Likelihood comparison of alternative Markov models incorporating duration of stay

Markov chains are commonly used to model transitions in a system partitioned into categories. In manpower planning models these categories are, for example, job levels or grades in the firm under study. Building a Markov model starts with selecting its states that are assumed to be homogeneous; i.e. the system units in a same state have similar transition probabilities. For systems where the transitions among the categories depend on the duration of stay in the outgoing categories, previous work considered Markov models where the states are subdivisions of the categories into duration of stay intervals, and the more complex semi-Markov models. The present work investigates alternative Markov models for systems where the categories have transition probabilities depending on the duration of stay by selecting the states in different ways: state selection by duration intervals and state selection by duration values. The resulting Markov models are compared based on the likelihood of a set of panel data given the model. For a system with two categories, we prove that the model with states defined by duration values has a better maximum likelihood fit than the base model having the initial categories as states, while this is not the case for the model with states defined by duration intervals under conditions that seem realistic in practice. Although the duration-interval approach is considered in previous studies, the likelihood-comparison is less in favor of this model.

Publication year:2019