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Maximum likelihood estimation of an extended latent markov model for clustered binary panel data

Author

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  • Francesco Bartolucci

    () (Dipartimento diEconomia, Finanza e Statistica, Universit`a di Perugia,)

  • Valentina Nigro

    () (Dipartimento di Studi Economico-Finanziari e Metodi Quantitativi Universit`a di Roma “Tor Vergata”,)

Abstract

Computational aspects concerning a model for clustered binary panel data are analysed. The model is based on the representation of the behavior of a subject (individual panel member) in a given cluster by means of a latent process that is decomposed into a cluster-specific component, which follows a first-order Markov chain, and an individual-specific component, which is timeinvariant and is represented by a discrete random variable. In particular, an algorithm for computing the joint distribution of the response variables is introduced. The algorithm may be used even in the presence of a large number of subjects in the same cluster. Also an Expectation-Maximization (EM) scheme for the maximum likelihood estimation of the model is described showing how the Fisher information matrix can be estimated on the basis of the numerical derivative of the score vector. The estimate of this matrix is used to compute standard errors for the parameter estimates and to check the identifiability of the model and the convergence of the EM algorithm. The approach is illustrated by means of an application to a dataset concerning Italian employees illness benefits.

Suggested Citation

  • Francesco Bartolucci & Valentina Nigro, 2007. "Maximum likelihood estimation of an extended latent markov model for clustered binary panel data," CEIS Research Paper 96, Tor Vergata University, CEIS.
  • Handle: RePEc:rtv:ceisrp:96
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    File URL: ftp://www.ceistorvergata.it/repec/rpaper/No-96.pdf
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    References listed on IDEAS

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    Cited by:

    1. Bartolucci, Francesco & Farcomeni, Alessio, 2009. "A Multivariate Extension of the Dynamic Logit Model for Longitudinal Data Based on a Latent Markov Heterogeneity Structure," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 816-831.
    2. Bartolucci, Francesco & Montanari, Giorgio E. & Pandolfi, Silvia, 2015. "Three-step estimation of latent Markov models with covariates," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 287-301.
    3. Bartolucci, Francesco & Lupparelli, Monia, 2012. "Nested hidden Markov chains for modeling dynamic unobserved heterogeneity in multilevel longitudinal data," MPRA Paper 40588, University Library of Munich, Germany.

    More about this item

    Keywords

    EM algorithm; Finite mixture models; Heterogeneity; Latent class model; State dependence.;

    JEL classification:

    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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