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Title: A misspecification test for hidden Markov models based on finite mixture models Authors:  Silvia Pandolfi - University of Perugia (Italy) [presenting]
Francesco Bartolucci - University of Perugia (Italy)
Fulvia Pennoni - University of Milano-Bicocca (Italy)
Abstract: In the context of longitudinal data, we investigate the relation between hidden Markov (HM) models and finite mixture (FM) models, to provide a misspecification test for the class of former ones. We show that an HM model may be seen as a particular FM model. Based on this idea, we develop a new class of FM models, denoted FM2 models, which is based on an augmented set of components and suitable constraints on the conditional response probabilities, given these components. We also derive conditions under which the two model formulations become equivalent, based on suitable constraints on the parameters of the FM2 model. Based on these results, we develop a likelihood ratio misspecification test for the latent structure of an HM model and a multiple version of this test, based on the Bonferroni correction for multiple tests, which may be used in presence of many latent states or time occasions. The proposal is studied by a series of simulations, aimed at assessing the performance of the proposed tests under different circumstances, and by a real data application, which also shows that the testing procedure may be used as a criterion for selecting the number of latent states of an HM model.