A Bayesian Joint Modeling Using Gaussian Linear Latent Variables for Mixed Correlated Outcomes with Possibility of Missing Values

Abstract

This paper proposes a Bayesian approach for the analysis of mixed correlated nominal, ordinal and continuous outcomes with possibility of missing values using a variation of Markov Chain Monte Carlo (MCMC) method named Parameter Expanded and Reparamerized Metropolis Hastings (PX-RPMH) method. A general latent variable model is given and a Gibbs sampler is developed to incorporate PX-RPMH and Data Augmentation (DA) steps, to estimate parameters and to impute missing values. The performance of the algorithm is evaluated by some simulation studies. An application of the model to the foreign language attitude scale dataset is also enclosed.

Keywords

• Mixed Data; Correlated Outcomes; Parameter Expansion; MCMC; Data Augmentation; Longitudinal Data.