A semiparametric approach to mixed non-homogeneous hidden Markov models
نویسندگان
چکیده
Longitudinal data, where the same set of subjects is repeatedly observed over time, are frequently analyzed by using HiddenMarkov models (HMMs). In this situation, heterogeneity may arise at individual and/or time level affecting the hidden process, i.e. the transition probabilities among hidden states. Non-homogeneous (NH) HMMs face with this problem by expressing the transition probabilities as a function of a set of observed covariates, time and/or individual dependent, able to explain the non-homogeneity of the hidden processes. In this paper we introduce a finite mixture of NH-HMMs where each component is a NH-HMM differing only in the hidden process. The aim is twofold: classify subjects according to their behavior dynamic; estimate by non parametric maximum likelihood a mixed NH-HMM, where a random term is inserted accounting for omitted covariates at the individual level. The effectiveness of the proposal is tested through a simulation study.
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