Bayesian analysis of latent variable models with non-ignorable missing outcomes from exponential family

To provide a comprehensive framework for analysing complex non-normal medical and biological data, we propose a Bayesian approach for a non-linear latent variable model with covariates, and non-ignorable missing data, under the exponential family of distributions. The non-ignorable missing mechanism is defined via a logistic regression model. Based on conjugate prior distributions, full conditional distributions for the implementation of Markov chain Monte Carlo methods in simulating observations from the joint posterior distribution are derived. These observations are used in computing the Bayesian estimates, as well as in implementing a path sampling procedure to evaluate the Bayes factor for model comparison. The proposed methods are illustrated using real data from a study on the non-adherence of hypertension patients.