Testlet Response Theory and Its Applications

by Howard Wainer , Eric T. Bradlow , Xiaohui Wang

• ISBN13: 9780521681261
• ISBN10: 052168126X
• Edition: 1st
• Format: Paperback
• Copyright: 2007-03-19
• Publisher: Cambridge University Press

Summary

The measurement models employed to score tests have been evolving over the past century from those that focus on the entire test (true score theory) to models that focus on individual test items (item response theory) to models that use small groups of items (testlets) as the fungible unit from which tests are constructed and scored (testlet response theory, or TRT). In this book, the inventors of TRT trace the history of this evolution and explain the character of modern TRT. Written for researchers and professionals in statistics, psychometrics, and educational psychology, the first part of the book offers an accessible introduction to TRT and its applications. The second part presents a comprehensive, self-contained discussion of the model couched within a fully Bayesian framework. Its parameters are estimated using Markov chain Monte Carlo procedures, and the resulting posterior distributions of the parameter estimates yield insights into score stability that were previously unsuspected.

Author Biography

Howard Wainer is a Distinguished Research Scientist for the National Board of Medical Examiners and Adjunct Professor of Statistics at the Wharton School of the University of Pennsylvania Eric T. Bradlow is the K. P. Chao Professor; Professor of Marketing, Statistics, and Education; and Academic Director of the Wharton Small Business Development Center at the Wharton School of the University of Pennsylvania Xiaohui Wang is an Assistant Professor in the Department of Statistics at the University of Virginia

Table of Contents

Peface	p. ix
Introduction to Testlets	p. 1
Introduction	p. 3
True score theory	p. 14
Item response theory	p. 24
What's a testlet and why do we need them?	p. 44
The origins of testlet response theory - three alternatives	p. 60
Fitting testlets with polytomous IRT models	p. 72
Bayesian Testlet Response Theory	p. 105
A brief history and the basic ideas of modern testlet response theory	p. 110
The 2-PL Bayesian testlet model	p. 118
The 3-PL Bayesian testlet model	p. 134
A Bayesian testlet model for a mixture of binary and polytomous data	p. 144
A Bayesian testlet model with covariates	p. 154
Testlet nonresponse theory: dealing with missing data	p. 186
Two Applications and a Tutorial	p. 205
Using posterior distributions to evaluate passing scores: the PPoP curve	p. 207
A Bayesian method for studying DIF: a cautionary tale filled with surprises and delights	p. 219
A Bayesian primer	p. 234
Glossary of terms	p. 247
Epilogue	p. 249
Bibliography	p. 251
Author Index	p. 261
Subject Index	p. 263
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