It is observed that many sorts of difficulties may preclude the uneventful construction of tests by a computerized algorithm, such as those currently in favor in Computerized Adaptive Testing (CAT). In this essay we discuss a number of these problems, as well as some possible avenues of solution. We conclude with the development of the “testlet,” a bundle of items that can be arranged either hierarchically or linearly, thus maintaining the efficiency of an adaptive test while keeping the quality control of test construction that is possible currently only with careful expert scrutiny. Performance on the separate testlets is aggregated to yield ability estimates.

It is proved that under very general circumstances coefficients in multiple regression models can be replaced with equal weights with almost no loss in accuracy on the original data sample. It is then shown that these equal weights will have greater robustness than least squares regression coefficients. The implications for problems of prediction are discussed.

Gibbs sampler, Data augmentation, Testlets,

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 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.

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