Bayesian Item Response Modeling

1. Front Matter

   Pages I-XIV

   PDF

2. Introduction to Bayesian Response Modeling

   • Jean-Paul Fox

   Pages 1-29

3. Bayesian Hierarchical Response Modeling

   • Jean-Paul Fox

   Pages 31-44

4. Basic Elements of Bayesian Statistics

   • Jean-Paul Fox

   Pages 45-66

5. Estimation of Bayesian Item Response Models

   • Jean-Paul Fox

   Pages 67-106

6. Assessment of Bayesian Item Response Models

   • Jean-Paul Fox

   Pages 107-139

7. Multilevel Item Response Theory Models

   • Jean-Paul Fox

   Pages 141-191

8. Random Item Effects Models

   • Jean-Paul Fox

   Pages 193-225

9. Response Time Item Response Models

   • Jean-Paul Fox

   Pages 227-254

10. Randomized Item Response Models

    • Jean-Paul Fox

    Pages 255-288

11. Back Matter

    Pages 289-313

    PDF

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.

• Excel
• Item
• MCMC
• bayesian
• bayesian statistics
• hierarchical modeling
• item response theory
• mixed effects
• nonlinear modeling
• test theory

From the reviews:

“Item response theory is a general paradigm for the design and analysis of questionnaires measuring abilities and attitudes of individuals. … the book is written in a concise style and the technical level of the book is relatively high. … I believe this book makes an important contribution in summarizing much of the important literature in Bayesian IRT and I think it will lead to future books focusing on the use and interpretation of these models from a practitioner’s perspective.” (Jim Albert, Journal of the American Statistical Association, Vol. 106 (495), September, 2011)

“This book covers the parameter estimation of standard and extended IRT models using the Bayesian simulation based MCMC method. There are many Bayesian data analysis books, but this is the first book purely devoted to the Bayesian estimation of IRT models. … Overall, it is a good book for advanced learners to grasp the theoretical and technical detail of Bayesian MCMC estimation ofextended IRT models adapted to a specific measurement setting.” (Hong Jiao, Psychometrika, Vol. 76 (2), April, 2011)

“This book develops a comprehensive treatment of Bayesian item response modelling … . The book is mostly self-contained. … Each chapter ends with a section of carefully thought-out exercises covering both the mathematical aspects of the models and their application to the analysis of interesting real-life data. … This book will equally cater for those users who just want to apply the models to analyze their data, and more technical users willing to get a deeper understanding of the models … .” (Eduardo Gutiérrez-Peña, International Statistical Review, Vol. 79 (3), 2011)

• , Department of Research Methodology, Meas, University of Twente, Enschede, Netherlands

  Jean-Paul Fox

Jean-Paul Fox is Associate Professor of Measurement and Data Analysis, University of Twente, The Netherlands. His main research activities are in several areas of Bayesian response modeling. Dr. Fox has published numerous articles in the areas of Bayesian item response analysis, statistical methods for analyzing multivariate categorical response data, and nonlinear mixed effects models.

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