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Francesco Bartolucci

Other affiliations: University of Urbino
Bio: Francesco Bartolucci is an academic researcher from University of Perugia. The author has contributed to research in topics: Latent class model & Expectation–maximization algorithm. The author has an hindex of 31, co-authored 214 publications receiving 2629 citations. Previous affiliations of Francesco Bartolucci include University of Urbino.


Papers
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TL;DR: An approach based on nested hidden (latent) Markov chains, which are associated to every sample unit and to every cluster, which allows us to account for the forms of unobserved heterogeneity in a dynamic fashion and for the correlation which may arise between the responses provided by the units belonging to the same cluster.
Abstract: In the context of multilevel longitudinal data, where sample units are collected in clusters, an important aspect that should be accounted for is the unobserved heterogeneity between sample units and between clusters. For this aim we propose an approach based on nested hidden (latent) Markov chains, which are associated to every sample unit and to every cluster. The approach allows us to account for the mentioned forms of unobserved heterogeneity in a dynamic fashion; it also allows us to account for the correlation which may arise between the responses provided by the units belonging to the same cluster. Given the complexity in computing the manifest distribution of these response variables, we make inference on the proposed model through a composite likelihood function based on all the possible pairs of subjects within every cluster. The proposed approach is illustrated through an application to a dataset concerning a sample of Italian workers in which a binary response variable for the worker receiving an illness benefit was repeatedly observed.

2 citations

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TL;DR: In this article, a test of misspecification for finite-mixture models is proposed which is based on the comparison between the Marginal and the Conditional Maximum Likelihood estimates of the fixed effects as in the Hausman's test.
Abstract: An alternative to using normally distributed random effects in modeling clustered binary and ordered responses is based on using a finite-mixture. This approach gives rise to a flexible class of generalized linear mixed models for item responses, multilevel data, and longitudinal data. A test of misspecification for these finite-mixture models is proposed which is based on the comparison between the Marginal and the Conditional Maximum Likelihood estimates of the fixed effects as in the Hausman’s test. The asymptotic distribution of the test statistic is derived; it is of chi-squared type with a number of degrees of freedom equal to the number of covariates that vary within the cluster. It turns out that the test is simple to perform and may also be used to select the number of components of the finite-mixture, when this number is unknown. The approach is illustrated by a series of simulations and three empirical examples covering the main fields of application.

2 citations

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TL;DR: A Bayesian Latent Class model for capture-recapture data is proposed and the Reversible Jump algorithm and the Delayed Rejection strategy are used to improve its efficiency.
Abstract: In this paper we propose a Bayesian Latent Class model for capture-recapture data. Through two appliations, the first concerning a sample of snowshoe hares and the second concerning a sample of diabetics in a small Italian town, we show how the proposed approach may be effectively used to obtain point estimates and credibility intervals for the size of a closed-population. To estimate the model we use the Reversible Jump algorithm and the Delayed Rejection strategy to improve its efficiency.

1 citations

Journal ArticleDOI
TL;DR: This Special Section is intended to propose recent advances on LV models for longitudinal data and their applications to real-life studies in the biometrical domain.
Abstract: Latent variable (LV) models (see, e.g. Bartholomew et al., 2011) have found an important field of application in the context of life sciences. Their use is justified by the complexity of the biological systems, with implications in terms of sophisticated dependencies between observable variables. In LV models, as it is well known, the observable response variables are affected by (discrete or continuous) variables that are not directly observed. LV models are based on specific assumptions on the conditional distribution of the response variables, given the latent ones. This allows us to model the effect of unobservable covariates (factors) and, thus, to account for the unobserved heterogeneity between subjects. In the last decades, particular attention has been paid to LV models for longitudinal data. In such cases, the phenomenon under investigation evolves over time. This is very common in the field of biometrics and life sciences, where longitudinal studies frequently occur. It is clear that longitudinal designs lead to a more precise and deeper insights into the phenomenon under study. However, they pose problems from a theoretical point of view. Versions of LV models that are specially tailored to the analysis of longitudinal data are based on the assumption that the response variables depend, for instance, on a latent process corresponding to a sequence of continuous latent variables (see, e.g. Skrondal and Rabe-Hesketh, 2004) or on an unobservable Markov chain (see, e.g. Bartolucci et al., 2013). In this way, it is possible to account for time-constant and time-varying unobserved heterogeneity between subjects. Moreover, in longitudinal studies it may occur that only few subjects have complete data records, as individuals participating into the study typically leave it in advance. If this interruption depends on events associated with the outcome of interest, an informative drop-out arises that must be properly modeled. LV models for longitudinal data can also account for this aspect in a sensible way. This Special Section is intended to propose recent advances on LV models for longitudinal data and their applications to real-life studies in the biometrical domain. In the following, we provide a brief introduction to the articles included in this Special Section. The paper by Asar et al. (2016) analyzes data from an an ongoing cohort study on chronic kidney disease. An ad-hoc LV model for longitudinal data is proposed, where the fixed effects are modeled by a piece-wise linear function with three change-points and the random effects are expressed through the sum of a random intercept, a stationary stochastic process with Matérn correlation structure and measurement error. Parameter estimation is carried out through a maximum likelihood approach assuming, for the random effects, a multivariate Normal distribution and a multivariate t distribution, where the latter seems to be more appropriate for the case study considered. To assess the effectiveness of the proposal, the plug-in predictive distributions of the random effects given the data are studied

1 citations

Posted Content
TL;DR: A Bayesian inference approach for a class of latent Markov models, which does not account for individual covariates, and its version that includes such covariates in the measurement model is proposed.
Abstract: 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.

1 citations


Cited by
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TL;DR: A theme of the text is the use of artificial regressions for estimation, reference, and specification testing of nonlinear models, including diagnostic tests for parameter constancy, serial correlation, heteroscedasticity, and other types of mis-specification.
Abstract: Offering a unifying theoretical perspective not readily available in any other text, this innovative guide to econometrics uses simple geometrical arguments to develop students' intuitive understanding of basic and advanced topics, emphasizing throughout the practical applications of modern theory and nonlinear techniques of estimation. One theme of the text is the use of artificial regressions for estimation, reference, and specification testing of nonlinear models, including diagnostic tests for parameter constancy, serial correlation, heteroscedasticity, and other types of mis-specification. Explaining how estimates can be obtained and tests can be carried out, the authors go beyond a mere algebraic description to one that can be easily translated into the commands of a standard econometric software package. Covering an unprecedented range of problems with a consistent emphasis on those that arise in applied work, this accessible and coherent guide to the most vital topics in econometrics today is indispensable for advanced students of econometrics and students of statistics interested in regression and related topics. It will also suit practising econometricians who want to update their skills. Flexibly designed to accommodate a variety of course levels, it offers both complete coverage of the basic material and separate chapters on areas of specialized interest.

4,284 citations

Journal ArticleDOI
TL;DR: This work considers approximate Bayesian inference in a popular subset of structured additive regression models, latent Gaussian models, where the latent field is Gaussian, controlled by a few hyperparameters and with non‐Gaussian response variables and can directly compute very accurate approximations to the posterior marginals.
Abstract: Structured additive regression models are perhaps the most commonly used class of models in statistical applications. It includes, among others, (generalized) linear models, (generalized) additive models, smoothing spline models, state space models, semiparametric regression, spatial and spatiotemporal models, log-Gaussian Cox processes and geostatistical and geoadditive models. We consider approximate Bayesian inference in a popular subset of structured additive regression models, latent Gaussian models, where the latent field is Gaussian, controlled by a few hyperparameters and with non-Gaussian response variables. The posterior marginals are not available in closed form owing to the non-Gaussian response variables. For such models, Markov chain Monte Carlo methods can be implemented, but they are not without problems, in terms of both convergence and computational time. In some practical applications, the extent of these problems is such that Markov chain Monte Carlo sampling is simply not an appropriate tool for routine analysis. We show that, by using an integrated nested Laplace approximation and its simplified version, we can directly compute very accurate approximations to the posterior marginals. The main benefit of these approximations is computational: where Markov chain Monte Carlo algorithms need hours or days to run, our approximations provide more precise estimates in seconds or minutes. Another advantage with our approach is its generality, which makes it possible to perform Bayesian analysis in an automatic, streamlined way, and to compute model comparison criteria and various predictive measures so that models can be compared and the model under study can be challenged.

4,164 citations

Journal ArticleDOI

3,152 citations

BookDOI
10 May 2011
TL;DR: A Markov chain Monte Carlo based analysis of a multilevel model for functional MRI data and its applications in environmental epidemiology, educational research, and fisheries science are studied.
Abstract: Foreword Stephen P. Brooks, Andrew Gelman, Galin L. Jones, and Xiao-Li Meng Introduction to MCMC, Charles J. Geyer A short history of Markov chain Monte Carlo: Subjective recollections from in-complete data, Christian Robert and George Casella Reversible jump Markov chain Monte Carlo, Yanan Fan and Scott A. Sisson Optimal proposal distributions and adaptive MCMC, Jeffrey S. Rosenthal MCMC using Hamiltonian dynamics, Radford M. Neal Inference and Monitoring Convergence, Andrew Gelman and Kenneth Shirley Implementing MCMC: Estimating with confidence, James M. Flegal and Galin L. Jones Perfection within reach: Exact MCMC sampling, Radu V. Craiu and Xiao-Li Meng Spatial point processes, Mark Huber The data augmentation algorithm: Theory and methodology, James P. Hobert Importance sampling, simulated tempering and umbrella sampling, Charles J.Geyer Likelihood-free Markov chain Monte Carlo, Scott A. Sisson and Yanan Fan MCMC in the analysis of genetic data on related individuals, Elizabeth Thompson A Markov chain Monte Carlo based analysis of a multilevel model for functional MRI data, Brian Caffo, DuBois Bowman, Lynn Eberly, and Susan Spear Bassett Partially collapsed Gibbs sampling & path-adaptive Metropolis-Hastings in high-energy astrophysics, David van Dyk and Taeyoung Park Posterior exploration for computationally intensive forward models, Dave Higdon, C. Shane Reese, J. David Moulton, Jasper A. Vrugt and Colin Fox Statistical ecology, Ruth King Gaussian random field models for spatial data, Murali Haran Modeling preference changes via a hidden Markov item response theory model, Jong Hee Park Parallel Bayesian MCMC imputation for multiple distributed lag models: A case study in environmental epidemiology, Brian Caffo, Roger Peng, Francesca Dominici, Thomas A. Louis, and Scott Zeger MCMC for state space models, Paul Fearnhead MCMC in educational research, Roy Levy, Robert J. Mislevy, and John T. Behrens Applications of MCMC in fisheries science, Russell B. Millar Model comparison and simulation for hierarchical models: analyzing rural-urban migration in Thailand, Filiz Garip and Bruce Western

2,415 citations

Journal Article
TL;DR: A detailed review of the education sector in Australia as in the data provided by the 2006 edition of the OECD's annual publication, 'Education at a Glance' is presented in this paper.
Abstract: A detailed review of the education sector in Australia as in the data provided by the 2006 edition of the OECD's annual publication, 'Education at a Glance' is presented. While the data has shown that in almost all OECD countries educational attainment levels are on the rise, with countries showing impressive gains in university qualifications, it also reveals that a large of share of young people still do not complete secondary school, which remains a baseline for successful entry into the labour market.

2,141 citations