Covariate–Dependent Markov Models

In many longitudinal studies, we observe a series of outcome data at equal intervals of time where time can be considered as discrete. In this chapter, Markov models are presented with covariate dependence which provide important findings associated with transitions from one state to another state of outcome variable. As there have been remarkable increase in collecting data longitudinally in various fields including reliability, economics, survival analysis, engineering, social sciences, environmental studies, biological sciences, etc., the emergence for regression modeling of transition probabilities is a necessity. For analyzing repeated measures data emerging from longitudinal studies, Markov models provide conditional models which can be useful for studying transitions along with factors associated with such transitions in longitudinal data. One obvious advantage of such model is that we can understand the process of change in individual responses over time. As these changes occur conditionally in a sequence, depending on the change from previous status of the outcome of interest, Markov models provide more insights than marginal models because marginal models disregard the important aspects of transitions. In this chapter, first and higher order Markov models are described along with inferential procedures and illustrated with examples.