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

We propose a criterion for selecting a capture-recapture model for closed populations which follows the basic idea of the Focused Information Criterion (FIC) of Claeskens and Hjort (2003). The proposed criterion aims at selecting the model which, among the available models, leads to the smallest Mean Squared Error (MSE) of the resulting estimator of the population size and is based on an index which, up to a constant term, is equal to the asymptotic MSE of the estimator. Two alternative approaches to estimate this FIC index are proposed. We also deal with multimodel inference; in this case, the population size is estimated by using a weighted average of the estimates coming from difierent models, with weights chosen as to minimize the MSE of the resulting estimator. The proposed model selection approach is compared with more common approaches through a series of simulations performed along the same lines as Stanley and Burnham (1998). It is also illustrated by an application based on a dataset coming from a live-trapping experiment.

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Focused Information Criterion for Capture-Recapture Models for Closed Populations

https://u-pad.unimc.it/bitstream/11393/123407/1/CSDA2012.pdf

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

With reference to a questionnaire aimed at assessing the performance of Italian nursing homes on the basis of the health conditions of their patients, we investigate two relevant issues: dimensionality of the latent structure and discriminating power of the items composing the questionnaire. The approach is based on a multidimensional item response theory model, which assumes a two-parameter logistic parameterization for the response probabilities. This model represents the health status of a patient by latent variables having a discrete distribution and, therefore, it may be seen as a constrained version of the latent class model. On the basis of the adopted model, we implement a hierarchical clustering algorithm aimed at assessing the actual number of dimensions measured by the questionnaire. These dimensions correspond to disjoint groups of items. Once the number of dimensions is selected, we also study the discriminating power of every item, so that it is possible to select the subset of these items which is able to provide an amount of information close to that of the full set. We illustrate the proposed approach on the basis of the data collected on 1,051 elderly people hosted in a sample of Italian nursing homes.

Dimensionality of the Latent Structure and Item Selection Via Latent Class Multidimensional IRT Models

Objectives We investigate about the differences in birthweight between firstand second-borns, evaluating the impact of changes in pregnancy (e.g., gestational age), demographic (e.g., age), and social (e.g., education level, marital status) maternal characteristics. Data and Methods All analyses are performed on data collected in Umbria (Italy) taking into account a set of 792 women who delivered twice from 2005 to 2008. Firstly, we use a univariate paired t-test for the comparison between weights of first- and second-borns. Secondly, we use linear and nonlinear regression approaches in order to: (i) evaluate the effect of demographic and social maternal characteristics and (ii) predict the odds-ratio of low and high birthweight infants, respectively. Results We find that the birthweight of second-borns is significantly higher than that of first-borns. Statistically significant effects are related with a longer gestational age, an increased number of visits during the pregnancy, and the gender of infants. On the other hand, we do not observe any significant effect related with mother’s age and with other characteristics of interest.

Differences in birth-weight outcomes: A longitudinal study based on siblings

We illustrate the R package cquad for conditional maximum likelihood estimation of the quadratic exponential (QE) model proposed by Bartolucci and Nigro (2010) for the analysis of binary panel data. The package also allows us to estimate certain modified versions of the QE model, which are based on alternative parametrizations, and it includes a function for the pseudo-conditional likelihood estimation of the dynamic logit model, as proposed by Bartolucci and Nigro (2012). We also illustrate a reduced version of this package that is available in Stata. The use of the main functions of this package is based on examples using labor market data.

Francesco Bartolucci

Papers

Focused Information Criterion for Capture-Recapture Models for Closed Populations

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

Dimensionality of the Latent Structure and Item Selection Via Latent Class Multidimensional IRT Models

Differences in birth-weight outcomes: A longitudinal study based on siblings

cquad: An R and Stata Package for Conditional Maximum Likelihood Estimation of Dynamic Binary Panel Data Models