A mixed non-homogeneous hidden Markov model for categorical data, with application to alcohol consumption
A mixed non-homogeneous hidden Markov model for categorical data, with application to alcohol consumption
Hidden Markov models (HMMs) are frequently used to analyse longitudinal data, where the same set of subjects is repeatedly observed over time. In this context, several sources of heterogeneity may arise at individual and/or time level, which affect the hidden process, that is, the transition probabilities between the hidden states. In this paper, we propose the use of a finite mixture of non-homogeneous HMMs (NH-HMMs) to face the heterogeneity problem. The non-homogeneity of the model allows us to take into account observed sources of heterogeneity by means of a proper set of covariates, time and/or individual dependent, explaining the variations in the transition probabilities. Moreover, we handle the unobserved sources of heterogeneity at the individual level, due to, for example, omitted covariates, by introducing a random term with a discrete distribution. The resulting model is a finite mixture of NH-HMM that can be used to classify individuals according to their dynamic behaviour or to estimate a mixed NH-HMM without any assumption regarding the distribution of the random term following the non-parametric maximum likelihood approach. We test the effectiveness of the proposal through a simulation study and an application to real data on alcohol abuse.
mixed hidden markov models, random effects models, penalized npml, longitudinal data
871-886
Maruotti, Antonello
7096256c-fa1b-4cc1-9ca4-1a60cc3ee12e
Rocci, Roberto
233fb7c5-8eb7-4fca-b6ea-4caa3a082f5f
30 April 2012
Maruotti, Antonello
7096256c-fa1b-4cc1-9ca4-1a60cc3ee12e
Rocci, Roberto
233fb7c5-8eb7-4fca-b6ea-4caa3a082f5f
Maruotti, Antonello and Rocci, Roberto
(2012)
A mixed non-homogeneous hidden Markov model for categorical data, with application to alcohol consumption.
Statistics in Medicine, 31 (9), .
(doi:10.1002/sim.4478).
(PMID:22302505)
Abstract
Hidden Markov models (HMMs) are frequently used to analyse longitudinal data, where the same set of subjects is repeatedly observed over time. In this context, several sources of heterogeneity may arise at individual and/or time level, which affect the hidden process, that is, the transition probabilities between the hidden states. In this paper, we propose the use of a finite mixture of non-homogeneous HMMs (NH-HMMs) to face the heterogeneity problem. The non-homogeneity of the model allows us to take into account observed sources of heterogeneity by means of a proper set of covariates, time and/or individual dependent, explaining the variations in the transition probabilities. Moreover, we handle the unobserved sources of heterogeneity at the individual level, due to, for example, omitted covariates, by introducing a random term with a discrete distribution. The resulting model is a finite mixture of NH-HMM that can be used to classify individuals according to their dynamic behaviour or to estimate a mixed NH-HMM without any assumption regarding the distribution of the random term following the non-parametric maximum likelihood approach. We test the effectiveness of the proposal through a simulation study and an application to real data on alcohol abuse.
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e-pub ahead of print date: 3 February 2012
Published date: 30 April 2012
Keywords:
mixed hidden markov models, random effects models, penalized npml, longitudinal data
Organisations:
Statistics, Statistical Sciences Research Institute
Identifiers
Local EPrints ID: 340813
URI: http://eprints.soton.ac.uk/id/eprint/340813
ISSN: 0277-6715
PURE UUID: 43121c42-49b4-4341-99f8-3b598a88c074
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Date deposited: 04 Jul 2012 09:23
Last modified: 14 Mar 2024 11:30
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Author:
Antonello Maruotti
Author:
Roberto Rocci
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