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

Computational aspects concerning a model for clustered binary panel data are analyzed. 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. This latent process is decomposed into a cluster-specific component and an individual-specific component. The first component follows a first-order Markov chain, whereas the second is time-invariant and is represented by a discrete random variable. 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. An Expectation-Maximization (EM) scheme for the maximum likelihood estimation of the model is also described together with the estimation of the Fisher information matrix on the basis of the numerical derivative of the score vector. The estimate of this matrix is used to obtain 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 data set concerning Italian employees' illness benefits.