Markov models for duration-dependent transitions: selecting the states using duration values or duration intervals?

Philippe Carette and Marie-Anne Guerry ()
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Philippe Carette: Ghent University
Marie-Anne Guerry: Vrije Universiteit Brussel

Statistical Methods & Applications, 2022, vol. 31, issue 5, No 5, 1203-1223

Abstract: Abstract In a Markov model the transition probabilities between states do not depend on the time spent in the current state. The present paper explores two ways of selecting the states of a discrete-time Markov model for a system partitioned into categories where the duration of stay in a category affects the probability of transition to another category. For a set of panel data, we compare the likelihood fits of the Markov models with states based on duration intervals and with states defined by duration values. For hierarchical systems, we show that the model with states based on duration values has a better maximum likelihood fit than the baseline Markov model where the states are the categories. We also prove that this is not the case for the duration-interval model, under conditions on the data that seem realistic in practice. Furthermore, we use the Akaike and Bayesian information criteria to compare these alternative Markov models. The theoretical findings are illustrated by an analysis of a real-world personnel data set.

Keywords: Markov chain; Maximum likelihood; Duration of stay; Model selection (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10260-022-00637-2

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