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June 2009 Latent Markov model for longitudinal binary data: An application to the performance evaluation of nursing homes
Francesco Bartolucci, Monia Lupparelli, Giorgio E. Montanari
Ann. Appl. Stat. 3(2): 611-636 (June 2009). DOI: 10.1214/08-AOAS230


Performance evaluation of nursing homes is usually accomplished by the repeated administration of questionnaires aimed at measuring the health status of the patients during their period of residence in the nursing home. We illustrate how a latent Markov model with covariates may effectively be used for the analysis of data collected in this way. This model relies on a not directly observable Markov process, whose states represent different levels of the health status. For the maximum likelihood estimation of the model we apply an EM algorithm implemented by means of certain recursions taken from the literature on hidden Markov chains. Of particular interest is the estimation of the effect of each nursing home on the probability of transition between the latent states. We show how the estimates of these effects may be used to construct a set of scores which allows us to rank these facilities in terms of their efficacy in taking care of the health conditions of their patients. The method is used within an application based on data concerning a set of nursing homes located in the Region of Umbria, Italy, which were followed for the period 2003–2005.


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Francesco Bartolucci. Monia Lupparelli. Giorgio E. Montanari. "Latent Markov model for longitudinal binary data: An application to the performance evaluation of nursing homes." Ann. Appl. Stat. 3 (2) 611 - 636, June 2009.


Published: June 2009
First available in Project Euclid: 22 June 2009

zbMATH: 1166.62330
MathSciNet: MR2750675
Digital Object Identifier: 10.1214/08-AOAS230

Keywords: EM algorithm , hidden Markov chains , item response theory , latent variable models

Rights: Copyright © 2009 Institute of Mathematical Statistics


Vol.3 • No. 2 • June 2009
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