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

by George Engelhard, Jr., Jue Wang

Overview

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.

Product Details

ISBN-13:	9781040251591
Publisher:	Taylor & Francis
Publication date:	11/22/2024
Sold by:	Barnes & Noble
Format:	eBook
Pages:	340

About the Author

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.

Table of Contents

Preface
Acknowledgments
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?
Applications
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

References
Glossary (definitions of terms)
Author Index
Subject Index

Editorial Reviews

Winner of 2015 Qiyas Award

"Invariant Measurement fills a much needed void in the library of Rasch measurement books. This book is a favorite among Rasch measurement enthusiasts for many reasons, not the least of which is the authors’ use of practical language coupled with a consistent tone. Invariant Measurement, however, is sure to be another favorite in the Rasch measurement anthology as its crisp, clear writing and practical approach will be easily digestible for both measurement experts and curious students alike." - Kenneth D. Royal, University of North Carolina at Chapel Hill

"Professor Engelhard Jr. has long been one of the strongest and most respected and thoughtful measurement specialists in our field. His book on measurement invariance in the social sciences brings great clarity for practitioners to what many have called the cornerstone of item response theory." - Ronald K. Hambleton, Distinguished University Professor, University of Massachusetts - Amherst, USA

"Measurement is fundamental to any scientific research but unless the measures are valid and dependable, the research will be misleading and futile. This book is a must-read for every serious researcher who needs to construct quality measures. It gives a thorough treatment on both the concepts and the methodology of Rasch measurement." - Magdalena M. C. Mok, The Hong Kong Institute of Education, China

"George Engelhard is one of the world’s premier theorists on invariant measurement. … This will be a useful textbook for a graduate course on item response theory as well as a good desk reference for many psychometric researchers and practitioners." -Richard M. Luecht, University of North Carolina – Greensboro, USA

"I found each chapter easy to read and follow. ... [It] includes more authentic examples and supplements which ... make it (in my opinion) more accessible for graduate students." – Jennifer Randall, University of Massachusetts – Amherst, USA

"The conversational tone makes the book … more engaging – as if one were having a conversation with the author. ... I believe readers (particularly graduate students) will find the text engaging." - RJ DeAyala, University of Nebraska- Lincoln, USA

"The project makes a significant contribution to the field of measurement. I know of no other resource that has as their focus the basic concepts and principles of invariant measurement. …I …see this book as useful in introduction to Rasch measurement courses." – Carol Myford, University of Illinois at Chicago, USA

From the Publisher