Item Response Theory

This is a highly accessible, comprehensive introduction to item response theory (IRT) models and their use in various aspects of assessment/testing. The book employs a mixture of graphics and simulated data sets to ease the reader into the material and covers the basics required to obtain a solid grounding in IRT. Written in an easily accessible way that assumes little mathematical knowledge, Carlson presents detailed descriptions of several commonly used IRT models, including those for items scored on a two-point (dichotomous) scale such as correct/incorrect, and those scored on multiple-point (polytomous) scales, such as degrees of correctness. One chapter describes a model in-depth and is followed by a chapter of instructions and illustrations showing how to apply the models to the reader’s own work. This book is an essential text for instructors and higher level undergraduate and postgraduate students of statistics, psychometrics, and measurement theory across the behavioral and social sciences, as well as testing professionals.

Introduction to measurement -- The one-parameter model -- Joint maximum likelihood parameter estimation -- Marginal maximum likelihood parameter estimation -- The two-parameter model -- The three-parameter model -- Rasch models for ordered polytomous data -- Non-Rasch models for ordered polytomous data -- Models for nominal polytomous data -- Models for multidimensional data -- Linking and equating -- Differential item functioning -- Multilevel IRT models.

First thorough treatment of multidimensional item response theory Description of methods is supported by numerous practical examples Describes procedures for multidimensional computerized adaptive testing

By using familiar concepts from classical measurement methods and basic statistics, this book introduces the basics of item response theory (IRT) and explains the application of IRT methods to problems in test construction, identification of potentially biased test items, test equating and computerized-adaptive testing. The book also includes a thorough discussion of alternative procedures for estimating IRT parameters and concludes with an exploration of new directions in IRT research and development.

In the decade of the 1970s, item response theory became the dominant topic for study by measurement specialists. But, the genesis of item response theory (IRT) can be traced back to the mid-thirties and early forties. In fact, the term "Item Characteristic Curve," which is one of the main IRT concepts, can be attributed to Ledyard Tucker in 1946. Despite these early research efforts, interest in item response theory lay dormant until the late 1960s and took a backseat to the emerging development of strong true score theory. While true score theory developed rapidly and drew the attention of leading psychometricians, the problems and weaknesses inherent in its formulation began to raise concerns. Such problems as the lack of invariance of item parameters across examinee groups, and the inadequacy of classical test procedures to detect item bias or to provide a sound basis for measurement in "tailored testing," gave rise to a resurgence of interest in item response theory. Impetus for the development of item response theory as we now know it was provided by Frederic M. Lord through his pioneering works (Lord, 1952; 1953a, 1953b). The progress in the fifties was painstakingly slow due to the mathematical complexity of the topic and the nonexistence of computer programs.

Item response theory (IRT) is widely used in education and psychology and is expanding its applications to other social science areas, medical research, and business as well. Using R for Item Response Theory Model Applications is a practical guide for students, instructors, practitioners, and applied researchers who want to learn how to properly use R IRT packages to perform IRT model calibrations with their own data. This book provides practical line-by-line descriptions of how to use R IRT packages for various IRT models. The scope and coverage of the modeling in the book covers almost all models used in practice and in popular research, including: dichotomous response modeling polytomous response modeling mixed format data modeling concurrent multiple group modeling fixed item parameter calibration modelling with latent regression to include person-level covariate(s) simple structure, or between-item, multidimensional modeling cross-loading, or within-item, multidimensional modeling high-dimensional modeling bifactor modeling testlet modeling two-tier modeling For beginners, this book provides a straightforward guide to learn how to use R for IRT applications. For more intermediate learners of IRT or users of R, this book will serve as a great time-saving tool for learning how to create the proper syntax, fit the various models, evaluate the models, and interpret the output using popular R IRT packages.

Item response theory has become an essential component in the toolkit of every researcher in the behavioral sciences. It provides a powerful means to study individual responses to a variety of stimuli, and the methodology has been extended and developed to cover many different models of interaction. This volume presents a wide-ranging handbook to item response theory - and its applications to educational and psychological testing. It will serve as both an introduction to the subject and also as a comprehensive reference volume for practitioners and researchers. It is organized into six major sections: the nominal categories model, models for response time or multiple attempts on items, models for multiple abilities or cognitive components, nonparametric models, models for nonmonotone items, and models with special assumptions. Each chapter in the book has been written by an expert of that particular topic, and the chapters have been carefully edited to ensure that a uniform style of notation and presentation is used throughout. As a result, all researchers whose work uses item response theory will find this an indispensable companion to their work and it will be the subject's reference volume for many years to come.

This graduate-level textbook is a tutorial for item response theory that covers both the basics of item response theory and the use of R for preparing graphical presentation in writings about the theory. Item response theory has become one of the most powerful tools used in test construction, yet one of the barriers to learning and applying it is the considerable amount of sophisticated computational effort required to illustrate even the simplest concepts. This text provides the reader access to the basic concepts of item response theory freed of the tedious underlying calculations. It is intended for those who possess limited knowledge of educational measurement and psychometrics. Rather than presenting the full scope of item response theory, this textbook is concise and practical and presents basic concepts without becoming enmeshed in underlying mathematical and computational complexities. Clearly written text and succinct R code allow anyone familiar with statistical concepts to explore and apply item response theory in a practical way. In addition to students of educational measurement, this text will be valuable to measurement specialists working in testing programs at any level and who need an understanding of item response theory in order to evaluate its potential in their settings.