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

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.

An extended Markov-switching model approach to modelling latent heterogeneity in departmentalized manpower systems

“…This unpredictability of human behaviour affects manpower system personnel propensity towards internal transitions, from one category to another within the system, and also attrition from the system. It is then obvious that manpower personnel with similar propensity towards these manpower flows need to be classed together in order to obtain valid estimates of model parameters needed for statistical manpower planning through description, prediction or control (Carette and Guerry, 2022).…”

Likelihood Ratio Search Procedure for Optimum Number of States in a Hidden Markov Manpower Model

“…Ugwuowo and McClean [9] emphasize that apart from the observable classes of a manpower system due to observable heterogeneity in personnel transitions there are hidden classes due to the problem of unobserved heterogeneity. Observable classes of a manpower system are determined by observing the manpower system structure and data, see, for example, [10,11]. The hidden classes cannot be chosen in the same way because the data from where they evolve are not observable.…”