Bayesian quantile regression for analyzing ordinal longitudinal responses in the presence of non-ignorable missingness

Abstract

In this paper, we develop a quantile regression model for analyzing ordinal longitudinal responses with random effects in the presence of non-ignorable and non-monotone missing data. The ordinal responses are related to underlying latent variables which are considered to have asymmetric Laplace distribution. For modeling the missing data mechanism an ordinary probit model is used via specifying another latent variable. In order to consider non-ignorable missing data, a shared parameter model is used for joint modeling of ordinal longitudinal responses and missing data mechanism. We use a Bayesian approach via Markov chain Monte Carlo method for analyzing the proposed joint model. Especially to estimate unknown parameters, a Gibbs sampler algorithm is used. Moreover, we use the Schizophrenia data set to illustrate an application of the proposed model.