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

Author

Listed:
  • Philippe Carette

    (Ghent University)

  • Marie-Anne Guerry

    (Vrije Universiteit Brussel)

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.

Suggested Citation

  • Philippe Carette & Marie-Anne Guerry, 2022. "Markov models for duration-dependent transitions: selecting the states using duration values or duration intervals?," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(5), pages 1203-1223, December.
    • Handle: RePEc:spr:stmapp:v:31:y:2022:i:5:d:10.1007_s10260-022-00637-2
    DOI: 10.1007/s10260-022-00637-2
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    References listed on IDEAS

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    1. Tim De Feyter, 2006. "Modelling heterogeneity in manpower planning: dividing the personnel system into more homogeneous subgroups," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 22(4), pages 321-334, July.
    2. Guglielmo D’Amico & Jacques Janssen & Raimondo Manca, 2006. "Homogeneous semi-Markov reliability models for credit risk management," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 28(2), pages 79-93, February.
    3. S. Bacci & S. Pandolfi & F. Pennoni, 2014. "A comparison of some criteria for states selection in the latent Markov model for longitudinal data," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 8(2), pages 125-145, June.
    4. Durland, J Michael & McCurdy, Thomas H, 1994. "Duration-Dependent Transitions in a Markov Model of U.S. GNP Growth," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(3), pages 279-288, July.
    5. Frank A. Sonnenberg & J. Robert Beck, 1993. "Markov Models in Medical Decision Making," Medical Decision Making, , vol. 13(4), pages 322-338, December.
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