Bayesian joint analysis using a semiparametric latent variable model with non-ignorable missing covariates for CHNS data

Abstract

Motivated by the China Health and Nutrition Survey (CHNS) data, a semiparametric latent variable model with a Dirichlet process (DP) mixtures prior on the latent variable is proposed to jointly analyse mixed binary and continuous responses. Non-ignorable missing covariates are considered through a selection model framework where a missing covariate model and a missing data mechanism model are included. The logarithm of the pseudo-marginal likelihood (LPML) is applied for selecting the priors, and the deviance information criterion measure focusing on the missing data mechanism model only is used for selecting different missing data mechanisms. A Bayesian index of local sensitivity to non-ignorability (ISNI) is extended to explore the local sensitivity of the parameters in our model. A simulation study is carried out to examine the empirical performance of the proposed methodology. Finally, the proposed model and the ISNI index are applied to analyse the CHNS data in the motivating example.