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Statistics and Computing

, 19:381 | Cite as

A semiparametric approach to hidden Markov models under longitudinal observations

  • Antonello MaruottiEmail author
  • Tobias Rydén
Article

Abstract

We propose a hidden Markov model for longitudinal count data where sources of unobserved heterogeneity arise, making data overdispersed. The observed process, conditionally on the hidden states, is assumed to follow an inhomogeneous Poisson kernel, where the unobserved heterogeneity is modeled in a generalized linear model (GLM) framework by adding individual-specific random effects in the link function.

Due to the complexity of the likelihood within the GLM framework, model parameters may be estimated by numerical maximization of the log-likelihood function or by simulation methods; we propose a more flexible approach based on the Expectation Maximization (EM) algorithm. Parameter estimation is carried out using a non-parametric maximum likelihood (NPML) approach in a finite mixture context. Simulation results and two empirical examples are provided.

Keywords

Hidden Markov models Longitudinal data Mixed hidden Markov models Random effects NPML 

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Dipartimento di Istituzioni Pubbliche Economia e SocietàUniversità di Roma TreRomeItaly
  2. 2.Centre for Mathematical SciencesLund UniversityLundSweden

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