Showing papers by "Francesco Bartolucci published in 2006"

Likelihood inference for a class of latent Markov models under linear hypotheses on the transition probabilities

Abstract: Summary. For a class of latent Markov models for discrete variables having a longitudinal structure, we introduce an approach for formulating and testing linear hypotheses on the transition probabilities of the latent process. For the maximum likelihood estimation of a latent Markov model under hypotheses of this type, we outline an EM algorithm that is based on well-known recursions in the hidden Markov literature. We also show that, under certain assumptions, the asymptotic null distribution of the likelihood ratio statistic for testing a linear hypothesis on the transition probabilities of a latent Markov model, against a less stringent linear hypothesis on the transition probabilities of the same model, is of X2 type. As a particular case, we derive the asymptotic distribution of the likelihood ratio statistic between a latent class model and its latent Markov version, which may be used to test the hypothesis of absence of transition between latent states. The approach is illustrated through a series of simulations and two applications, the first of which is based on educational testing data that have been collected within the National Assessment of Educational Progress 1996, and the second on data, concerning the use of marijuana, which have been collected within the National Youth Survey 19761980.

A Class of Latent Marginal Models for Capture–Recapture Data With Continuous Covariates

Abstract: We introduce a new family of latent class models for the analysis of capture–recapture data where continuous covariates are available. The present approach exploits recent advances in marginal parameterizations to model simultaneously, and conditionally on individual covariates, the size of the latent classes, the marginal probabilities of being captured by each list given the latent, and possible higher-order marginal interactions among lists conditionally on the latent. An EM algorithm for maximum likelihood estimation is described, and an expression for the expected information matrix is derived. In addition, a new method for computing confidence intervals for the size of the population having given covariate configurations is proposed and its asymptotic properties are derived. Applications to data on patients with human immunodeficiency virus, in the region of Veneto, Italy, and to new cases of cancer in Tuscany are discussed.

Efficient Bayes factor estimation from the reversible jump output

Abstract: SUMMARY We propose a class of estimators of the Bayes factor which is based on an extension of the bridge sampling identity of Meng & Wong (1996) and makes use of the output of the reversible jump algorithm of Green ( 1995). Within this class we give the optimal estimator and also a suboptimal one which may be simply computed on the basis of the acceptance probabilities used within the reversible jump algorithm for jumping between models. The proposed estimators are very easily computed and lead to a substantial gain of efficiency in estimating the Bayes factor over the standard estimator based on the reversible jump output. This is illustrated through a series of Monte Carlo simulations involving a linear and a logistic regression model.

Model Building for Semiparametric Mixtures

Abstract: An important and yet difficult problem in fitting multivariate mixture models is determining the mixture complexity. We develop theory and a unified framework for finding the nonparametric maximum likelihood estimator of a multivariate mixing distribution and consequently estimating the mixture complexity. Multivariate mixtures provide a flexible approach to fitting high-dimensional data while offering data reduction through the number, location and shape of the component densities. The central principle of our method is to cast the mixture maximization problem in the concave optimization framework with finitely many linear inequality constraints and turn it into an unconstrained problem using a "penalty function". We establish the existence of parameter estimators and prove the convergence properties of the proposed algorithms. The role of a "sieve parameter'' in reducing the dimensionality of mixture models is demonstrated. We derive analytical machinery for building a collection of semiparametric mixture models, including the multivariate case, via the sieve parameter. The performance of the methods are shown with applications to several data sets including the cdc15 cell-cycle yeast microarray data.

A quadratic exponential model for the analysis of item response data

Abstract: Riassunto: Si propone un metodo di stima del modello logistico a due parametri (2-PL) per l’analisi di dati derivanti dalla somministrazione di un questionario con domande valutate in modo dicotomico. Il metodo e basato su un’approssimazione, formulata seguendo Cox e Wermuth (1994), del modello in questione tramite un modello esponenziale quadratico i cui parametri sono stimabili tramite una semplice procedura iterativa. Vengono considerati uno studio per simulazione ed un’applicazione su dati reali. Infine si accenna ad una possibile estensione del modello al caso multidimensionale.