Showing papers by "Francesco Bartolucci published in 2001"

Positive Quadrant Dependence and Marginal Modeling in Two-Way Tables With Ordered Margins

Abstract: For a collection of two-way tables, where subjects are cross-classified according to the same pair of ordinal categorical variables conditionally on the value of one or more discrete explanatory variables, we propose a general approach to likelihood inference that combines marginal modeling with fitting and testing of inequality constraints such as those implied by the assumption that one marginal distribution is stochastically larger than the other, positive dependence and stronger positive dependence. The approach is based on parameterizing bivariate conditional distributions with global logits and global log-odds ratios, and we provide a general framework for handling models defined by equality and inequality constraints on these parameters. In this way, such models as marginal homogeneity, proportional odds among row or columns margins, and Plackett distribution may be treated together with various models defined by inequality constraints on the same parameters, such as, for instance, those implied by...

Analysis of capture-recapture data with a Rasch-type model allowing for conditional dependence and multidimensionality.

Abstract: Summary. In this article, we show that, if subjects are assumed to be homogeneous within a finite set of latent classes, the basic restrictions of the Rasch model (conditional independence and unidimensionality) can be relaxed in a flexible way by simply adding appropriate columns to a basic design matrix. When discrete covariates are available so that subjects may be classified into strata, we show how a joint modeling approach can achieve greater parsimony. Parameter estimates may be obtained by maximizing the conditional likelihood (given the total number of captures) with a combined use of the EM and Fisher scoring algorithms. We also discuss a technique for obtaining confidence intervals for the size of the population under study based on the profile likelihood.

Maximum likelihood estimation of a latent variable time‐series model

Abstract: Recently, Fridman and Harris proposed a method which allows one to approximate the likelihood of the basic stochastic volatility model. They also propose to estimate the parameters of such a model maximising the approximate likelihood by an algorithm which makes use of numerical derivatives. In this paper we propose an extension of their method which enables the computation of the first and second analytical derivatives of the approximate likelihood. As will be shown, these derivatives may be used to maximize the approximate likelihood through the Newton–Raphson algorithm, with a saving in the computational time. Moreover, these derivatives approximate the corresponding derivatives of the exact likelihood. In particular, the second derivative may be used to compute the standard error of the estimator and confidence intervals for the parameters. The paper presents also the results of a simulation study which allows one to compare our approach with other existing approaches. Copyright © 2001 John Wiley & Sons, Ltd.