Handbook of Polytomous Item Response Theory Models

Michael Nering, Remo Ostini, Michael L. Nering, Remo Ostini, Michael Nering, Michael L. Nering, Remo Ostini

• Publisher: Routledge
• Year: 2011
• Print ISBN: 9780805859928
• eBook ISBN: 9781135168711
• Topic: Psychology
• Subtopic: Education General
• Index: Psychology

This comprehensive Handbook focuses on the most used polytomous item response theory (IRT) models. These models help us understand the interaction between examinees and test questions where the questions have various response categories. The book reviews all of the major models and includes discussions about how and where the models originated, conceptually and in practical terms. Diverse perspectives on how these models can best be evaluated are also provided. Practical applications provide a realistic account of the issues practitioners face using these models. Disparate elements of the book are linked through editorial sidebars that connect common ideas across chapters, compare and reconcile differences in terminology, and explain variations in mathematical notation. These sidebars help to demonstrate the commonalities that exist across the field. By assembling this critical information, the editors hope to inspire others to use polytomous IRT models in their own research so they too can achieve the type of improved measurement that such models can provide.

Part 1 examines the most commonly used polytomous IRT models, major issues that cut across these models, and a common notation for calculating functions for each model. An introduction to IRT software is also provided. Part 2 features distinct approaches to evaluating the effectiveness of polytomous IRT models in various measurement contexts. These chapters appraise evaluation procedures and fit tests and demonstrate how to implement these procedures using IRT software. The final section features groundbreaking applications. Here the goal is to provide solutions to technical problems to allow for the most effective use of these models in measuring educational, psychological, and social science abilities and traits. This section also addresses the major issues encountered when using polytomous IRT models in computerized adaptive testing. Equating test scores across different testing contexts is the focus of the last chapter. The various contexts include personality research, motor performance, health and quality of life indicators, attitudes, and educational achievement.

Featuring contributions from the leading authorities, this handbook will appeal to measurement researchers, practitioners, and students who want to apply polytomous IRT models to their own research. It will be of particular interest to education and psychology assessment specialists who develop and use tests and measures in their work, especially researchers in clinical, educational, personality, social, and health psychology. This book also serves as a supplementary text in graduate courses on educational measurement, psychometrics, or item response theory.

Part I
Development of Polytomous IRT Models

CHAPTER 1
New Perspectives and Applications

Remo Ostini

Healthy Communities Research Centre, University of Queensland

Michael L. Nering

Measured Progress

Polytomous item response theory (IRT) models are mathematical models used to help us understand the interaction between examinees and test questions where the test questions have various response categories. These test questions are not scored in a simple dichotomous manner (i.e., correct/incorrect); rather, they are scored in way that reflects the particular score category that an examinee has achieved, been classified into, or selected (e.g., a score point of 2 on an item that is scored from 0 to 4, or selecting “somewhat agree” on a survey).

Polytomous items have become omnipresent in the educational and psychological testing community because they offer a much richer testing experience for the examinee while also providing more psychometric information about the construct being measured. There are many terms used to describe polytomous items (e.g., constructed response items, survey items), and polytomous items can take on various forms (e.g., writing prompts, Likert type items). Essentially, polytomous IRT models can be used for any test question where there are several response categories available.

The development of measurement models that are specifically designed around polytomous items is complex, spans several decades, and involves a variety of researchers and perspectives. In this book we intend to tell the story behind the development of polytomous IRT models, explain how model evaluation can be done, and provide some concrete examples of work that can be done with polytomous IRT models. Our goal in this text is to give the reader a broad understanding of these models and how they might be used for research and operational purposes.

Who Is This Book For?

This book is intended for anyone that wants to learn more about polytomous IRT models. Many of the concepts discussed in this book are technical in nature, and will require an understanding of measurement theory and some familiarity with dichotomous IRT models. There are several excellent sources for learning more about measurement generally (Allen & Yen, 1979; Anastasi, 1988; Crocker & Algina, 1986; Cronbach, 1990) and dichotomous IRT models specifically (e.g., Embretson & Reise, 2000; Rogers, Swaminathan, & Hambleton, 1991). Throughout the book there are numerous references that are valuable resources for those interested in learning more about polytomous IRT.

The Approach of This Book and Its Goals

This handbook is designed to bring together the major polytomous IRT models in a way that helps both students and practitioners of social science measurement understand where these state-of-the-art models come from, how they work, and how they can be used. As Hambleton, van der Linden, and Wells (Chapter 2) point out, the handbook is not an exhaustive catalogue of all polytomous IRT models, but the most commonly used models are presented in a comprehensive manner.

It speaks to the maturation of this field that there are now models that appear to have fallen by the wayside despite what could be considered desirable functional properties. Rost’s (1988) successive intervals model might be an example of such a model in that very little research has been focused on it. Polytomous IRT also has its share of obscure models that served their purpose as the field was finding its feet but which have been supplanted by more flexible models (e.g., Andrich’s (1982) dispersion model has given way to the partial credit model) or by mathematically more tractable models (e.g., Samejima’s (1969) normal ogive model is more difficult to use than her logistic model).

Perhaps the most prominent model to not receive separate treatment in this handbook is the generalized partial credit model (GPCM; Muraki, 1992). Fortunately, the structure and functioning of the model are well covered in a number of places in this book, including Hambleton and colleagues’ survey of the major polytomous models (Chapter 2) and Kim, Harris, and Kolen’s exposition of equating methods (Chapter 11).

Rather than focus on an exhaustive coverage of available models, this handbook tries to make polytomous IRT more accessible to a wider range of potential users in two ways. First, providing material on the origins and development of the most influential models brings together the historical and conceptual setting for those models that are not easily found elsewhere. The appendix to Thissen, Cai, and Bock’s chapter (Chapter 3) is an example of previously unpublished material on the development context for the nominal model.

Second, this handbook addresses important issues around using the models, including the challenge of evaluating model functioning (Bock & Gibbons, Chapter 7; Glas, Chapter 8) and applying the models in computerized adaptive testing (CAT; Boyd, Dodd, & Choi, Chapter 10), equating test scores derived from polytomous models (Kim et al., Chapter 11), and using a polytomous IRT model to investigate examinee test-taking strategies (Huang & Mislevy, Chapter 9).

Part 1: Development

In this book we attempt to bring together a collection of different polytomous IRT models with the story of the development of each model told by the people whose work is most closely associated with the models. We begin with a chapter by Hambleton, van der Linden, and Wells (Chapter 2), which broadly outlines various influential polytomous models, introducing their mathematical form and providing some of the common historical setting for the models. Introducing a range of models in this consistent way forms a solid basis for delving into the more complex development and measurement issues addressed in later chapters. Hambleton and colleagues also introduce models that are not addressed in later model development chapters (e.g., generalized partial credit model, nonparametric IRT models) and touch on parameter estimation issues and other challenges facing the field.

Thissen and Cai (Chapter 3) provide a succinct introduction to the nominal categories item response model (often known in other places as the nominal response model). They neatly describe derivations and alternative parameterizations of the model as well as showing various applications of the model. Saving the best for last, Thissen and Cai provide a completely new parameterization for the nominal model. This new parameterization builds on 30 years of experience to represent the model in a manner that facilitates extensions of the model and simplifies the implementation of estimation algorithms for the model. The chapter closes by coming full circle with a special contribution by R. Darrell Bock, which provides previously unpublished insight into the background to t...

Table of contents

• Cover
• Half Title
• Title
• Copyright
• Contents
• Preface
• Contributors
• PART I Development of Polytomous IRT Models
• PART II Polytomous IRT Model Evaluation
• PART III Application of Polytomous IRT Models
• Index