Showing papers by "Francesco Bartolucci published in 2005"

Likelihood Inference on the Underlying Structure of IRT Models.

Abstract: The assumptions underlying item response theory (IRT) models may be expressed as a set of equality and inequality constraints on the parameters of a latent class model. It is well known that the same assumptions imply that the parameters of the manifest distribution have to satisfy a more complicated set of inequality constraints which, however, are necessary but not sufficient. In this paper, we describe how the theory for likelihood-based inference under equality and inequality constraints may be used to test the underlying assumptions of IRT models. It turns out that the analysis based directly on the latent structure is simpler and more flexible. In particular, we indicate how several interesting extensions of the Rasch model may be obtained by partial relaxation of the basic constraints. An application to a data set provided by Educational Testing Service is used to illustrate the approach.

Clustering Univariate Observations via Mixtures of Unimodal Normal Mixtures

Abstract: A mixture model is proposed in which any component is modelled in a flexible way through a unimodal mixture of normal distributions with the same variance and equispaced support points. The main application of the model is for clustering univariate observations where any component identifies a different cluster and conventional mixture models may lead to an overestimate of the number of clusters when the component distribution is misspecified. Maximum likelihood estimation of the model is carried on through an EM algorithm where the maximization of the complete log-likelihood under the constraint of unimodality is performed by solving a series of least squares problems under linear inequality constraints. The Bayesian Information Criterion is used to select the number of components. A simulation study shows that this criterion performs well even when the true component distribution has strong skewness and/or kurtosis. This is due to the flexibility of the proposed model and is particularly useful when the model is used for clustering.

A Hierarchical Mixture Model for Gene Expression Data

Abstract: We illustrate the use of a mixture of multivariate Normal distributions for clustering genes on the basis of Microarray data. We follow a hierarchical Bayesian approach and estimate the parameters of the mixture using Markov chain Monte Carlo (MCMC) techniques. The number of components (groups) is chosen on the basis of the Bayes factor, numerically evaluated using the Chib and Jelaizkov (2001) method. We also show how the proposed approach can be easily applied in recovering missing observations, which generally affect Microarray data sets. An application of the approach for clustering yeast genes according to their temporal profiles is illustrated.