2nd Edition

Invariant Measurement Using Rasch Models in the Social, Behavioral, and Health Sciences

By George Engelhard, Jr., Jue Wang Copyright 2025
    340 Pages 62 B/W Illustrations
    by Routledge

    340 Pages 62 B/W Illustrations
    by Routledge

    This is the second edition of an introductory text that describes the principles of invariant measurement; how invariant measurement can be achieved using Rasch measurement theory; and how to use invariant measurement to solve a variety of measurement problems in the social, behavioral, and health sciences. Rasch models are used throughout the text, but brief comparisons of Rasch models to other item response theory (IRT) models are also provided.
    Written with students in mind, this new edition was class-tested to help maximize accessibility. Chapters open with an introduction and close with a discussion and summary. All chapters have been updated from the first edition, and a new chapter on explanatory Rasch models has been added. Features include numerous examples and exercises to demonstrate the main issues addressed in each chapter. Key terms are defined when first introduced and included in a helpful end-of-text glossary.
    This book also benefits from online materials which include: the data sets used in the book, sample syntax files for running the Facets program, Excel files for creating item and person response functions, and links to related websites.
    This book will act as a supplementary text for graduate or advanced undergraduate courses on measurement or test theory, item response theory, scaling theory, psychometrics, advanced measurement techniques, research methods, or evaluation research taught in education, psychology, and other social and health sciences. It will also appeal to practitioners and researchers in these fields who develop or use scales and instruments. Only a basic mathematical level is required including a basic course in statistics, ensuring it is an accessible resource for students and researchers alike.

    About the authors

    Part I: Introduction
    1. Introduction and Overview
    Variable maps
    What are logits?
    The dichotomous Rasch model
    Five requirements of invariant measurement
    Method and meaning of Rasch measurement
    Illustrative data set: Measuring the home environment
    Discussion and summary

    Part II: Conceptual and Theoretical Issues
    2. Invariant Measurement
    What is measurement?
    What is invariant measurement?
    Ideal-type scales and the structure of measurement data
    What are Rasch Models?
    Item-invariant person measurement
    Person-invariant item calibration
    Discussion and Summary

    3. Rasch Models
    Operating characteristic functions
    Dichotomous Rasch model
    Polytomous Rasch Models
    Partial Credit model
    Rating Scale model
    Many Facet Model
    Discussion and Summary

    4. Researcher-Constructed Measures
    Building Blocks for Researcher-Constructed Measures
    1. Latent variable: What is the latent variable being measured?
    2. Observational Design: What is the plan for collecting structured observations or responses from persons in order to define the latent variable?
    3. Scoring rules: How do we categorize the systematic observations, and then assign scores to the categories to be used as indicators of the latent variable?
    4. Rasch Measurement model: How are person and item responses or observations mapped onto the latent variable?
    1. Learning stimulation in the home environments of preschool children
    2. Assessment in the health sciences: The five rights of safe administration of medications
    Discussion and summary

    5. An Historical and Comparative Perspective on Research Traditions in Measurement
    What are measurement theories?
    What are research traditions?
    What are the three major research traditions in measurement?
    Test-Score Tradition
    1. The founding of classical test theory: Spearman
    2. Generalizability Theory: Cronbach and his colleagues
    Scaling Tradition
    1. Psychophysics and the beginning of the scaling tradition: Thorndike
    2. Absolute scaling and psychophysics: Thurstone
    3. Item response theory: Birnbaum and Rasch
    4. Non-Parametric item response theory: Guttman, Lazarsfeld, and Mokken
    Structural Tradition
    1. Factor analysis: Spearman and Thurstone
    2. Path analysis: Wright
    3. Structural equation modeling: Joreskog
    4. Explanatory Item Response Models: De Boeck & Wilson
    Discussion and summary

    6. The Quest for Invariant Measurement within the Scaling Tradition
    General issues guiding the comparisons among the scaling theories
    Item-invariant person measurement
    1. Parametric models: Thorndike, Thurstone, Birnbaum and Rasch
    2. Non-parametric models: Guttman, Lazarsfeld and Mokken
    Person-invariant item calibration
    1. Parametric models: Thorndike, Thurstone, Birnbaum and Rasch
    2. Non-parametric models: Guttman, Lazarsfeld and Mokken
    Operating characteristic functions
    1. Item response functions
    2. Person response functions
    Variable maps
    Discussion and summary

    Part III: Technical Issues
    7. Methods of Estimation for the Dichotomous Rasch Model
    Dichotomous Model for Rasch Measurement
    Methods of Estimation
    Non-iterative Estimation Methods
    1. LOG Method
    2. PAIR Method
    3. PROX Method
    Iterative Estimation Methods
    1. Joint Maximum Likelihood Estimation Method
    2. Marginal Maximum Likelihood Method
    3. Conditional Maximum Likelihood Method
    4. Bayesian Estimation Method
    Item calibration: Comparison of non-iterative, MLE, and Bayesian methods
    Person measurement: Illustrative data analysis of JMLE Method
    Discussion and Summary

    8. Model-Data Fit for the Dichotomous Rasch Model
    Brief history of model-data fit for categorical data
    Conceptual framework for model-data fit based on residual analyses
    1. Guttman’s Perspective on Model-Data Fit
    2. Model-data fit statistics for dichotomous Rasch Model
    Additional issues related to model-data fit
    Discussion and Summary

    9. Rasch Measurement Theory and Generalized Linear Mixed Models
    What are generalized linear mixed models?
    Specifying Explanatory Rasch Models with Generalized Linear Mixed Models
    1. Dichotomous Model with no covariates
    2. Linear Logistic Rasch Model with item covariates
    3. Latent Regression Rasch Model with person covariates
    4. Combined Covariates Rasch Model with item and person covariates
    Illustrations of Explanatory Rasch Models with the Learning Stimulation Scale
    1. Dichotomous Model with no covariates
    2. LLRM with items classified as child or adult activities
    3. LRRM with homes categorized by education level of mother
    4. CCRM with both item classification and home categorization
    5. Model Comparisons
    Discussion and Summary

    Part IV: Assessments with raters: Rater-invariant measurement
    10. Rater-mediated assessments: A Conceptual framework
    Rater-mediated assessments
    Brief description of measurement models for raters
    Rater-invariant measurement
    1. Extending the requirements of invariant measurement
    2. Criteria for developing and evaluating rater-mediated assessments
    3. Guidelines for evaluating functioning of rating categories
    The Many Facet Rasch Model
    Using variable maps with rater-mediated assessments
    Discussion and summary

    11. Evaluating the quality of rater-mediated assessments I:
    Indices of rater errors and systematic biases
    Rater Errors and Systematic Biases
    Illustrative data analyses
    1. Rater Facet
    2. Domain Facet
    3. Person Facet
    Rater Invariant Measurement
    Discussion and Summary

    12. Evaluating the quality of rater-mediated assessments II:
    Direct Indices of rater accuracy
    What is rater accuracy?
    Rater accuracy as the underlying construct
    Indices of rating accuracy
    Illustrative data analyses
    Relationship between rater error and accuracy
    Discussion and Summary

    Part V: Final Word
    13. Invariant measurement: Discussion and summary
    Perennial issues in assessment from the perspective of invariant measurement
    Measurement Models
    Assessment Development
    Administration of assessments
    Use of assessments
    Evaluation of assessments
    Final word

    Glossary (definitions of terms)
    Author Index
    Subject Index



    George Engelhard, Jr. is a professor of educational measurement and policy at the University of Georgia.
    Jue Wang is a professor at the University of Science and Technology of China.