Presents both the 'how-to' and the 'why' of Item response theory (IRT). This book describes simple and more complex IRT models and shows how they are applied with the help of widely available software packages.

Symbols and Acronyms 1. Introduction to Measurement - Measurement - Some Measurement Issues - Item Response Theory - Classical Test Theory - Latent Class Analysis - Summary 2. The One-Parameter Model - Conceptual Development of the Rasch Model - The One-Parameter Model - The One-Parameter Logistic Model and the Rasch Model - Assumptions underlying the Model - An Empirical Data Set: The Mathematics Data Set - Conceptually Estimating an Individual's Location - Some Pragmatic Characteristics of Maximum Likelihood Estimates - The Standard Error of Estimate and Information - An Instrument's Estimation Capacity - Summary 3. Joint Maximum Likelihood Parameter Estimation - Joint Maximum Likelihood Estimation - Indeterminacy of Parameter Estimates - How Large a Calibration Sample? - Example: Application of the Rasch Model to the Mathematics Data, JMLE - Summary 4. Marginal Maximum Likelihood Parameter Estimation - Marginal Maximum Likelihood Estimation - Estimating an Individual's Location: Expected A Posteriori - Example: Application of the Rasch Model to the Mathematics Data, MMLE - Metric Transformation and the Total Characteristic Function - Summary 5. The Two-Parameter Model - Conceptual Development of the Two-Parameter Model - Information for the Two-Parameter Model - Conceptual Parameter Estimation for the 2PL Model - How Large a Calibration Sample? - Metric Transformation, 2PL Model - Example: Application of the 2PL Model to the Mathematics Data, MMLE - Information and Relative Efficiency - Summary 6. The Three-Parameter Model - Conceptual Development of the Three-Parameter Model - Additional Comments about the Pseudo-Guessing Parameter, Xⱼ - Conceptual Estimation for the 3PL Model - How Large a Calibration Sample? - Assessing Conditional Independence - Example: Application of the 3PL Model to the Mathematics Data, MMLE - Assessing Person Fit: Appropriateness Measurement - Information for the Three-Parameter Model - Metric Transformation, 3PL Model - Handling Missing Responses - Issues to Consider in Selecting among the 1PL, 2PL, and 3PL Models - Summary 7. Rasch Models for Ordered Polytomous Data - Conceptual Development of the Partial Credit Model - Conceptual Parameter Estimation of the PC Model - Example: Application of the PC Model to a Reasoning Ability Instrument, MMLE - The Rating Scale Model - Conceptual Estimation of the RS Model - Example: Application of the RS Model to an Attitudes toward Condom Scale, JMLE - How Large a Calibration Sample? - Information for the PC and RS Models - Metric Transformation, PC and RS Models - Summary 8. Non-Rasch Models for Ordered Polytomous Data - The Generalized Partial Credit Model - Example: Application of the GPC Model to a Reasoning Ability Instrument, MMLE - Conceptual Development of the Graded Response Model - How Large a Calibration Sample? - Example: Application of the GR Model to an Attitudes toward Condom Scale, MMLE - Information for Graded Data - Metric Transformation, GPC and GR Models - Summary 9. Models for Nominal Polytomous Data - Conceptual Development of the Nominal Response Model - How Large a Calibration Sample? - Example: Application of the NR Model to a Science Test, MMLE - Example: Mixed Model Calibration of the Science Test--NR and PC Models, MMLE - Example: NR and PC Mixed Model Calibration of the Science Test, Collapsed Options, MMLE - Information for the NR Model - Metric Transformation, NR Model - Conceptual Development of the Multiple-Choice Model - Example: Application of the MC Model to a Science Test, MMLE - Example: Application of the BS Model to a Science Test, MMLE - Summary 10. Models for Multidimensional Data - Conceptual Development of a Multidimensional IRT Model - Multidimensional Item Location and Discrimination - Item Vectors and Vector Graphs - The Multidimensional Three-Parameter Logistic Model - Assumptions of the MIRT Model - Estimation of the M2PL Model - Information for the M2PL Model - Indeterminacy in MIRT - Metric Transformation, M2PL Model - Example: Application of the M2PL Model, Normal-Ogive Harmonic Analysis Robust Method - Obtaining Person Location Estimates - Summary 11. Linking and Equating - Equating Defined - Equating: Data Collection Phase - Equating: Transformation Phase - Example: Application of the Total Characteristic Function Equating - Summary 12. Differential Item Functioning - Differential Item Functioning and Item Bias - Mantel–Haenszel Chi-Square - The TSW Likelihood Ratio Test - Logistic Regression - Example: DIF Analysis - Summary Appendix A. Maximum Likelihood Estimation of Person Locations - Estimating an Individual's Location: Empirical Maximum Likelihood Estimation - Estimating an Individual's Location: Newton's Method for MLE - Revisiting Zero Variance Binary Response Patterns Appendix B. Maximum Likelihood Estimation of Item Locations Appendix C. The Normal Ogive Models - Conceptual Development of the Normal Ogive Model - The Relationship between IRT Statistics and Traditional Item Analysis Indices - Relationship of the Two-Parameter Normal Ogive and Logistic Models - Extending the Two-Parameter Normal Ogive Model to a Multidimensional Space Appendix D. Computerized Adaptive Testing - A Brief History - Fixed-Branching Techniques - Variable-Branching Techniques - Advantages of Variable-Branching over Fixed-Branching Methods - IRT-Based Variable-Branching Adaptive Testing Algorithm Appendix E. Miscellanea - Linear Logistic Test Model (LLTM) - Using Principal Axis for Estimating Item Discrimination - Infinite Item Discrimination Parameter Estimates - Example: NOHARM Unidimensional Calibration - An Approximate Chi-Square Statistic for NOHARM - Mixture Models - Relative Efficiency, Monotonicity, and Information - FORTRAN Formats - Example: Mixed Model Calibration of the Science Test--NR and 2PL Models, MMLE - Example: Mixed Model Calibration of the Science Test--NR and GR Models, MMLE - Odds, Odds Ratios, and Logits - The Person Response Function - Linking: A Temperature Analogy Example - Should DIF Analyses Be Based on Latent Classes? - The Separation and Reliability Indices - Dependency in Traditional Item Statistics and Observed Scores References Author Index Subject Index

. - The main strength of the text is in the descriptions and elaborations of the common IRT models....De Ayala also covers fundamental relationships that exist between models, such as the relationships between the parameters of the nominal response model and the partial credit model. In addition, the chapters contain practical advice for sample sizes commonly used with each model and how to interpret the parameters. De Ayala also presents results as statistical indices and graphics for various examples across different contexts, which allows readers the ability to see how the models work from several different perspectives....Does a good job of introducing common estimation strategies employed in IRT software packages. Especially helpful are the illustrations de Ayala includes with the code from IRT software packages. --Psychometrika, 1/1/2009ƒƒ A must read for practitioners who use item response theory to calibrate test data. It also would serve as a tremendous resource for measurement researchers who daily navigate the circuitous paths of various IRT estimation software programs to analyze and understand their assessment data....Each of the 12 chapters is packed with annotated examples of how to use IRT estimation software and the subsequent output....The author does an excellent job of supplementing explanations of various models with calibration examples and output of multiple data sets using several different IRT calibration software programs including BILOG, MULTILOG, BIGSTEPS, and NOHARM....The book is more practitioner-oriented and applied than previous classic books that provide foundational understanding of IRT models and applications....Would be an excellent text for a graduate level IRT class in which the goal of the course would be to review dichotomous, polytomous, and multidimensional IRT models an how to estimate parameters in the various models using a variety of commercially available software....I would encourage all testing practitioners who work with various IRT models, as well as graduate students who plan to go into the measurement field, to seriously consider this book. It is an excellent resource book and one that provides the reader with insight into the rationale and application of the different IRT models. I applaud Dr. de Ayala for all the time and effort he has put into this book. He has clearly done the measurement field a great service. --Journal of Educational Measurement, 1/1/2009