AN EMPIRICAL BAYES MODEL FOR MARKOV-DEPENDENT BINARY SEQUENCES WITH RANDOMLY MISSING OBSERVATIONS

We develop an improved empirical Bayes estimation methodology for the analysis of two-state Markov chains observed from heterogeneous indivi duals. First, the two transition probabilities corresponding to each c hain are assumed to be drawn from a common, bivariate distribution tha t has beta marginals. Second, randomly missing observations are incorp orated into the likelihood for the hyperparameters by efficiently summ ing over all possible values for the missing observations. A likelihoo d ratio test is used to test for dependence between the transition pro babilities. Posterior distributions for the transition probabilities a re also derived, as is an approximation for the equilibrium probabilit ies. The proposed procedures are illustrated in a numerical example an d in an analysis of longitudinal store display data.