Statistical Models for Test Equating, Scaling, and Linking

1. Front Matter

   Pages i-xix

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2. Research Questions and Data Collection Designs

   1. Front Matter

      Pages 19-19

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3. A Statistical Perspective on Equating Test Scores

   1. A Statistical Perspective on Equating Test Scores

      • Alina A. von Davier

      Pages 1-17

4. Research Questions and Data Collection Designs

   1. Front Matter

      Pages 19-19

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   2. Equating Test Scores: Toward Best Practices

      • Neil J. Dorans, Tim P. Moses, Daniel R. Eignor

      Pages 21-42

   3. Scoring and Scaling Educational Tests

      • Michael J. Kolen, Ye Tong, Robert L. Brennan

      Pages 43-58

   4. Statistical Models for Vertical Linking

      • James E. Carlson

      Pages 59-70

   5. An Empirical Example of Change Analysis by Linking Longitudinal Item Response Data From Multiple Tests

      • John J. McArdle, Kevin J. Grimm

      Pages 71-88

   6. How to Average Equating Functions, If You Must

      • Paul W. Holland, William E. Strawderman

      Pages 89-107

   7. New Approaches to Equating With Small Samples

      • Samuel A. Livingston, Sooyeon Kim

      Pages 109-122

5. Measurement and Equating Models

   1. Front Matter

      Pages 123-123

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   2. Using Exponential Families for Equating

      • Shelby J. Haberman

      Pages 125-140

   3. An Alternative Continuization Method: The Continuized Log-Linear Method

      • Tianyou Wang

      Pages 141-157

   4. Equating Through Alternative Kernels

      • Yi-Hsuan Lee, Alina A. von Davier

      Pages 159-173

   5. A Bayesian Nonparametric Model for Test Equating

      • George Karabatsos, Stephen G. Walker

      Pages 175-184

   6. Generalized Equating Functions for NEAT Designs

      • Haiwen H. Chen, Samuel A. Livingston, Paul W. Holland

      Pages 185-200

   7. Local Observed-Score Equating

      • Wim J. van der Linden

      Pages 201-223

   8. A General Model for IRT Scale Linking and Scale Transformations

      • Matthias von Davier, Alina A. von Davier

      Pages 225-242

   9. Linking With Nonparametric IRT Models

      • Xueli Xu, Jeff A. Douglas, Young-Sun Lee

      Pages 243-258

6. Evaluation

   1. Front Matter

      Pages 259-259

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The goal of this book is to emphasize the formal statistical features of the practice of equating, linking, and scaling. The book encourages the view and discusses the quality of the equating results from the statistical perspective (new models, robustness, fit, testing hypotheses, statistical monitoring) as opposed to placing the focus on the policy and the implications, which although very important, represent a different side of the equating practice.

The book contributes to establishing “equating” as a theoretical field, a view that has not been offered often before. The tradition in the practice of equating has been to present the knowledge and skills needed as a craft, which implies that only with years of experience under the guidance of a knowledgeable practitioner could one acquire the required skills. This book challenges this view by indicating how a good equating framework, a sound understanding of the assumptions that underlie the psychometric models, and the use of statistical tests and statistical process control tools can help the practitioner navigate the difficult decisions in choosing the final equating function. 

This book provides a valuable reference for several groups: (a) statisticians and psychometricians interested in the theory behind equating methods, in the use of model-based statistical methods for data smoothing, and in the evaluation of the equating results in applied work; (b) practitioners who need to equate tests, including those with these responsibilities in testing companies, state testing agencies, and school districts; and (c) instructors in psychometric, measurement, and psychology programs.

• Measurement Model
• Psychometric Model
• Standardized Assessment
• Test Equating

From the reviews:

“The intended audience of the book consists of graduate students, researchers, statisticians and psychometricians who are interested in equating theory, as well as practitioners who equate tests. … volume is easy to understand since overall it is clear and well written, and has examples that are nice and easy to follow. … I recommend this book for anyone with an interest in the equating research field, and … the book has succeeded in providing a statistical view on equating which has long been searched for.” (Marie Wiberg, Psychometrika, Vol. 78 (1), January, 2013)

• Educational Testing Service, Princeton, USA

  Alina A. Davier

Dr. Alina A. von Davier is a Strategic Advisor and a Director of Special Projects in Research and Development at Educational Testing Service (ETS). During her tenure at ETS, she has led an ETS Research Initiative called “Equating and Applied Psychometrics” and has directed the Global Psychometric Services Center. The center supports the psychometric work for all ETS international programs, including TOEFL iBT and TOEIC. She is a co-author of a book on the kernel method of test equating, an author of a book on hypotheses testing in regression models, and a guest co-editor for a special issue on population invariance of linking functions for the journal Applied Psychological Measurement.

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