Item Response Theory

Item Response Theory

by R. Darrell Bock, Robert D. Gibbons
Released July 2021
Publisher(s): Wiley
ISBN: 9781119716686

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Book description

A complete discussion of fundamental and advanced topics in Item Response Theory written by pioneers in the field

In Item Response Theory, accomplished psychometricians Darrell Bock and Robert Gibbons deliver a comprehensive and up-to-date exploration of the theoretical foundations and applications of Item Response Theory (IRT). Covering both unidimensional and multidimensional IRT, as well as related adaptive test administration of previously calibrated item banks, the book addresses the growing need for understanding of this topic as the use of IRT spreads to other fields.

The first book on the topic that offers a complete and unified treatment of its subject, Item Response Theory prepares researchers and students to understand and apply IRT and multidimensional IRT to fields like education, mental health and marketing. Accessible to first year-graduate students with a foundation in the behavioral or social sciences, basic statistics, and generalized linear models, the book walks readers through everything from the logic of IRT to cutting edge applications of the technique.

Readers will also benefit from the inclusion of:

• A thorough introduction to the foundations of Item Response Theory, including its logic and origins, model-based measurement, psychological scaling, and classical test theory

• An exploration of selected mathematical and statistical results, including points, point sets, and set operations, probability, sampling, and joint, conditional, and marginal probability

• Discussions of unidimensional and multidimensional IRT models, including item parameter estimation with binary and polytomous data

• Analysis of dimensionality, differential item functioning, and multiple group IRT

Perfect for graduate students and researchers studying and working with psychometrics in psychology, quantitative psychology, educational measurement, marketing, and statistics, Item Response Theory will also benefit researchers interested in patient reported outcomes in health research.

Table of contents

  1. Cover
  2. Title page
  3. Copyright
  4. Dedication
  5. Preface
  6. Acknowledgments
  7. 1: Foundations
    1. 1.1 The Logic of Item Response Theory
    2. 1.2 Model‐Based Data Analysis
    3. 1.3 Origins
    4. 1.4 The Population Concept in IRT
    5. 1.5 Generalizability Theory
    6. Notes
  8. 2: Selected Mathematical and Statistical Results
    1. 2.1 Points, Point Sets, and Set Operations
    2. 2.2 Probability
    3. 2.3 Sampling
    4. 2.4 Joint, Conditional, and Marginal Probability
    5. 2.5 Probability Distributions and Densities
    6. 2.6 Describing Distributions
    7. 2.7 Functions of Random Variables
    8. 2.8 Elements of Matrix Algebra
    9. 2.9 Determinants
    10. 2.10 Matrix Differentiation
    11. 2.11 Theory of Estimation
    12. 2.12 Maximum Likelihood Estimation
    13. 2.13 Bayes Estimation
    14. 2.14 The Maximum A Posteriori (MAP) Estimator
    15. 2.15 Marginal Maximum Likelihood Estimation (MMLE)
    16. 2.16 Probit and Logit Analysis
    17. 2.17 Some Results from Classical Test Theory
    18. Notes
  9. 3: Unidimensional IRT Models
    1. 3.1 The General IRT Framework
    2. 3.2 Item Response Models
  10. 4: Item Parameter Estimation – Binary Data
    1. 4.1 Estimation of Item Parameters Assuming Known Attribute Values of the Respondents
    2. 4.2 Estimation of Item Parameters Assuming Unknown Attribute Values of the Respondents
  11. 5: Item Parameter Estimation – Polytomous Data
    1. 5.1 General Results
    2. 5.2 The Normal Ogive Model
    3. 5.3 The Nominal Categories Model
    4. 5.4 The Graded Categories Model
    5. 5.5 The Generalized Partial Credit Model
    6. 5.6 Boundary Problems
    7. 5.7 Multiple Group Models
    8. 5.8 Discussion
    9. 5.9 Conclusions
  12. 6: Multidimensional IRT Models
    1. 6.1 Classical Multiple Factor Analysis of Test Scores
    2. 6.2 Classical Item Factor Analysis
    3. 6.3 Item Factor Analysis Based on Item Response Theory
    4. 6.4 Maximum Likelihood Estimation of Item Slopes and Intercepts
    5. 6.5 Indeterminacies of Item Factor Analysis
    6. 6.6 Estimation of Item Parameters and Respondent Scores in Item Bifactor Analysis
    7. 6.7 Estimating Factor Scores
    8. 6.8 Example
    9. 6.9 Two‐Tier Model
    10. 6.10 Summary
  13. 7: Analysis of Dimensionality
    1. 7.1 Unidimensional Models and Multidimensional Data
    2. 7.2 Limited‐Information Goodness of Fit Tests
    3. 7.3 Example
    4. 7.4 Discussion
  14. 8: Computerized Adaptive Testing
    1. 8.1 What Is Computerized Adaptive Testing?
    2. 8.2 Computerized Adaptive Testing – An Overview
    3. 8.3 Item Selection
    4. 8.4 Terminating an Adaptive Test
    5. 8.5 Additional Considerations
    6. 8.6 An Example from Mental Health Measurement
  15. 9: Differential Item Functioning
    1. 9.1 Introduction
    2. 9.2 Types of DIF
    3. 9.3 The Mantel–Haenszel Procedure
    4. 9.4 Lord's Wald Test
    5. 9.5 Lagrange Multiplier Test
    6. 9.6 Logistic Regression
    7. 9.7 Assessing DIF for the Bifactor Model
    8. 9.8 Assessing DIF from CAT Data
  16. 10: Estimating Respondent Attributes
    1. 10.1 Introduction
    2. 10.2 Ability Estimation
  17. 11: Multiple Group Item Response Models
    1. 11.1 Introduction
    2. 11.2 IRT Estimation When the Grouping Structure Is Known: Traditional Multiple Group IRT
    3. 11.3 IRT Estimation When the Grouping Structure Is Unknown: Mixtures of Gaussian Components
    4. 11.4 Multivariate Probit Analysis
    5. 11.5 Multilevel IRT Models
  18. 12: Test and Scale Development and Maintenance
    1. 12.1 Introduction
    2. 12.2 Item Banking
    3. 12.3 Item Calibration
    4. 12.4 IRT Equating
    5. 12.5 Harmonization
    6. 12.6 Item Parameter Drift
    7. 12.7 Summary
  19. 13: Some Interesting Applications
    1. 13.1 Introduction
    2. 13.2 Biobehavioral Synthesis
    3. 13.3 Mental Health Measurement
    4. 13.4 IRT in Machine Learning
  20. Bibliography
  21. Index
  22. End User License Agreement

Product information

  • Title: Item Response Theory
  • Author(s): R. Darrell Bock, Robert D. Gibbons
  • Release date: July 2021
  • Publisher(s): Wiley
  • ISBN: 9781119716686