Likelihood Inference for a Class of Latent Markov Models under Linear Hypotheses on the Transition Probabilities

Likelihood Inference for a Class of Latent Markov Models under Linear Hypotheses on the Transition Probabilities

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...

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Veröffentlicht in:Journal of the Royal Statistical Society. Series B (Statistical Methodology). - Blackwell Publishers. - 68(2006), 2, Seite 155-178
1. Verfasser: Bartolucci, Francesco (VerfasserIn)
Format: Online-Aufsatz
Sprache:English
Veröffentlicht: 2006
Zugriff auf das übergeordnete Werk:Journal of the Royal Statistical Society. Series B (Statistical Methodology)
Schlagworte:Boundary Problem Constrained Statistical Inference EM Algorithm Item Response Theory Latent Class Model Longitudinal Data Mathematics Behavioral sciences Applied sciences
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520 |a 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 $\bar\chi^2$ 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. 
540 |a Copyright 2006 The Royal Statistical Society and Blackwell Publishing Ltd. 
650 4 |a Boundary Problem 
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