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This book describes the new generation of discrete choice methods, focusing on the many advances that are made possible by simulation. Researchers use these statistical methods to examine the choices that consumers, households, firms, and other agents make. Each of the major models is covered: logit, generalized extreme value, or GEV (including nested and cross-nested logits), probit, and mixed logit, plus a variety of specifications that build on these basics. Simulation-assisted estimation procedures are investigated and compared, including maximum stimulated likelihood, method of simulated moments, and method of simulated scores. Procedures for drawing from densities are described, including variance reduction techniques such as anithetics and Halton draws. Recent advances in Bayesian procedures are explored, including the use of the Metropolis-Hastings algorithm and its variant Gibbs sampling. The second edition adds chapters on endogeneity and expectation-maximization (EM) algorithms. No other book incorporates all these fields, which have arisen in the past 25 years. The procedures are applicable in many fields, including energy, transportation, environmental studies, health, labor, and marketing.
Drawing on the work of internationally acclaimed experts in the field, Handbook of Item Response Theory, Volume 3: Applications presents applications of item response theory to practical testing problems. While item response theory may be known primarily for its advances in theoretical modeling of responses to test items, equal progress has been made in its providing innovative solutions to daily testing problems. This third volume in a three-volume set highlights the major applications. Specifically, this volume covers applications to test item calibration, item analysis, model fit checking, test-score interpretation, optimal test design, adaptive testing, standard setting, and forensic analyses of response data. It describes advances in testing in areas such as large-scale educational assessment, psychological testing, health measurement, and measurement of change. In addition, it extensively reviews computer programs available to run any of the models and applications in Volume One and Three. Features Includes contributions from internationally acclaimed experts with a history of advancing applications of item response theory Provides extensive cross-referencing and common notation across all chapters in this three-volume set Underscores the importance of treating each application in a statistically rigorous way Reviews major computer programs for item response theory analyses and applications. Wim J. van der Linden is a distinguished scientist and director of research and innovation at Pacific Metrics Corporation. Dr. van der Linden is also a professor emeritus of measurement and data analysis at the University of Twente. His research interests include test theory, adaptive testing, optimal test assembly, parameter linking, test equating, and response-time modeling as well as decision theory and its applications to problems of educational decision making.
The modeling of item response data is governed by item response theory, also referred to as modern test theory. The eld of inquiry of item response theory has become very large and shows the enormous progress that has been made. The mainstream literature is focused on frequentist statistical methods for - timating model parameters and evaluating model t. However, the Bayesian methodology has shown great potential, particularly for making further - provements in the statistical modeling process. The Bayesian approach has two important features that make it attractive for modeling item response data. First, it enables the possibility of incorpor- ing nondata information beyond the observed responses into the analysis. The Bayesian methodology is also very clear about how additional information can be used. Second, the Bayesian approach comes with powerful simulation-based estimation methods. These methods make it possible to handle all kinds of priors and data-generating models. One of my motives for writing this book is to give an introduction to the Bayesian methodology for modeling and analyzing item response data. A Bayesian counterpart is presented to the many popular item response theory books (e.g., Baker and Kim 2004; De Boeck and Wilson, 2004; Hambleton and Swaminathan, 1985; van der Linden and Hambleton, 1997) that are mainly or completely focused on frequentist methods. The usefulness of the Bayesian methodology is illustrated by discussing and applying a range of Bayesian item response models.
This open access book presents a large number of innovations in the world of operational testing. It brings together different but related areas and provides insight in their possibilities, their advantages and drawbacks. The book not only addresses improvements in the quality of educational measurement, innovations in (inter)national large scale assessments, but also several advances in psychometrics and improvements in computerized adaptive testing, and it also offers examples on the impact of new technology in assessment. Due to its nature, the book will appeal to a broad audience within the educational measurement community. It contributes to both theoretical knowledge and also pays attention to practical implementation of innovations in testing technology.
Bayesian statistics directed towards mainstream statistics. How to infer scientific, medical, and social conclusions from numerical data.
Bayesian Inference of State Space Models: Kalman Filtering and Beyond offers a comprehensive introduction to Bayesian estimation and forecasting for state space models. The celebrated Kalman filter, with its numerous extensions, takes centre stage in the book. Univariate and multivariate models, linear Gaussian, non-linear and non-Gaussian models are discussed with applications to signal processing, environmetrics, economics and systems engineering. Over the past years there has been a growing literature on Bayesian inference of state space models, focusing on multivariate models as well as on non-linear and non-Gaussian models. The availability of time series data in many fields of science and industry on the one hand, and the development of low-cost computational capabilities on the other, have resulted in a wealth of statistical methods aimed at parameter estimation and forecasting. This book brings together many of these methods, presenting an accessible and comprehensive introduction to state space models. A number of data sets from different disciplines are used to illustrate the methods and show how they are applied in practice. The R package BTSA, created for the book, includes many of the algorithms and examples presented. The book is essentially self-contained and includes a chapter summarising the prerequisites in undergraduate linear algebra, probability and statistics. An up-to-date and complete account of state space methods, illustrated by real-life data sets and R code, this textbook will appeal to a wide range of students and scientists, notably in the disciplines of statistics, systems engineering, signal processing, data science, finance and econometrics. With numerous exercises in each chapter, and prerequisite knowledge conveniently recalled, it is suitable for upper undergraduate and graduate courses.
Bayesian Statistical Methods provides data scientists with the foundational and computational tools needed to carry out a Bayesian analysis. This book focuses on Bayesian methods applied routinely in practice including multiple linear regression, mixed effects models and generalized linear models (GLM). The authors include many examples with complete R code and comparisons with analogous frequentist procedures. In addition to the basic concepts of Bayesian inferential methods, the book covers many general topics: Advice on selecting prior distributions Computational methods including Markov chain Monte Carlo (MCMC) Model-comparison and goodness-of-fit measures, including sensitivity to priors Frequentist properties of Bayesian methods Case studies covering advanced topics illustrate the flexibility of the Bayesian approach: Semiparametric regression Handling of missing data using predictive distributions Priors for high-dimensional regression models Computational techniques for large datasets Spatial data analysis The advanced topics are presented with sufficient conceptual depth that the reader will be able to carry out such analysis and argue the relative merits of Bayesian and classical methods. A repository of R code, motivating data sets, and complete data analyses are available on the book’s website. Brian J. Reich, Associate Professor of Statistics at North Carolina State University, is currently the editor-in-chief of the Journal of Agricultural, Biological, and Environmental Statistics and was awarded the LeRoy & Elva Martin Teaching Award. Sujit K. Ghosh, Professor of Statistics at North Carolina State University, has over 22 years of research and teaching experience in conducting Bayesian analyses, received the Cavell Brownie mentoring award, and served as the Deputy Director at the Statistical and Applied Mathematical Sciences Institute.