Monia Lupparelli

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

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 takingcare 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. 1. Introduction. Both in European countries and in the United States, elderly people with chronic conditions or functional limitations can access nursing homes whenever they are no longer able or choose not to remain in their own homes. These facilities provide a diverse array of services such as housing, support systems, nursing and medical care for a sustained period of time. These services range from minimal personal assistance to virtually total care for the patients. The challenge for the nursing homes is to provide the opportunity for elderly people to live with dignity even though they may be physically or cognitively impaired. The quality of the assistance and the

Chain graph models of multivariate regression type for categorical data

We discuss a class of chain graph models for categorical variables defined by what we call a multivariate regression chain graph Markov property. First, the set of local independencies of these models is shown to be Markov equivalent to those of a chain graph model recently defined in the literature. Next we provide a parametrization based on a sequence of generalized linear models with a multivariate logistic link function that captures all independence constraints in any chain graph model of this kind.

Log-mean linear models for binary data

This paper introduces a novel class of models for binary data, which we call log-mean linear models. They are specified by linear constraints on the log-mean linear parameter, defined as a log-linear expansion of the mean parameter of the multivariate Bernoulli distribution. We show that marginal independence relationships between variables can be specified by setting certain log-mean linear interactions to zero and, more specifically, that graphical models of marginal independence are log-mean linear models. Our approach overcomes some drawbacks of the existing parameterizations of graphical models of marginal independence. Copyright 2013, Oxford University Press.

Marginal parameterizations of discrete models defined by a set of conditional independencies

It is well-known that a conditional independence statement for discrete variables is equivalent to constraining to zero a suitable set of log-linear interactions. In this paper we show that this is also equivalent to zero constraints on suitable sets of marginal log-linear interactions, that can be formulated within a class of smooth marginal log-linear models. This result allows much more flexibility than known until now in combining several conditional independencies into a smooth marginal model. This result is the basis for a procedure that can search for such a marginal parameterization, so that, if one exists, the model is smooth.

Pairwise Likelihood Inference for Nested Hidden Markov Chain Models for Multilevel Longitudinal Data

In the context of multilevel longitudinal data, where sample units are collected in clusters, an important aspect that should be accounted for is the unobserved heterogeneity between sample units and between clusters. For this aim, we propose an approach based on nested hidden (latent) Markov chains, which are associated with every sample unit and with every cluster. The approach allows us to account for the previously mentioned forms of unobserved heterogeneity in a dynamic fashion; it also allows us to account for the correlation that may arise between the responses provided by the units belonging to the same cluster. Under the assumed model, computing the manifest distribution of these response variables is infeasible even with a few units per cluster. Therefore, we make inference on this model through a composite likelihood function based on all the possible pairs of subjects within each cluster. Properties of the composite likelihood estimator are assessed by simulation. The proposed approach is illustrated through an application to a dataset concerning a sample of Italian workers in which a binary response variable for the worker receiving an illness benefit was repeatedly observed. Supplementary materials for this article are available online.

Conditional and marginal relative risk parameters for a class of recursive regression graph models

In linear regression modelling, the distortion of effects after marginalizing over variables of the conditioning set has been widely studied in several contexts. For Gaussian variables, the relationship between marginal and partial regression coefficients is well established and the issue is often addressed as a result of W. G. Cochran. Possible generalizations beyond the linear Gaussian case have been developed, nevertheless the case of discrete variables is still challenging, in particular in medical and social science settings. A multivariate regression framework is proposed for binary data with regression coefficients given by the logarithm of relative risks, and a multivariate Relative Risk formula is derived to define the relationship between marginal and conditional relative risks. The method is illustrated through the analysis of the morphine data in order to assess the effect of preoperative oral morphine administration on the postoperative pain relief.