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

Overview on Latent Markov Modeling Introduction Literature review on latent Markov models Alternative approaches Example datasets Background on Latent Variable and Markov Chain Models Introduction Latent variable models Expectation-Maximization algorithm Standard errors Latent class model Selection of the number of latent classes Applications Markov chain model for longitudinal data Applications Basic Latent Markov Model Introduction Univariate formulation Multivariate formulation Model identifiability Maximum likelihood estimation Selection of the number of latent states Applications Constrained Latent Markov Models Introduction Constraints on the measurement model Constraints on the latent model Maximum likelihood estimation Model selection and hypothesis testing Applications Including Individual Covariates and Relaxing Basic Model Assumptions Introduction Notation Covariates in the measurement model Covariates in the latent model Interpretation of the resulting models Maximum likelihood estimation Observed information matrix, identifiability, and standard errors Relaxing local independence Higher order extensions Applications Including Random Effects and Extension to Multilevel Data Introduction Random-effects formulation Maximum likelihood estimation Multilevel formulation Application to the student math achievement dataset Advanced Topics about Latent Markov Modeling Introduction Dealing with continuous response variables Dealing with missing responses Additional computational issues Decoding and forecasting Selection of the number of latent states Bayesian Latent Markov Models Introduction Prior distributions Bayesian inference via reversible jump Alternative sampling Application to the labor market dataset Appendix: Software List of Main Symbols Bibliography Index

Latent Markov Models for Longitudinal Data

For the analysis of multivariate categorical longitudinal data, we propose an extension of the dynamic logit model. The resulting model is based on a marginal parameterization of the conditional distribution of each vector of response variables given the covariates, the lagged response variables, and a set of subject-specific parameters for the unobserved heterogeneity. The latter ones are assumed to follow a first-order Markov chain. For the maximum likelihood estimation of the model parameters, we outline an EM algorithm. The data analysis approach based on the proposed model is illustrated by a simulation study and an application to a dataset, which derives from the Panel Study on Income Dynamics and concerns fertility and female participation to the labor market.

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A Multivariate Extension of the Dynamic Logit Model for Longitudinal Data Based on a Latent Markov Heterogeneity Structure

Nowadays, practitioners extensively apply quick and reliable scales of user satisfaction as part of their user experience analyses to obtain well-founded measures of user satisfaction within time and budget constraints. However, in the human–computer interaction literature the relationship between the outcomes of standardized satisfaction scales and the amount of product usage has been only marginally explored. The few studies that have investigated this relationship have typically shown that users who have interacted more with a product have higher satisfaction. The purpose of this article was to systematically analyze the variation in outcomes of three standardized user satisfaction scales (SUS, UMUX, UMUX-LITE) when completed by users who had spent different amounts of time with a website. In two studies, the amount of interaction was manipulated to assess its effect on user satisfaction. Measurements of the three scales were strongly correlated and their outcomes were significantly affected by the amo...

Assessing User Satisfaction in the Era of User Experience: Comparison of the SUS, UMUX, and UMUX-LITE as a Function of Product Experience

We illustrate a class of multidimensional item response theory models in which the items are allowed to have different discriminating power and the latent traits are represented through a vector having a discrete distribution. We also show how the hypothesis of unidimensionality may be tested against a specific bidimensional alternative by using a likelihood ratio statistic between two nested models in this class. For this aim, we also derive an asymptotically equivalent Wald test statistic which is faster to compute. Moreover, we propose a hierarchical clustering algorithm which can be used, when the dimensionality of the latent structure is completely unknown, for dividing items into groups referred to different latent traits. The approach is illustrated through a simulation study and an application to a dataset collected within the National Assessment of Educational Progress, 1996.

A class of multidimensional IRT models for testing unidimensionality and clustering items

We extend Bergsma and Rudas (2002)'s hierarchical complete marginal parameterization to allow for logits and higher order effects of global and continu- ation type which may be more suitable with ordinal data. We introduce a general definition of marginal interaction parameters and show that this parameterization constitutes a link function so that linear models defined by equality and inequality constraints may be fitted and tested by extending the methods of Colombi and Forcina (2001). Computation and asymptotic properties of maximum likelihood estimators are discussed, and the asymptotic distribution of the likelihood ratio test is derived.

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Francesco Bartolucci

Papers

Latent Markov Models for Longitudinal Data

A Multivariate Extension of the Dynamic Logit Model for Longitudinal Data Based on a Latent Markov Heterogeneity Structure

Assessing User Satisfaction in the Era of User Experience: Comparison of the SUS, UMUX, and UMUX-LITE as a Function of Product Experience

A class of multidimensional IRT models for testing unidimensionality and clustering items

An extended class of marginal link functions for modelling contingency tables by equality and inequality constraints