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Likelihood inference for a class of latent Markov models under linear hypotheses on the transition probabilities

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  • Francesco Bartolucci

Abstract

For a class of latent Markov models for discrete variables having a longitudinal structure, we introduce an approach for formulating and testing linear hypotheses on the transition probabilities of the latent process. For the maximum likelihood estimation of a latent Markov model under hypotheses of this type, we outline an EM algorithm that is based on well-known recursions in the hidden Markov literature. We also show that, under certain assumptions, the asymptotic null distribution of the likelihood ratio statistic for testing a linear hypothesis on the transition probabilities of a latent Markov model, against a less stringent linear hypothesis on the transition probabilities of the same model, is of type. As a particular case, we derive the asymptotic distribution of the likelihood ratio statistic between a latent class model and its latent Markov version, which may be used to test the hypothesis of absence of transition between latent states. The approach is illustrated through a series of simulations and two applications, the first of which is based on educational testing data that have been collected within the National Assessment of Educational Progress 1996, and the second on data, concerning the use of marijuana, which have been collected within the National Youth Survey 1976-1980. Copyright 2006 Royal Statistical Society.

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Bibliographic Info

Article provided by Royal Statistical Society in its journal Journal of the Royal Statistical Society Series B.

Volume (Year): 68 (2006)
Issue (Month): 2 ()
Pages: 155-178

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Handle: RePEc:bla:jorssb:v:68:y:2006:i:2:p:155-178

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Cited by:
  1. Erika Mansnerus, 2008. "What happens to facts after their construction?: characteristics and functional roles of facts in the dissemination of knowledge across modelling communities," Economic History Working Papers 22504, London School of Economics and Political Science, Department of Economic History.
  2. Francesco Bartolucci & Ivonne Solis-Trapala, 2010. "Multidimensional Latent Markov Models in a Developmental Study of Inhibitory Control and Attentional Flexibility in Early Childhood," Psychometrika, Springer, vol. 75(4), pages 725-743, December.
  3. Francesco Bartolucci & Fulvia Pennoni & Brian Francis, 2007. "A latent Markov model for detecting patterns of criminal activity," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 170(1), pages 115-132.
  4. Jörn Dannemann & Hajo Holzmann, 2008. "Likelihood Ratio Testing for Hidden Markov Models Under Non-standard Conditions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 35(2), pages 309-321.
  5. Bartolucci, Francesco & Farcomeni, Alessio, 2009. "A Multivariate Extension of the Dynamic Logit Model for Longitudinal Data Based on a Latent Markov Heterogeneity Structure," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 816-831.
  6. Francesco Bartolucci & Valentina Nigro, 2007. "Maximum likelihood estimation of an extended latent markov model for clustered binary panel data," CEIS Research Paper 96, Tor Vergata University, CEIS.
  7. Bartolucci, Francesco & Lupparelli, Monia, 2012. "Nested hidden Markov chains for modeling dynamic unobserved heterogeneity in multilevel longitudinal data," MPRA Paper 40588, University Library of Munich, Germany.
  8. Bartolucci, Francesco & Farcomeni, Alessio & Pennoni, Fulvia, 2012. "Latent Markov models: a review of a general framework for the analysis of longitudinal data with covariates," MPRA Paper 39023, University Library of Munich, Germany.
  9. Francesco Bartolucci & Alessio Farcomeni, 2010. "A note on the mixture transition distribution and hidden Markov models," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(2), pages 132-138, 03.

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