing the Bayes factor for model comparison is developed via path sampling. Sensitivity analyses of the results with respect to the assumed model for the missingness mechanism, the prior inputs, and the missing covariate distributions are conducted via simulation studies. An example is presented to illustrate the newly developed Bayesian methodologies.
Key words and phrases: Bayes factor, Gibbs sampler, Metropolis-Hastings algorithm, nonignorable missing data, Path sampling, sensitivity analysis.