Handbook of Item Response Theory: Three Volume Set, 1st Edition (Paperback) book cover

Handbook of Item Response Theory

Three Volume Set, 1st Edition

Edited by Wim J. van der Linden

Chapman and Hall/CRC

1,500 pages

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Drawing on the work of 75 internationally acclaimed experts in the field, Handbook of Item Response Theory, Three-Volume Set presents all major item response models, classical and modern statistical tools used in item response theory (IRT), and major areas of applications of IRT in educational and psychological testing, medical diagnosis of patient-reported outcomes, and marketing research. It also covers CRAN packages, WinBUGS, Bilog MG, Multilog, Parscale, IRTPRO, Mplus, GLLAMM, Latent Gold, and numerous other software tools.

A full update of editor Wim J. van der Linden and Ronald K. Hambleton’s classic Handbook of Modern Item Response Theory, this handbook has been expanded from 28 chapters to 85 chapters in three volumes. The three volumes are thoroughly edited and cross-referenced, with uniform notation, format, and pedagogical principles across all chapters. Each chapter is self-contained and deals with the latest developments in IRT.

Table of Contents



Wim J. van der Linden

Dichotomous Models

Unidimensional Logistic Models

Wim J. van der Linden

Rasch Model

Matthias von Davier

Nominal and Ordinal Models

Nominal Categories Models

David Thissen and Li Cai

Rasch Rating Scale Model

David Andrich

Graded Response Models

Fumiko Samejima

Partial Credit Model

Geoff N. Masters

Generalized Partial Credit Model

Eiji Muraki and Mari Muraki

Sequential Models for Ordered Responses

Gerhard Tutz

Models for Continuous Responses

Gideon J. Mellenbergh

Multidimensional and Multicomponent Models

Normal-Ogive Multidimensional Models

Hariharan Swaminathan and H. Jane Rogers

Logistic Multidimensional Models

Mark D. Reckase

Linear Logistic Models

Rianne Janssen

Multicomponent Models

Susan E. Embretson

Models for Response Times

Poisson and Gamma Models for Reading Speed and Error

Margo G. H. Jansen

Lognormal Response-Time Model

Wim J. van der Linden

Diffusion-Based Response-Time Models

Francis Tuerlinckx, Dylan Molenaar, and Han L. J. van der Maas

Nonparametric Models

Mokken Models

Klaas Sijtsma and Ivo W. Molenaar

Bayesian Nonparametric Response Models

George Karabatsos

Functional Approaches to Modeling Response Data

James Ramsay

Models for Nonmonotone Items

Hyperbolic Cosine Model for Unfolding Responses

David Andrich

Generalized Graded Unfolding Model

James S. Roberts

Hierarchical Response Models

Logistic Mixture-Distribution Response Models

Matthias von Davier and Jürgen Rost

Multilevel Response Models with Covariates and Multiple Groups

Jean-Paul Fox and Cees A. W. Glas

Two-Tier Item Factor Analysis Modeling

Li Cai

Item-Family Models

Cees A. W. Glas, Wim J. van der Linden, and Hanneke Geerlings

Hierarchical Rater Models

Jodi M. Casabianca, Brian W. Junker, and Richard J. Patz

Randomized Response Models for Sensitive Measurements

Jean-Paul Fox

Joint Hierarchical Modeling of Responses and Response Times

Wim J. van der Linden and Jean-Paul Fox

Generalized Modeling Approaches

Generalized Linear Latent and Mixed Modeling

Sophia Rabe-Hesketh and Anders Skrondal

Multidimensional, Multilevel, and Multi-Timepoint Item Response Modeling

Bengt Muthén and Tihomir Asparouhov

Mixed-Coefficients Multinomial Logit Models

Raymond. J. Adams, Mark R. Wilson, and Margaret L. Wu

Explanatory Response Models

Paul De Boeck and Mark R. Wilson


Basic Tools

Logit, Probit, and Other Response Functions

James H. Albert

Discrete Distributions

Jodi M. Casabianca and Brian W. Junker

Multivariate Normal Distribution

Jodi M. Casabianca and Brian W. Junker

Exponential Family Distributions Relevant to IRT

Shelby J. Haberman

Loglinear Models for Observed-Score Distributions

Tim Moses

Distributions of Sums of Nonidentical Random Variables

Wim J. van der Linden

Information Theory and Its Application to Testing

Hua-Hua Chang, Chun Wang, and Zhiliang Ying

Modeling Issues

Identification of Item Response Theory Models

Ernesto San Martín

Models with Nuisance and Incidental Parameters

Shelby J. Haberman

Missing Responses in Item Response Modeling

Robert J. Mislevy

Parameter Estimation

Maximum-Likelihood Estimation

Cees A. W. Glas

Expectation Maximization Algorithm and Extensions

Murray Aitkin

Bayesian Estimation

Matthew S. Johnson and Sandip Sinharay

Variational Approximation Methods

Frank Rijmen, Minjeong Jeon, and Sophia Rabe-Hesketh

Markov ChainMonte Carlo for Item Response Models

Brian W. Junker, Richard J. Patz, and Nathan M. VanHoudnos

Statistical Optimal Design Theory

Heinz Holling and Rainer Schwabe

Model Fit and Comparison

Frequentist Model-Fit Tests

Cees A. W. Glas

Information Criteria

Allan S. Cohen and Sun-Joo Cho

Bayesian Model Fit and Model Comparison

Sandip Sinharay

Model Fit with Residual Analyses

Craig S. Wells and Ronald K. Hambleton


Item Calibration and Analysis

Item-Calibration Designs

Martijn P.F. Berger

Parameter Linking

Wim J. van der Linden and Michelle D. Barrett

Dimensionality Analysis

Robert D. Gibbons and Li Cai

Differential Item Functioning

Dani Gamerman, Flávio B. Goncalves, and Tufi M. Soares

Calibrating Technology-Enhanced Items

Richard M. Luecht

Person Fit and Scoring

Person Fit

Cees A. W. Glas and Naveed Khalid

Score Reporting and Interpretation

Ronald K. Hambleton and April L. Zenisky

IRT Observed-Score Equating

Wim J. van der Linden

Test Design

Optimal Test Design

Wim J. van der Linden

Adaptive Testing

Wim J. van der Linden

Standard Setting

Daniel Lewis and Jennifer Lord-Bessen

Test Speededness and Time Limits

Wim J. van der Linden

Item and Test Security

Wim J. van der Linden

Areas of Application

Large-Scale Group-Score Assessments

John Mazzeo

Psychological Testing

Paul De Boeck

Cognitive Diagnostic Assessment

Chung Wang and Hua-Hua Chang

Health Measurement

Richard C. Gershon, Ron D. Hays, and Michael Kallen

Marketing Research

Martijn G. de Jong and Ulf Böckenholt

Measuring Change Using Rasch Models

Gerhard H. Fischer

Computer Programs

IRT Packages in R

Thomas Rusch, Patrick Mair, and Reinhold Hatzinger

Bayesian Inference Using Gibbs Sampling (BUGS) for IRT Models

Matthew S. Johnson


Michele F. Zimowski


Eiji Muraki


Li Cai

Xcalibre 4

Nathan A. Thompson and Jieun Lee


Peter M. Bentler, Eric Wu, and Patrick Mair

ACER ConQuest

Raymond J. Adam, Margaret L. Wu, and Mark R. Wilson


Bengt Muthén and Linda Muthén


Sophia Rabe-Hesketh and Anders Skrondal

Latent GOLD

Jeroen K. Vermunt


Kyung (Chris) T. Han


Seung W. Choi


J. Patrick Meyer

About the Editor

Wim J. van der Linden is a distinguished scientist and director of research innovation at Pacific Metrics Corporation. He is also a professor emeritus of measurement and data analysis at the University of Twente. He is a past president of the Psychometric Society and National Council on Measurement in Education (NCME) and a recipient of career achievement awards from NCME, Association of Test Publishers (ATP), and American Educational Research Association (AERA). His research interests include test theory, computerized adaptive testing, optimal test assembly, parameter linking, test equating, and response-time modeling as well as decision theory and its application to problems of educational decision making. Dr. van der Linden earned a PhD in psychometrics from the University of Amsterdam.

Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Probability & Statistics / General