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

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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
Statistics, Probability and Uncertainty, Statistics and Probability, Markov chain, Maximum likelihood, Duration of stay, Model selection, HETEROGENEITY, MOBILITY, CRITERIA, SYSTEM

Citation

Please use this url to cite or link to this publication:

MLA
Carette, Philippe, and Marie-Anne Guerry. “Markov Models for Duration-Dependent Transitions : Selecting the States Using Duration Values or Duration Intervals?” STATISTICAL METHODS AND APPLICATIONS, 2022, doi:10.1007/s10260-022-00637-2.
APA
Carette, P., & Guerry, M.-A. (2022). Markov models for duration-dependent transitions : selecting the states using duration values or duration intervals? STATISTICAL METHODS AND APPLICATIONS. https://doi.org/10.1007/s10260-022-00637-2
Chicago author-date
Carette, Philippe, and Marie-Anne Guerry. 2022. “Markov Models for Duration-Dependent Transitions : Selecting the States Using Duration Values or Duration Intervals?” STATISTICAL METHODS AND APPLICATIONS. https://doi.org/10.1007/s10260-022-00637-2.
Chicago author-date (all authors)
Carette, Philippe, and Marie-Anne Guerry. 2022. “Markov Models for Duration-Dependent Transitions : Selecting the States Using Duration Values or Duration Intervals?” STATISTICAL METHODS AND APPLICATIONS. doi:10.1007/s10260-022-00637-2.
Vancouver
1.
Carette P, Guerry M-A. Markov models for duration-dependent transitions : selecting the states using duration values or duration intervals? STATISTICAL METHODS AND APPLICATIONS. 2022;
IEEE
[1]
P. Carette and M.-A. Guerry, “Markov models for duration-dependent transitions : selecting the states using duration values or duration intervals?,” STATISTICAL METHODS AND APPLICATIONS, 2022.
@article{8749716,
  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.}},
  author       = {{Carette, Philippe and Guerry, Marie-Anne}},
  issn         = {{1618-2510}},
  journal      = {{STATISTICAL METHODS AND APPLICATIONS}},
  keywords     = {{Statistics,Probability and Uncertainty,Statistics and Probability,Markov chain,Maximum likelihood,Duration of stay,Model selection,HETEROGENEITY,MOBILITY,CRITERIA,SYSTEM}},
  language     = {{eng}},
  title        = {{Markov models for duration-dependent transitions : selecting the states using duration values or duration intervals?}},
  url          = {{http://dx.doi.org/10.1007/s10260-022-00637-2}},
  year         = {{2022}},
}

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