Bayesian Test of Homogeneity in Transition Model for Longitudinal Ordinal Response Data with Missing Values

Abstract

For analyzing longitudinal ordinal response data, many methods are available to take into account the correlations between responses of the same individual where different methods use different approaches. One of the methods to consider this correlation is the transition (Markov) model. In this paper, we present a Bayesian test of homogeneity of a transition model for analyzing longitudinal ordinal response data. In other words we test whether the transition probabilities pmabt ’s, which are probabilities of moving to state b from state a of mth individual at time t, are the same for any given time t, i.e., pmabt = pmab. A cumulative logistic regression model and the Bayesian method, using MCMC, are implemented for testing the null hypothesis of homogeneity. We also define what a specific homogeneous covariate is. Our approach is applied on three-period longitudinal Fluvoxamine (a treatment for deregulation of serotonin in brain) data.

Keywords

• Bayesian Analysis; Fluvoxamine Data; Homogeneity; Logistic Regression Model; Non-homogeneity; Transition (Markov) Models.