In the context of longitudinal data, we show that a general class of hidden Markov (HM, [1]) models may be equivalent to a class of finite mixture (FM, [3]) models based on an augmented set of components and suitable constraints on the conditional response probabilities, given these components. We formulate a misspecification test for the latent structure of an HM model comparing maximum likelihood values of the two models for the same data, and when the number of possible latent state sequences is excessive, we propose a multiple version of this test including the Bonferroni correction. The procedure is simple since it is based on the output of the Expectation-Maximization estimation algorithm [2]. The properties of this testing procedure are evaluated through a simulation study. An empirical application illustrates it through data from the National Longitudinal Survey of Youth, in which we jointly consider wages and years of experience after labour force entry. We show that the proposed testing procedure may also be used as an alternative model selection criterion for the number of latent states of an HM model to those usually employed.

Bartolucci, F., Pandolfi, F., & Pennoni, F. (In corso di stampa). Mispecification tests for hidden Markov models based on a new class of finite mixture models. In Book of Abstract Classification and Data Science in the Digital Age (pp.271-271).

Mispecification tests for hidden Markov models based on a new class of finite mixture models

Pennoni F
In corso di stampa

Abstract

In the context of longitudinal data, we show that a general class of hidden Markov (HM, [1]) models may be equivalent to a class of finite mixture (FM, [3]) models based on an augmented set of components and suitable constraints on the conditional response probabilities, given these components. We formulate a misspecification test for the latent structure of an HM model comparing maximum likelihood values of the two models for the same data, and when the number of possible latent state sequences is excessive, we propose a multiple version of this test including the Bonferroni correction. The procedure is simple since it is based on the output of the Expectation-Maximization estimation algorithm [2]. The properties of this testing procedure are evaluated through a simulation study. An empirical application illustrates it through data from the National Longitudinal Survey of Youth, in which we jointly consider wages and years of experience after labour force entry. We show that the proposed testing procedure may also be used as an alternative model selection criterion for the number of latent states of an HM model to those usually employed.
No
abstract + slide
Scientifica
Expectation-Maximization algorithm; likelihood ratio test; model selection; multiple testing
English
17th Conference of the International Federation of Classification Societies
978-989-98955-9-1
https://ifcs2022.fep.up.pt/wp-content/uploads/2022/07/IFCS2022_Book_Abstracts_v1.pdf
Bartolucci, F., Pandolfi, F., & Pennoni, F. (In corso di stampa). Mispecification tests for hidden Markov models based on a new class of finite mixture models. In Book of Abstract Classification and Data Science in the Digital Age (pp.271-271).
Bartolucci, F; Pandolfi, F; Pennoni, F
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10281/388567
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