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Abstract
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.
Keywords
Markov chain, likelihood, duration of stay, model selection

Citation

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

MLA
Guerry, Marie-Anne, and Philippe Carette. “Likelihood Comparison of Alternative Markov Models Incorporating Duration of Stay.” Book of Abstracts of the 18th Applied Stochastic Models and Data Analysis International Conference with the Demographics 2019 Workshop, edited by Christos Skiadas, ISAST: International Society for the Advancement of Science and Technology, 2019, pp. 95–95.
APA
Guerry, M.-A., & Carette, P. (2019). Likelihood comparison of alternative Markov models incorporating duration of stay. In C. Skiadas (Ed.), Book of Abstracts of the 18th Applied Stochastic Models and Data Analysis International Conference with the Demographics 2019 Workshop (pp. 95–95). ISAST: International Society for the Advancement of Science and Technology.
Chicago author-date
Guerry, Marie-Anne, and Philippe Carette. 2019. “Likelihood Comparison of Alternative Markov Models Incorporating Duration of Stay.” In Book of Abstracts of the 18th Applied Stochastic Models and Data Analysis International Conference with the Demographics 2019 Workshop, edited by Christos Skiadas, 95–95. ISAST: International Society for the Advancement of Science and Technology.
Chicago author-date (all authors)
Guerry, Marie-Anne, and Philippe Carette. 2019. “Likelihood Comparison of Alternative Markov Models Incorporating Duration of Stay.” In Book of Abstracts of the 18th Applied Stochastic Models and Data Analysis International Conference with the Demographics 2019 Workshop, ed by. Christos Skiadas, 95–95. ISAST: International Society for the Advancement of Science and Technology.
Vancouver
1.
Guerry M-A, Carette P. Likelihood comparison of alternative Markov models incorporating duration of stay. In: Skiadas C, editor. Book of Abstracts of the 18th Applied Stochastic Models and Data Analysis International Conference with the Demographics 2019 Workshop. ISAST: International Society for the Advancement of Science and Technology; 2019. p. 95–95.
IEEE
[1]
M.-A. Guerry and P. Carette, “Likelihood comparison of alternative Markov models incorporating duration of stay,” in Book of Abstracts of the 18th Applied Stochastic Models and Data Analysis International Conference with the Demographics 2019 Workshop, Florence, Italy, 2019, pp. 95–95.
@inproceedings{8619476,
  abstract     = {{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.}},
  author       = {{Guerry, Marie-Anne and Carette, Philippe}},
  booktitle    = {{Book of Abstracts of the 18th Applied Stochastic Models and Data Analysis International Conference with the Demographics 2019 Workshop}},
  editor       = {{Skiadas, Christos}},
  keywords     = {{Markov chain,likelihood,duration of stay,model selection}},
  language     = {{eng}},
  location     = {{Florence, Italy}},
  pages        = {{95--95}},
  publisher    = {{ISAST: International Society for the Advancement of Science and Technology}},
  title        = {{Likelihood comparison of alternative Markov models incorporating duration of stay}},
  url          = {{http://www.asmda.es/images/Book_of_Abstracts_ASMDA2019-Demographics2019.pdf#page=105}},
  year         = {{2019}},
}