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.

Estimation and Inference in Econometrics

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.

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Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations

Statistical Analysis with Missing Data

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

Handbook of Markov Chain Monte Carlo

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.

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Education at a Glance

I review a class of models for longitudinal data, showing how it may be applied in a meaningful way for the analysis of data collected by the administration of a series of items finalized to educational or psychological measurement In this class of models, the unobserved individual characteristics of interest are represented by a sequence of discrete latent variables, which follows a Markov chain Inferential problems involved in the application of these models are discussed considering, in particular, maximum likelihood estimation based on the Expectation-Maximization algorithm, model selection, and hypothesis testing Most of these problems are common to hidden Markov models for time-series data The approach is illustrated by different applications in education and psychology

https://www.springer.com/cda/content/document/cda_downloaddocument/9783319066912-c2.pdf?SGWID=0-0-45-1468407-p176723958

Modeling Longitudinal Data by Latent Markov Models with Application to Educational and Psychological Measurement

We propose a structural equation model, which reduces to a multidimensional latent class item response theory model, for the analysis of binary item responses with non-ignorable missingness. The missingness mechanism is driven by two sets of latent variables: one describing the propensity to respond and the other referred to the abilities measured by the test items. These latent variables are assumed to have a discrete distribution, so as to reduce the number of parametric assumptions regarding the latent structure of the model. Individual covariates may also be included through a multinomial logistic parametrization of the probabilities of each support point of the distribution of the latent variables. Given the discrete nature of this distribution, the proposed model is efficiently estimated by the Expectation-Maximization algorithm. A simulation study is performed to evaluate the finite sample properties of the parameter estimates. Moreover, an application is illustrated to data coming from a Students' Entry Test for the admission to some university courses.

A multidimensional latent class IRT model for non-ignorable missing responses

The work describes a multidimensional latent class Rasch model and its application to data about the measurement of some aspects of Health-related Quality of Life and Anxiety and Depression in oncological patients

A multidimensional latent class Rasch model for the assessment of the Health-related Quality of Life

We introduce a model for categorical panel data which is tailored to the dynamic evaluation of the impact of job training programs. The model may be seen as an extension of the dynamic logit model in which unobserved heterogeneity between subjects is taken into account by the introduction of a discrete latent variable. For the estimation of the model parameters we use an EM algorithm and we compute standard errors on the basis of the numerical derivative of the score vector of the complete data log-likelihood. The approach is illustrated through the analysis of a dataset containing the work histories of the employees of the private firms of the province of Milan between 2003 and 2005, some of whom attended job training programs supported by the European Social Fund.

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Impact Evaluation of Job Training Programs by a Latent Variable Model

The evaluation of nursing homes and the assessment of the quality of the health care provided to their patients are usually based on the administration of questionnaires made of a large number of polytomous items. In applications involving data collected by questionnaires of this type, the Latent Class (LC) model represents a useful tool for classifying subjects in homogenous groups. In this paper, we propose an algorithm for item selection, which is based on the LC model. The proposed algorithm is aimed at finding the smallest subset of items which provides an amount of information close to that of the initial set. The method sequentially eliminates the items that do not significantly change the classification of the subjects in the sample with respect to the classification based on the full set of items. The LC model, and then the item selection algorithm, may be also used with missing responses that are dealt with assuming a form of latent ignorability. The potentialities of the proposed approach are illustrated through an application to a nursing home dataset collected within the ULISSE project, which concerns the quality-of-life of elderly patients hosted in Italian nursing homes. The dataset presents several issues, such as missing responses and a very large number of items included in the questionnaire.

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Francesco Bartolucci

Papers

Modeling Longitudinal Data by Latent Markov Models with Application to Educational and Psychological Measurement

A multidimensional latent class IRT model for non-ignorable missing responses

A multidimensional latent class Rasch model for the assessment of the Health-related Quality of Life

Impact Evaluation of Job Training Programs by a Latent Variable Model

Item Selection by an Extended Latent Class Model: An Application to Nursing Homes Evaluation