First and Higher Order Transition Models with Covariate Dependence

The covariate dependent Markov models can be employed in various fields of research for analyzing time series or repeated measures data. This paper highlights the covariate dependent Markov models for the first and higher orders. The first order covariate dependent Markov model developed by Muenz and Rubinstein (1985) is reviewed and then second and higher order models for binary sequence are developed along with their estimation and test procedures based on Islam and Chowdhury (2006). The models for more than two outcomes are also shown. A general procedure based on the Chapman-Kolmogorov equations is proposed here in order to take account of the transitions at unequal intervals. A simple test procedure is suggested here to determine the order of the underlying Markov models. The proposed methods are illustrated with the Health and Retirement Survey data from the USA on the mobility difficulty of the elderly population. The results indicate the utility of the transitional models for first or higher orders of underlying transitions with binary or multiple outcomes.