The Annals of Applied Statistics

Latent Markov model for longitudinal binary data: An application to the performance evaluation of nursing homes

Francesco Bartolucci, Monia Lupparelli, and Giorgio E. Montanari

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Abstract

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.

Article information

Source
Ann. Appl. Stat. Volume 3, Number 2 (2009), 611-636.

Dates
First available in Project Euclid: 22 June 2009

Permanent link to this document
http://projecteuclid.org/euclid.aoas/1245676188

Digital Object Identifier
doi:10.1214/08-AOAS230

Mathematical Reviews number (MathSciNet)
MR2750675

Zentralblatt MATH identifier
1166.62330

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

Citation

Bartolucci, Francesco; Lupparelli, Monia; Montanari, Giorgio E. Latent Markov model for longitudinal binary data: An application to the performance evaluation of nursing homes. Ann. Appl. Stat. 3 (2009), no. 2, 611--636. doi:10.1214/08-AOAS230. http://projecteuclid.org/euclid.aoas/1245676188.


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Supplemental materials

  • Supplementary material: Matlab functions for LM models with covariates.
    Digital Object Identifier: doi:10.1214/08-AOAS230SUPP
    Supplemental files available for subscribers.

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