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A comparison of some criteria for states selection in the latent Markov model for longitudinal data

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  • S. Bacci
  • S. Pandolfi
  • F. Pennoni

Abstract

We compare different selection criteria to choose the number of latent states of a multivariate latent Markov model for longitudinal data. This model is based on an underlying Markov chain to represent the evolution of a latent characteristic of a group of individuals over time. Then, the response variables observed at different occasions are assumed to be conditionally independent given this chain. Maximum likelihood estimation of the model is carried out through an Expectation–Maximization algorithm based on forward–backward recursions which are well known in the hidden Markov literature for time series. The selection criteria we consider are based on penalized versions of the maximum log-likelihood or on the posterior probabilities of belonging to each latent state, that is, the conditional probability of the latent state given the observed data. Among the latter criteria, we propose an appropriate entropy measure tailored for the latent Markov models. We show the results of a Monte Carlo simulation study aimed at comparing the performance of the above states selection criteria on the basis of a wide set of model specifications. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • 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.
    • Handle: RePEc:spr:advdac:v:8:y:2014:i:2:p:125-145
    DOI: 10.1007/s11634-013-0154-2
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    1. Montanari, Giorgio E. & Doretti, Marco & Bartolucci, Francesco, 2017. "A multilevel latent Markov model for the evaluation of nursing homes' performance," MPRA Paper 80691, University Library of Munich, Germany.
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    3. F. Bartolucci & A. Farcomeni & F. Pennoni, 2014. "Latent Markov models: a review of a general framework for the analysis of longitudinal data with covariates," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(3), pages 433-465, September.
    4. Francesca Bassi & Fulvia Pennoni & Luca Rossetto, 2020. "The Italian market of sparkling wines: Latent variable models for brand positioning, customer loyalty, and transitions across brands' preferences," Agribusiness, John Wiley & Sons, Ltd., vol. 36(4), pages 542-567, October.
    5. Silvia Bacci & Francesco Bartolucci & Giulia Bettin & Claudia Pigini, 2017. "A mixture growth model for migrants' remittances: An application to the German Socio-Economic Panel," Mo.Fi.R. Working Papers 145, Money and Finance Research group (Mo.Fi.R.) - Univ. Politecnica Marche - Dept. Economic and Social Sciences.
    6. David Aristei & Silvia Bacci & Francesco Bartolucci & Silvia Pandolfi, 2021. "A bivariate finite mixture growth model with selection," 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. 15(3), pages 759-793, September.
    7. Morgan, Grant B. & Hodge, Kari J. & Baggett, Aaron R., 2016. "Latent profile analysis with nonnormal mixtures: A Monte Carlo examination of model selection using fit indices," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 146-161.
    8. Simon DeDeo, 2016. "Conflict and Computation on Wikipedia: A Finite-State Machine Analysis of Editor Interactions," Future Internet, MDPI, vol. 8(3), pages 1-23, July.
    9. Renske E. Kuijpers & Ingmar Visser & Dylan Molenaar, 2021. "Testing the Within-State Distribution in Mixture Models for Responses and Response Times," Journal of Educational and Behavioral Statistics, , vol. 46(3), pages 348-373, June.
    10. Qi Chen & Wen Luo & Gregory J. Palardy & Ryan Glaman & Amber McEnturff, 2017. "The Efficacy of Common Fit Indices for Enumerating Classes in Growth Mixture Models When Nested Data Structure Is Ignored," SAGE Open, , vol. 7(1), pages 21582440177, March.
    11. Dylan Molenaar & Paul Boeck, 2018. "Response Mixture Modeling: Accounting for Heterogeneity in Item Characteristics across Response Times," Psychometrika, Springer;The Psychometric Society, vol. 83(2), pages 279-297, June.
    12. Silvia Bacci & Bruno Bertaccini, 2022. "A Mixture Hidden Markov Model to Mine Students’ University Curricula," Data, MDPI, vol. 7(2), pages 1-19, February.
    13. Giorgio E. Montanari & Silvia Pandolfi, 2018. "Evaluation of long-term health care services through a latent Markov model with covariates," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(1), pages 151-173, March.
    14. Leonard Paas, 2014. "Comments on: Latent Markov models: a review of a general framework for the analysis of longitudinal data with covariates," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(3), pages 473-477, September.
    15. Antonello Maruotti, 2015. "Handling non-ignorable dropouts in longitudinal data: a conditional model based on a latent Markov heterogeneity structure," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(1), pages 84-109, March.
    16. Geir D. Berentsen & Jan Bulla & Antonello Maruotti & Bård Støve, 2022. "Modelling clusters of corporate defaults: Regime‐switching models significantly reduce the contagion source," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(3), pages 698-722, June.
    17. Giorgio E. Montanari & Marco Doretti, 2019. "Ranking Nursing Homes’ Performances Through a Latent Markov Model with Fixed and Random Effects," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 146(1), pages 307-326, November.
    18. Francesco Bartolucci & Fulvia Pennoni & Giorgio Vittadini, 2016. "Causal Latent Markov Model for the Comparison of Multiple Treatments in Observational Longitudinal Studies," Journal of Educational and Behavioral Statistics, , vol. 41(2), pages 146-179, April.
    19. Giorgio Eduardo Montanari & Marco Doretti & Maria Francesca Marino, 2022. "Model-based two-way clustering of second-level units in ordinal multilevel latent Markov models," 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. 16(2), pages 457-485, June.
    20. Hans Jørn Juhl & Morten H. J. Fenger & John Thøgersen, 2017. "Will the Consistent Organic Food Consumer Step Forward? An Empirical Analysis," Journal of Consumer Research, Journal of Consumer Research Inc., vol. 44(3), pages 519-535.
    21. 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.

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