Maximum Likelihood Estimation of an Extended Latent Markov Model for Clustered Binary Panel Data

22 Pages Posted: 6 Mar 2007

See all articles by Francesco Bartolucci

Francesco Bartolucci

Università di Perugia - Finanza e Statistica - Dipartimento di Economia

Valentina Nigro

Bank of Italy

Date Written: March 2007

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.

Keywords: EM algorithm, Finite mixture models, Heterogeneity, Latent class model, State

JEL Classification: C23, C25, C51, C63

Suggested Citation

Bartolucci, Francesco and Nigro, Valentina, Maximum Likelihood Estimation of an Extended Latent Markov Model for Clustered Binary Panel Data (March 2007). CEIS Working Paper No. 97, Available at SSRN: https://ssrn.com/abstract=967378 or http://dx.doi.org/10.2139/ssrn.967378

Francesco Bartolucci (Contact Author)

Università di Perugia - Finanza e Statistica - Dipartimento di Economia ( email )

06123

Valentina Nigro

Bank of Italy ( email )

Via Nazionale 91
Rome, 00184
Italy

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