LATENT MARKOV MODEL FOR LONGITUDINAL BINARY DATA: AN APPLICATION TO THE PERFORMANCE EVALUATION OF NURSING HOMES

被引：43

作者：

Bartolucci, Francesco ^{[1
]}

Lupparelli, Monia ^{[2
]}

Montanari, Giorgio E. ^{[1
]}

机构：

[1] Univ Perugia, Dipartimento Econ Finanza & Stat, I-06123 Perugia, Italy

[2] Univ Bologna, Dipartimento Sci Stat, I-40126 Bologna, Italy

来源：

ANNALS OF APPLIED STATISTICS | 2009年 / 3卷 / 02期

关键词：

EM algorithm; hidden Markov chains; item response theory; latent variable models; LIKELIHOOD INFERENCE; PROBABILISTIC FUNCTIONS; QUALITY; NUMBER; CRITERION; CLUSTERS;

D O I：

10.1214/08-AOAS230

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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 Lis 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.

引用

页码：611 / 636

页数：26

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