A higher order Markov model for analyzing covariate dependence

Abstract

During the recent past, there has been a renewed interest in Markov chain for its attractive properties for analyzing real life data emerging from time series or longitudinal data in various fields. The models were proposed for fitting first or higher order Markov chains. However, there is a serious lack of realistic methods for linking covariate dependence with transition probabilities in order to analyze the factors associated with such transitions especially for higher order Markov chains. L.R. Muenz and L.V. Rubinstein [Markov models for covariate dependence of binary sequences, Biometrics 41 (1985) 91–101] employed logistic regression models to analyze the transition probabilities for a first order Markov model. The methodology is still far from generalization in terms of formulating a model for higher order Markov chains. In this study, it is aimed to provide a comprehensive covariate-dependent Markov model for higher order. The proposed model generalizes the estimation procedure for Markov models for any order. The proposed models and inference procedures are simple and the covariate dependence of the transition probabilities of any order can be examined without making the underlying model complex. An example from rainfall data is illustrated in this paper that shows the utility of the proposed model for analyzing complex real life problems. The application of the proposed method indicates that the higher order covariate dependent Markov models can be conveniently employed in a very useful manner and the results can provide in-depth insights to both the researchers and policymakers to resolve complex problems of underlying factors attributing to different types of transitions, reverse transitions and repeated transitions. The estimation and test procedures can be employed for any order of Markov model without making the theory and interpretation difficult for the common users.