Applying the Rasch Model: Fundamental Measurement in the Human Sciences, 4th Edition (Paperback) book cover

Applying the Rasch Model

Fundamental Measurement in the Human Sciences, 4th Edition

By Trevor Bond, Zi Yan, Moritz Heene


440 pages | 174 B/W Illus.

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Recognised as the most influential publication in the field, ARM facilitates deep understanding of the Rasch model and its practical applications. The authors review the crucial properties of the model and demonstrate its use with examples across the human sciences. Readers will be able to understand and critically evaluate Rasch measurement research, perform their own Rasch analyses and interpret their results. The glossary and illustrations support that understanding, and the accessible approach means that it is ideal for readers without a mathematical background.

Highlights of the new edition include:

  • More learning tools to strengthen readers’ understanding including chapter introductions, boldfaced key terms, chapter summaries, activities, and suggested readings.
  • Greater emphasis on the use of R packages; readers can download the R code from the Routledge website.
  • Explores the distinction between numerical values, quantity, and units, to understand the measurement and the role of the Rasch logit scale (chpt 4).
  • A new four-option data set from the IASQ (Instrumental Attitude towards Self-assessment Questionnaire) for the Rating Scale Model (RSM) analysis exemplar (chpt 6).
  • Clarifies the relationship between Rasch measurement, path analysis and SEM, with a host of new examples of Rasch measurement applied across health sciences, education and psychology (chpt 10).

Intended as a text for graduate courses in measurement, item response theory, (advanced) research methods or quantitative analysis taught in psychology, education, human development, business, and other social and health sciences. Professionals in these areas will also appreciate the book’s accessible introduction.


From a previous edition:

"The tiresome debate about Rasch vs. IRT is over -- if you want to construct valid measurements from uncertain observations you need to understand and learn how to use Rasch measurement.  Bond and Fox is your huckleberry -- read it and get to work!" – Robert W. Massof, Johns Hopkins University School of Medicine, USA

"Bond & Fox's book is a must read for anyone interested in measurement. This book is my go-to for introducing graduate students to the Rasch model." Kelly D. Bradley, University of Kentucky, USA

"The authors have successfully made sophisticated measurement theory into feasible practice for practitioners by providing clear and intuitive explanations, numerous examples, and nice computer outputs. It is a textbook that I have used and will continue to use in the future." Wen Chung Wang, Hong Kong Institute of Education, Hong Kong

"Bond and Fox provide a clear and accessible introduction to the Rasch model… I always recommend their book when a student or colleagues asks me to explain Rasch measurement theory."George Engelhard, Jr., The University of Georgia, USA

"The Rasch model represents modern measurement theory at its best … Rasch models are used around the world to create psychometrically defensible scales and tests. Bond and Fox provide an accessible introduction to the Rasch model that describes the logic and essential importance of fundamental measurement in the human sciences." George Engelhard, Jr., The University of Georgia, USA

Table of Contents



About the Authors

  1. Why Measurement Is Fundamental
  2. 1.1 Children Can Construct Measures

    1.2 Interval scales v. ratio scales: A conceptual explanation

    1.3 Statistics and/or Measurement

    1.4 Why Fundamental Measurement?

    1.5 Derived Measures

    1.6 Conjoint Measurement

    1.7 The Rasch Model for Measurement

    1.8 A More Suitable Analogy for Measurement in the Human Sciences

    1.9 In Conclusion

    1.10 Summary

  3. Important Principles of Measurement Made Explicit
  4. 2.1 An example: "By how much?"

    2.2 Moving From Observations to Measures

    2.3 The basic Rasch assumptions

    2.4 Summary

  5. Basic Principles of the Rasch Model
  6. 3.1 The Pathway Analogy

    3.2 Unidimensionality

    3.3 Item Fit

    3.4 Difficulty/Ability Estimation and Error

    3.5 Reliability

    3.6 A Basic Framework for Measurement

    3.7 Fit (Quality Control)

    3.8 The Rasch Model

    3.9 Summary

  7. Building a Set of Items for Measurement
  8. 4.1 The Nature of the Data

    4.2 Analyzing Dichotomous Data: The BLOT

    4.3 A Simple Rasch Summary: The Item Pathway

    4.4 Item Statistics

    4.5 Item Fit

    4.6 The Wright Map

    4.7 Targeting

    4.8 Comparing Persons and Items

    4.9 Summary

    4.10 Extended Understanding—Chapter 4

    4.11 The Problem of Guessing

    4.12 Difficulty, Ability, and Fit

    4.13 The Theory–Practice Dialogue

    4.14 Summary

  9. Invariance: A Crucial Property of Scientific Measurement
  10. 5.1 Person and Item Invariance

    5.2 Common Item Linking

    5.3 Anchoring Item Values

    5.4 Vertical Scaling

    5.5 Common-Person Linking

    5.6 Invariance of Person Estimates Across Tests: Concurrent Validity

    5.7 The PRTIII-Pendulum

    5.8 Common-Person Linking

    5.9 The Theory–Practice Dialogue

    5.10 Measurement Invariance: Where It Really Matters

    5.11 Failures of Invariance: DIF

    5.12 Differential Rater Functioning

    5.13 DIF: Not just a problem, but an opportunity

    5.14 Summary

  11. Measurement Using Likert Scales
  12. 6.1 The Rasch Model for Polytomous Data

    6.2 Analyzing Rating Scale Data: The Instrumental Attitude towards Self-assessment Questionnaire

    6.3 Item Ordering

    6.4 Targeting and Reliability

    6.5 Summary

    6.6 Extended Understanding—Chapter 6

    6.7 Summary

  13. The Partial Credit Rasch Model
  14. 7.1 Clinical Interview Analysis: A Rasch-Inspired Breakthrough

    7.2 Scoring Interview Transcripts

    7.3 Partial Credit Model Results

    7.4 Interpretation

    7.5 The Theory–Practice Dialogue

    7.6 Unidimensionality

    7.7 Summary

    7.8 Extended Understanding—Chapter 7

    7.9 Category Functioning

    7.10 Point–Measure Correlations

    7.11 Fit Statistics

    7.12 Dimensionality: Primary Components Factor Analysis

    7.13 Summary

  15. Measuring Facets Beyond Ability and Difficulty
  16. 8.1 A Basic Introduction to the Many-Facets Rasch Model

    8.2 Why Not Use Interrater Reliability?

    8.3 Relations Among the Rasch Family of Models

    8.4 Data Specifications of the Many-Facets Rasch Model

    8.5 Rating Creativity of Junior Scientists

    8.6 Many-Facets Analysis of Eighth-Grade Writing

    8.7 Summary

    8.8 Extended Understanding—Chapter 8

    8.9 Invariance of Rated Creativity Scores

    8.10 Rasch Measurement of Facets Beyond Rater Effects

    8.11 Summary

  17. Making Measures, Setting Standards, and Rasch Regression
  18. 9.1 Creating a Measure from Existing Data

    9.2 Method

    9.3 Physical Fitness Indicators

    9.4 Data Analysis

    9.5 Seven Criteria to Investigate the Quality of Physical Fitness Indicators

    9.6 Results and Discussion

    9.7 Optimizing Response Categories

    9.8 Influence of Underfitting Persons on the RMPFS

    9.9 Properties of the RMPFS With Subsamples

    9.10 Age Dependent or Age Related?

    9.11 The Final Version of RMPFS

    9.12 Objective Standard Setting: The OSS Model

    9.13 Early Definitions

    9.14 The Objective Standard Setting Models

    9.15 Objective Standard Setting for Dichotomous Examinations

    9.16 Objective Standard Setting for Judge-Mediated Examinations

    9.17 Fair Standards, Not Absolute Values

    9.18 Rasch Regression

    9.19 Predicting Physician Assistant Faculty Intention to Leave Academia

    9.20 Rasch Regression Using the Anchored Formulation

    9.21 Rasch Regression: Alternative Approaches

    9.22 Discussion

    9.23 Summary

  19. The Rasch Model Applied Across the Human Sciences
  20. 10.1 Rasch Measurement in Health Sciences

    10.2 Establishing Rasch psychometric properties: The A-ONE J

    10.3 More than mere psychometric indicators: The PAM

    10.4 Refining an existing instrument: The POSAS

    10.5 Optimizing an existing instrument: The NIHSS and a central role for PCA

    10.6 Creating a Short Form of an Existing Instrument: The FSQ

    10.7 Theory guides assessment revisions: The PEP–S8

    10.8 Applications in Education and Psychology

    10.9 Test development

    10.10 The Goodenough Draw-a-Man Test: One Drawing is Good enough

    10.11 Rasch Gain Calculations: Racking and Stacking

    10.12 Rasch Learning Gain Calculations: The CCI

    10.13 Racking and stacking

    10.14 Stacking can be enough: UPAM

    10.15 Sub-test structure informs scoring models

    10.16 Applications to classroom testing

    10.17 Can Rasch measurement help S. S. Stevens?

    10.18 Using Rasch Measures with Path Analysis (SEM framework)

    10.19 Rasch person measures used in a partial least squares (PLS) framework

    10.20 And those Rasch measurement SEs?

    10.21 Can we really combine SEM and Rasch models?

    10.22 Conclusion

    10.23 Summary

  21. Rasch Modeling Applied: Rating Scale Design
  22. 11.1 Rating Scale Design

    11.2 Category Frequencies and Average Measures

    11.3 Thresholds and Category Fit

    11.4 Revising a Rating Scale

    11.5 An Example

    11.6 Guidelines for Collapsing Categories

    11.7 Problems With Negatively Worded Items

    11.7 The Invariance of the Measures Across Groups

    11.8 Summary

  23. Rasch Model Requirements: Model Fit and Unidimensionality
  24. 12.1 The Data, the Model, and the Residuals

    12.2 Residuals

    12.3 Fit Statistics

    12.4 Expectations of Variation

    12.5 Fit, Misfit, and Interpretation

    12.6 Fit: Issues for Resolution

    12.7 Misfit: A Fundamental Issue

    12.8 In the Interim

    12.9 Detecting Multiple Dimensions

    12.10 Linear Factor Analysis—Problems and Promise

    12.11 Rasch Factor Analysis (PCA)

    12.12 Principal Components Analysis of Rasch Residuals—The BLOT as An Exemplar

    12.13 One Dimension, Two Dimensions, Three Dimensions, More?

    12.14 Extended Understanding—Chapter 12

    12.15 A Further Investigation: BLOT and PRTIII

    12.16 Summary

  25. A Synthetic Overview

13.1 Additive Conjoint Measurement—ACM

13.2 True Score Theory, Latent Traits, and Item Response Theory

13.3 Would You Like an Interval Scale With That?

13.4 Model Assumptions and Measurement Requirements

13.5 Construct Validity

13.6 The Rasch Model and Progress of Science

13.7 Back to the Beginning and Back to the End

13.8 Summary

Appendix A: Getting Started

Appendix B: Technical Aspects of the Rasch Model

Appendix C: Going All the Way


Author Index

Subject Index

About the Authors

Trevor G. Bond is currently Adjunct Professor at the College of Arts, Society and Education at James Cook University, Australia.

Dr. Yan Zi’s research interests focus on the application of Rasch models in solving practical measurement problems in different contexts and, fundamentally, enact the principles of objective measurement in social science research and practices so as to contributes to individual, community and societal well-being.

Moritz Heene is Full Professor of Learning Sciences Research Methodologies (i.e., Quantitative Methods) at the Ludwig-Maximilians Universität München, Germany

Subject Categories

BISAC Subject Codes/Headings:
EDUCATION / Testing & Measurement
PSYCHOLOGY / Research & Methodology
PSYCHOLOGY / Statistics
PSYCHOLOGY / Assessment, Testing & Measurement