arXiv subjects

Francesco Bartolucci

Publications and source records attributed to Francesco Bartolucci.

32 records · Page 2Linked to original sources

arXiv2012

Mixtures of equispaced normal distributions and their use for testing symmetry in univariate data

Given a random sample of observations, mixtures of normal densities are often used to estimate the unknown continuous distribution from which the data come. Here we propose the use of this semiparametric framework for testing symmetry about an unknown value. More precisely, we show how the null hypothesis of symmetry may be formulated in terms of normal mixture model, with weights about the centre of symmetry constrained to be equal one another. The resulting model is nested in a more general unconstrained one, with same number of mixture components and free weights. Therefore, after having maximised the constrained and unconstrained log-likelihoods by means of a suitable algorithm, such as the Expectation-Maximisation, symmetry is tested against skewness through a likelihood ratio statistic. The performance of the proposed mixture-based test is illustrated through a Monte Carlo simulation study, where we compare two versions of the test, based on different criteria to select the number of mixture components, with the traditional one based on the third standardised moment. An illustrative example is also given that focuses on real data.

stat.ME↗

arXiv2012

Decomposition of the h-index

I introduce a decomposition of the h-index, which is nowadays the leading criterion to assess the relevance of a scientist in his/her research field. According to the proposed decomposition, the h-index is the product of two indicators, the first of which measures the impact of the scientist on the research community and the second may be seen as a measure of concentration of the citations in correspondence of a reduced number of papers. The decomposition is illustrated by an application based on data concerning a group of top level economists.

cs.DL↗

arXiv2012

Bayesian inference through encompassing priors and importance sampling for a class of marginal models for categorical data

We develop a Bayesian approach for selecting the model which is the most supported by the data within a class of marginal models for categorical variables formulated through equality and/or inequality constraints on generalised logits (local, global, continuation or reverse continuation), generalised log-odds ratios and similar higher-order interactions. For each constrained model, the prior distribution of the model parameters is formulated following the encompassing prior approach. Then, model selection is performed by using Bayes factors which are estimated by an importance sampling method. The approach is illustrated through three applications involving some datasets, which also include explanatory variables. In connection with one of these examples, a sensitivity analysis to the prior specification is also considered.

math.ST↗

arXiv2012

A class of Multidimensional Latent Class IRT models for ordinal polytomous item responses

We propose a class of Item Response Theory models for items with ordinal polytomous responses, which extends an existing class of multidimensional models for dichotomously-scored items measuring more than one latent trait. In the proposed approach, the random vector used to represent the latent traits is assumed to have a discrete distribution with support points corresponding to different latent classes in the population. We also allow for different parameterizations for the conditional distribution of the response variables given the latent traits - such as those adopted in the Graded Response model, in the Partial Credit model, and in the Rating Scale model - depending on both the type of link function and the constraints imposed on the item parameters. For the proposed models we outline how to perform maximum likelihood estimation via the Expectation-Maximization algorithm. Moreover, we suggest a strategy for model selection which is based on a series of steps consisting of selecting specific features, such as the number of latent dimensions, the number of latent classes, and the specific parametrization. In order to illustrate the proposed approach, we analyze data deriving from a study on anxiety and depression as perceived by oncological patients.

stat.ME↗

arXiv2011

An alternative to the Baum-Welch recursions for hidden Markov models

We develop a recursion for hidden Markov model of any order h, which allows us to obtain the posterior distribution of the latent state at every occasion, given the previous h states and the observed data. With respect to the well-known Baum-Welch recursions, the proposed recursion has the advantage of being more direct to use and, in particular, of not requiring dummy renormalizations to avoid numerical problems. We also show how this recursion may be expressed in matrix notation, so as to allow for an efficient implementation, and how it may be used to obtain the manifest distribution of the observed data and for parameter estimation within the Expectation-Maximization algorithm. The approach is illustrated by an application to financial data which is focused on the study of the dynamics of the volatility level of log-returns.

math.ST↗

arXiv2011

Mixture latent autoregressive models for longitudinal data

Many relevant statistical and econometric models for the analysis of longitudinal data include a latent process to account for the unobserved heterogeneity between subjects in a dynamic fashion. Such a process may be continuous (typically an AR(1)) or discrete (typically a Markov chain). In this paper, we propose a model for longitudinal data which is based on a mixture of AR(1) processes with different means and correlation coefficients, but with equal variances. This model belongs to the class of models based on a continuous latent process, and then it has a natural interpretation in many contexts of application, but it is more flexible than other models in this class, reaching a goodness-of-fit similar to that of a discrete latent process model, with a reduced number of parameters. We show how to perform maximum likelihood estimation of the proposed model by the joint use of an Expectation-Maximisation algorithm and a Newton-Raphson algorithm, implemented by means of recursions developed in the hidden Markov literature. We also introduce a simple method to obtain standard errors for the parameter estimates and a criterion to choose the number of mixture components. The proposed approach is illustrated by an application to a longitudinal dataset, coming from the Health and Retirement Study, about self-evaluation of the health status by a sample of subjects. In this application, the response variable is ordinal and time-constant and time-varying individual covariates are available.

math.ST↗

arXiv2011

Bayesian inference for a class of latent Markov models for categorical longitudinal data

We propose a Bayesian inference approach for a class of latent Markov models. These models are widely used for the analysis of longitudinal categorical data, when the interest is in studying the evolution of an individual unobservable characteristic. We consider, in particular, the basic latent Markov, which does not account for individual covariates, and its version that includes such covariates in the measurement model. The proposed inferential approach is based on a system of priors formulated on a transformation of the initial and transition probabilities of the latent Markov chain. This system of priors is equivalent to one based on Dirichlet distributions. In order to draw samples from the joint posterior distribution of the parameters and the number of latent states, we implement a reversible jump algorithm which alternates moves of Metropolis-Hastings type with moves of split/combine and birth/death types. The proposed approach is illustrated through two applications based on longitudinal datasets.

stat.ME↗

arXiv2010

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

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.

stat.AP↗

arXiv2009

Assessment of school performance through a multilevel latent Markov Rasch model

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, e.g. students clustered in classes. For each subject, the latent process is used to represent the characteristic of interest (e.g. ability) conditional on the effect of the cluster to which he/she belongs. The latter effect is modeled by a discrete latent variable associated with each cluster. For the maximum likelihood estimation of the model parameters we outline an EM algorithm. We show how the proposed model may be used for assessing the development of cognitive Math achievement. This approach is applied to the analysis of a dataset collected in the Lombardy Region (Italy) and based on test scores over three years of middle-school students attending public and private schools.

stat.AP↗

arXiv2009

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

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.

stat.AP↗

arXiv2008

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

We demonstrate the use of a multidimensional extension of the latent Markov model to analyse data from studies with correlated 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 and attentional flexibility 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 tests outcomes given the latent process depends on these abilities through a multidimensional two-parameter logistic parameterisation. We outline an EM algorithm to conduct 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 inhibitory control and attentional flexibility 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.

stat.AP↗

arXiv2008

On the conditional logistic estimator for repeated binary outcomes in two-arm experimental studies with non-compliance

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 its bias in estimating this quantity and the causal effect of the treatment over control on compliers. A two-step estimator results whose asymptotic properties are studied by exploiting the general theory on maximum likelihood estimation of misspecified models. Finite-sample properties of the estimator are studied by simulation and the extension to the case of missing responses is outlined. The approach is illustrated by an application to a dataset deriving from a study on the efficacy of a training course on the practise of breast self examination.

math.ST↗

arXiv2007

Approximate conditional inference for panel logit models allowing for state dependence and unobserved heterogeneity

We show that a dynamic logit model for binary panel data allowing for state dependence and unobserved heterogeneity may be accurately approximated by a quadratic exponential model, the parameters of which have the same interpretation that they have in the true model. We also show how we can eliminate the parameters for the unobserved heterogeneity from the approximating model by conditioning on the total scores, i.e. sum of the response variables for any individual in the panel. This allows to construct an approximate conditional likelihood for the dynamic logit model, by maximizing which we can estimate the parameters for the covariates and the state dependence. This estimator is very simple to compute and, by means of a simulation study, we show that it is competitive in terms of efficiency with the estimator of Honore' & Kyriazidou (2000). Finally, we outline the extension of the proposed approach to the case of more elaborated structures for the state dependence and to that of categorical response variables with more than two levels.

math.ST↗

arXiv2006

Model Building for Semiparametric Mixtures

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.

math.ST↗