Showing papers by "Francesco Bartolucci published in 2010"

A Dynamic Model for Binary Panel Data With Unobserved Heterogeneity Admitting a √n-Consistent Conditional Estimator

Abstract: A model for binary panel data is introduced which allows for state dependence and unobserved heterogeneity beyond the effect of available covariates. The model is of quadratic exponential type and its structure closely resembles that of the dynamic logit model. However, it has the advantage of being easily estimable via conditional likelihood with at least two observations (further to an initial observation) and even in the presence of time dummies among the regressors.

A generalization of the Multiple-try Metropolis algorithm for Bayesian estimation and model selection

Abstract: We propose a generalization of the Multipletry Metropolis (MTM) algorithm of Liu et al. (2000), which is based on drawing several proposals at each step and randomly choosing one of them on the basis of weights that may be arbitrary chosen. In particular, for Bayesian estimation we also introduce a method based on weights depending on a quadratic approximation of the posterior distribution. The resulting algorithm cannot be reformulated as an MTM algorithm and leads to a comparable gain of e‐ciency with a lower computational efiort. We also outline the extension of the proposed strategy, and then of the MTM strategy, to Bayesian model selection, casting it in a Reversible Jump framework. The approach is illustrated by real examples.

A note on the mixture transition distribution and hidden Markov models

Abstract: We discuss an interpretation of the mixture transition distribution (MTD) for discrete-valued time series which is based on a sequence of independent latent variables which are occasion-specific. We show that, by assuming that this latent process follows a first order Markov Chain, MTD can be generalized in a sensible way. A class of models results which also includes the hidden Markov model (HMM). For these models we outline an EM algorithm for the maximum likelihood estimation which exploits recursions developed within the HMM literature. As an illustration, we provide an example based on the analysis of stock market data referred to different American countries.

An overview of latent Markov models for longitudinal categorical data

Abstract: We provide a comprehensive overview of latent Markov (LM) models for the analysis of longitudinal categorical data. The main assumption behind these models is that the response variables are conditionally independent given a latent process which follows a first-order Markov chain. We first illustrate the basic LM model in which the conditional distribution of each response variable given the corresponding latent variable and the initial and transition probabilities of the latent process are unconstrained. For this model we also illustrate in detail maximum likelihood estimation through the Expectation-Maximization algorithm, which may be efficiently implemented by recursions known in the hidden Markov literature. We then illustrate several constrained versions of the basic LM model, which make the model more parsimonious and allow us to include and test hypotheses of interest. These constraints may be put on the conditional distribution of the response variables given the latent process (measurement model) or on the distribution of the latent process (latent model). We also deal with extensions of LM model for the inclusion of individual covariates and to multilevel data. Covariates may affect the measurement or the latent model; we discuss the implications of these two different approaches according to the context of application. Finally, we outline methods for obtaining standard errors for the parameter estimates, for selecting the number of states and for path prediction. Models and related inference are illustrated by the description of relevant socio-economic applications available in the literature.

Multidimensional latent Markov models in a developmental study of inhibitory control and attentional flexibility in early childhood

Abstract: We demonstrate the use of a multidimensional extension of the latent Markov model to analyse data from studies with repeated binary responses in developmental psychology. In particular, we consider an experiment based on a battery of tests which was administered to pre-school children, at three time periods, in order to measure their inhibitory control (IC) and attentional flexibility (AF) abilities. Our model represents these abilities by two latent traits which are associated to each state of a latent Markov chain. The conditional distribution of the test outcomes given the latent process depends on these abilities through a multidimensional one-parameter or two-parameter logistic parameterisation. We outline an EM algorithm for likelihood inference on the model parameters; we also focus on likelihood ratio testing of hypotheses on the dimensionality of the model and on the transition matrices of the latent process. Through the approach based on the proposed model, we find evidence that supports that IC and AF can be conceptualised as distinct constructs. Furthermore, we outline developmental aspects of participants’ performance on these abilities based on inspection of the estimated transition matrices.

Assessment of school performance through a multilevel latent Markov Rasch model

Abstract: An extension of the latent Markov Rasch model is described for the analysis of binary longitudinal data with covariates when subjects are collected in clusters, such as students clustered in classes. For each subject, a latent process is used to represent the characteristic of interest (e.g., ability) conditional on the effect of the cluster to which he or she belongs. The latter effect is modeled by a discrete latent variable associated to each cluster. For the maximum likelihood estimation of the model parameters, an Expectation-Maximization algorithm is outlined. Through the analysis of a data set collected in the Lombardy Region (Italy), it is shown how the proposed model may be used for assessing the development of cognitive achievement. The data set is based on test scores in mathematics observed over 3 years on middle school students attending public and non-state schools.Manuscript received March 20, 2009 Revision received July 2, 2010 Accepted July 10, 2010

On the conditional logistic estimator in two-arm experimental studies with non-compliance and before-after binary outcomes.

Abstract: The behavior of the conditional logistic estimator is analyzed under a causal model for two-arm experimental studies with possible non-compliance in which the effect of the treatment is measured by a binary response variable. We show that, when non-compliance may only be observed in the treatment arm, the effect (measured on the logit scale) of the treatment on compliers and that of the control on non-compliers can be identified and consistently estimated under mild conditions. The same does not happen for the effect of the control on compliers. A simple correction of the conditional logistic estimator is then proposed, which allows us to considerably reduce the bias in estimating this quantity and the causal effect of the treatment over control on compliers. A two-step estimator results on the basis of which we can also set up a Wald test for the hypothesis of absence of a causal effect of the treatment. The asymptotic properties of the estimator are studied by exploiting the general theory on maximum likelihood estimation of misspecified models. Finite-sample properties of the estimator and of the related Wald test are studied by simulation. The extension of the approach to the case of missing responses is also outlined. The approach is illustrated by an application to a dataset deriving from a study on the efficacy of a training course on the breast self examination practice. Copyright © 2010 John Wiley & Sons, Ltd.

A generalized Multiple-try Metropolis version of the Reversible Jump algorithm

Abstract: The Reversible Jump algorithm is one of the most widely used Markov chain Monte Carlo algorithms for Bayesian estimation and model selection. A generalized multiple-try version of this algorithm is proposed. The algorithm is based on drawing several proposals at each step and randomly choosing one of them on the basis of weights (selection probabilities) that may be arbitrary chosen. Among the possible choices, a method is employed which is based on selection probabilities depending on a quadratic approximation of the posterior distribution. Moreover, the implementation of the proposed algorithm for challenging model selection problems, in which the quadratic approximation is not feasible, is considered. The resulting algorithm leads to a gain in efficiency with respect to the Reversible Jump algorithm, and also in terms of computational effort. The performance of this approach is illustrated for real examples involving a logistic regression model and a latent class model.

An investigation of the discriminant power and dimensionality of items used for assessing health condition of elderly people

Abstract: With reference to the questionnaire adopted within the Italian project "Ulisse" to assess health condition of elderly people, we investigate two important issues: discriminant power and actual number of dimensions measured by the items composing the questionnaire. The adopted statistical approach is based on the joint use of the latent class model and a multidimensional item response theory model based on the 2PL parametrization. The latter allows us to account for the different discriminant power of these items. The analysis is based on the data collected on a sample of 1699 elderly people hosted in 37 nursing homes in Italy. This analysis shows that the selected items indeed measure a different number of dimensions of the health status and that they considerably differ in terms of discriminant power (effectiveness in measuring the actual health status). Implications for the assessment of the performance of nursing homes from a policy-maker prospective are discussed.

Point Estimation Methods with Applications to Item Response Theory Models

Abstract: Statistical inference is mainly concerned with providing some conclusions about the parameters which describe the distribution of a variable of interest in a certain population on the basis of a random sample. In this article, we review point estimation methods which consist of assigning a value to each unknown parameter. Basic properties of an estimator are illustrated together with the main methods of finding estimators: method of moments, maximum likelihood, and Bayesian methods. In particular, we discuss maximum likelihood estimation of the most well-known item response theory model, the Rasch model, and illustrate it through a data analysis example.

Pairwise likelihood inference for multilevel latent Markov models

Abstract: We propose an extended latent Markov model for categorical longitudinal data with a multilevel structure. This extension allows us to take into account the correlation which may arise between the responses provided by individuals belonging to the same cluster and to model the cluster effect in a dynamic fashion. Given the complexity of computing the manifest distribution, we make inference on the model through a composite likelihood function based on all the possible pairs of subjects within every cluster. The resulting approach is illustrated through an application to a dataset concerning a sample of Italian workers.