Generalized Linear Models (2nd ed.)

Statistical Inference from Capture Data on Closed Animal Populations

Seven things to remember about hidden Markov models: A tutorial on Markovian models for time series

The statistical literature discusses different types of Markov properties for chain graphs that lead to four possible classes of chain graph Markov models. The different models are rather well understood when the observations are continuous and multivariate normal, and it is also known that one model class, referred to as models of LWF (Lauritzen-Wermuth-Frydenberg) or block concentration type, yields discrete models for categorical data that are smooth. This paper considers the structural properties of the discrete models based on the three alternative Markov properties. It is shown by example that two of the alternative Markov properties can lead to non-smooth models. The remaining model class, which can be viewed as a discrete version of multivariate regressions, is proven to comprise only smooth models. The proof employs a sim ple change of coordinates that also reveals that the model's likelihood function is unimodal if the chain components of the graph are complete sets.

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Discrete chain graph models

In this paper we review statistical methods which combine hidden Markov models (HMMs) and random effects models in a longitudinal setting, leading to the class of so-called mixed HMMs. This class of models has several interesting features. It deals with the dependence of a response variable on covariates, serial dependence, and unobserved heterogeneity in an HMM framework. It exploits the properties of HMMs, such as the relatively simple dependence structure and the efficient computational procedure, and allows one to handle a variety of real-world time-dependent data. We give details of the Expectation-Maximization algorithm for computing the maximum likelihood estimates of model parameters and we illustrate the method with two real applications describing the relationship between patent counts and research and development expenditures, and between stock and market returns via the Capital Asset Pricing Model.

Mixed Hidden Markov Models for Longitudinal Data: An Overview

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

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.

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Chain graph models of multivariate regression type for categorical data

We discuss two parameterizations of models for marginal independencies for discrete distributions which are representable by bi-directed graph models, under the global Markov property. Such models are useful data analytic tools especially if used in combination with other graphical models. The first parameterization, in the saturated case, is also known as the multivariate logistic transformation, the second is a variant that allows, in some (but not all) cases, variation independent parameters. An algorithm for maximum likelihood fitting is proposed, based on an extension of the Aitchison and Silvey method.

Parameterizations and fitting of bi-directed graph models to categorical data

 We discuss two parameterizations of models for marginal independencies for discrete distributions which are representable by bi-directed graph models, under the global Markov property Such models are useful data analytic tools especially if used in combination with other graphical models The first parameterization, in the saturated case, is also known as thenation multivariate logistic transformation, the second is a variant that allows, in some (but not all) cases, variation-independent parameters An algorithm for maximum likelihood fitting is proposed, based on an extension of the Aitchison and Silvey method

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Parameterizations and Fitting of Bi-directed Graph Models to Categorical Data

This paper is devoted to the theory and application of a novel class of models for binary data, which we call log-mean linear (LML) models. The characterizing feature of these models is that they are specied by linear constraints on the

Monia Lupparelli

Papers

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

Chain graph models of multivariate regression type for categorical data

Parameterizations and fitting of bi-directed graph models to categorical data

Parameterizations and Fitting of Bi-directed Graph Models to Categorical Data

Log-mean linear models for binary data