The Theory and Practice of Item Response Theory

“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….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 (on the first edition)


“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 (on the first edition)


“The second edition of the IRT 'bible' is now even more accessible and useful for psychometricians and educational measurement specialists who are new to IRT or want to upgrade their knowledge of the field. It expands on the first edition in meaningful ways, primarily with regard to the implementation of IRT. Virtually every chapter has been expanded with examples of IRT analyses using R, SAS, and/or flexMIRT. A very helpful new chapter covers multilevel IRT models, and new appendices cover the LLTM and mixture Rasch models and discuss contemporary model fit indices and other recent topics. I have been using the first edition in my advanced measurement class since it was first published and it has been well received by my advanced undergraduates and graduate students; the new material in the second edition makes the book even better. In addition, this book will be very informative to measurement specialists—especially those who are not mathematically sophisticated—so that they can produce instruments that benefit from the enhanced measurement power of IRT.”

—David J. Weiss, PhD, Department of Psychology, University of Minnesota


“This is the most comprehensive and accessible text on IRT. De Ayala does a remarkable job of clearly describing fundamental IRT concepts, basic models, and even advanced models. The text's explanations do not heavily rely on equations; instead, de Ayala takes a conceptual approach and often utilizes graphs to illustrate key ideas. The second edition is up to date on the most frequently applied models and estimation procedures. It includes applied examples using popular IRT software, including R. I highly recommend this book for graduate-level courses focusing on measurement, psychometrics, and IRT, and as a guide for researchers using IRT.”

—Ojmarrh Mitchell, PhD, School of Criminology and Criminal Justice, Arizona State University


“I love this book, and find it quite readable. What sets this text apart are its extensive exposition of technical details related to models and estimation and its detailed explanations of concepts. For example, I had never seen an author decompose the partial credit model and show piece-by-piece computation of the probabilities, which de Ayala does very well. This text is a great contribution to the field of IRT that will be invaluable for both class and personal use.”

—Karen M. Schmidt, PhD, Department of Psychology, University of Virginia


“An excellent treatment of IRT that combines a clear exposition of theoretical concepts with applied examples that are relevant and useful.”

—Larry R. Price, PhD, College of Education, Texas State University