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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.
Written especially for psychometricians, scale developers, and practitioners interested in applications of Bayesian estimation and model checking of item response theory (IRT) models, this book teaches you how to accomplish all of this with the SAS MCMC Procedure, Because of its tutorial structure, Bayesian Analysis of Item Response Theory Models Using SAS will be of immediate practical use to SAS users with some introductory background in IRT models and the Bayesian paradigm. Working through this book's examples, you will learn how to write the PROC MCMC programming code to estimate various simple and more complex IRT models, including the choice and specification of prior distributions, specification of the likelihood model, and interpretation of results. Specifically, you will learn PROC MCMC programming code for estimating particular models and ways to interpret results that illustrate convergence diagnostics and inferences for parameters, as well as results that can be used by scale developers—for example, the plotting of item response functions. In addition, you will learn how to compare competing IRT models for an application, as well as evaluate the fit of models with the use of posterior predictive model checking methods. Numerous programs for conducting these analyses are provided and annotated so that you can easily modify them for your applications.
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.
Drawing on the work of 75 internationally acclaimed experts in the field, Handbook of Item Response Theory, Three-Volume Set presents all major item response models, classical and modern statistical tools used in item response theory (IRT), and major areas of applications of IRT in educational and psychological testing, medical diagnosis of patient-reported outcomes, and marketing research. It also covers CRAN packages, WinBUGS, Bilog MG, Multilog, Parscale, IRTPRO, Mplus, GLLAMM, Latent Gold, and numerous other software tools. A full update of editor Wim J. van der Linden and Ronald K. Hambleton’s classic Handbook of Modern Item Response Theory, this handbook has been expanded from 28 chapters to 85 chapters in three volumes. The three volumes are thoroughly edited and cross-referenced, with uniform notation, format, and pedagogical principles across all chapters. Each chapter is self-contained and deals with the latest developments in IRT.
A Single Cohesive Framework of Tools and Procedures for Psychometrics and Assessment Bayesian Psychometric Modeling presents a unified Bayesian approach across traditionally separate families of psychometric models. It shows that Bayesian techniques, as alternatives to conventional approaches, offer distinct and profound advantages in achieving many goals of psychometrics. Adopting a Bayesian approach can aid in unifying seemingly disparate—and sometimes conflicting—ideas and activities in psychometrics. This book explains both how to perform psychometrics using Bayesian methods and why many of the activities in psychometrics align with Bayesian thinking. The first part of the book introduces foundational principles and statistical models, including conceptual issues, normal distribution models, Markov chain Monte Carlo estimation, and regression. Focusing more directly on psychometrics, the second part covers popular psychometric models, including classical test theory, factor analysis, item response theory, latent class analysis, and Bayesian networks. Throughout the book, procedures are illustrated using examples primarily from educational assessments. A supplementary website provides the datasets, WinBUGS code, R code, and Netica files used in the examples.
The predominant model checking method used in Bayesian item response theory (IRT) models has been the posterior predictive (PP) method. In recent years, two new Bayesian model checking methods have been proposed that may be used as alternatives to the PP method. We refer to these as the prior-predictive posterior simulation (PPPS) method of Dey et al. (1998), and the pivotal discrepancy measure (PDM) method of Johnson (2007). These methods have shown to be effective in other Bayesian models, but have never been implemented with Bayesian IRT models. It is of practical interest to see if either of these two new methods will perform better than the PP method in assessing aspects of fit in an IRT model setting. In this dissertation, we compared the effectiveness of the PPPS and PDM model checking methods with the PP method in evaluating person fit in two-parameter normal ogive (2PN) IRT models, and overall model goodness-of-fit in 2PN testlet models. Two simulation studies were performed. The first study explored the performance of each method (PP, PPPS, and PDM) in assessing person fit, or the goodness-of-fit of an individual's set of test answers with the assumed Bayesian 2PN IRT model. Several classical person fit measures were employed under each method. We also introduced using the sum of squared Bayesian latent residuals as a person fit measure. Four different types of person miss-fit were taken from the literature, and response data sets were simulated with certain examinee's responses following these violations. We found that for most of the measures, the PPPS and PDM methods outperformed the PP method in detecting the examinee's response patterns simulated to be aberrant under the model. In particular, the sum of squared Bayesian latent residuals showed to be a very effective measure under the PPPS method. The second simulation study compares the performance of the PP method and the PPPS method in assessing the overall goodness-of-fit of a Bayesian 2PN IRT model fitted to data generated under a Bayesian 2PN testlet model with equal variance across testlets. Under the PP method we used three goodness-of-fit measures based on biserial correlations that were previously employed for checking the goodness-of-fit of a three-parameter logistic (3PL) IRT model to 3PL testlet data. For use under the PPPS method, we introduced three new goodness-of-fit measures which are calculated from posterior values of the item discrimination parameters. Data sets were simulated under four different values of testlet variance, ranging from very low to fairly high. Looking at the detection rates under the PP method, we saw that the measures performed very poorly in detecting a lack of fit of the 2PN IRT model for all data values of testlet variance. The detection rates of the new measures under the PPPS method showed to be higher than those under the PP method. However, the measures under the PPPS method only showed descent power in detecting lack of fit for large values of data generating testlet variance.
First thorough treatment of multidimensional item response theory Description of methods is supported by numerous practical examples Describes procedures for multidimensional computerized adaptive testing