Invariant Measurement

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, IRT, 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.

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.

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

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