Linear Models for Optimal Test Design
Over my nearly forty years of teaching and conducting research in the ?eld of psychometric methods, I have seen a number of major technical advances that respond to pressing educational and psychological measu- mentproblems. Thedevelopmentofcriterion-referencedassessmentwasthe ?rst, beginning in the late 1960s with the important work of Robert Glaser and Jim Popham, in response to the need for assessments that considered candidate performance in relation to a well-de?ned body of knowledge and skills rather than in relation to a norm group. The development of criterion-referenced testing methodology with a focus on decision-theoretic concepts and methods, content validity, standard-setting, and the recog- tionofthemeritsofbothcriterion-norm-referencedandcriterion-referenced assessments has tremendously in?uenced current test theory and testing . The second major advance was the introduction of item response-theory (IRT) and associated models and their applications to replace classical test theory (CTT) and related practices. Beginning slowly in the 1940s and 1950s with the pioneering work of Frederic Lord, Allan Birnbaum, and GeorgRasch,bythe1970sthemeasurementjournalswerefullofimportant research studies describing new IRT models, technical advances in model parameter estimation and model ?t, and research on applications of IRT models to equating, test development, the detection of potentially biased test items, and adaptive testing. The overall goal has been to improve and expand measurement practices by overcoming several shortcomings of cl- sicaltesttheory:dependenceoftest-itemstatisticsandreliabilityestimates on examinee samples, dependence of examinee true score estimates on the particular choices of test items, and the limitation in CTT of modeling ex- viii Foreword aminee performance at the test level rather than at the item level.
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Modern Test Design
Test Design in This Book
Formulating Test Specifications
Modeling TestAssembly Problems
Solving TestAssembly Problems
Models for Assembling Single Tests
Models for Assembling Tests
Basic Concepts in Linear Programming
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ability estimate adaptive test assembly Adema algorithm approach blueprint calculated categorical attributes chapter combinations of attributes content constraints decision variables denote design model design points design space empirical example equal exposure rates feasible fixed test formulated genetic algorithms greedy heuristic heuristic infeasibility information function integer integer programming item attributes item level item parameters item pool item selection item sets items and stimuli Linden linear lower bound LSAT maximize minimax minimize multiple tests multistage testing number of items number of variables objective function Observed Score observed-score distributions optimal pivot item possible quantitative attributes reference test relative target selection of items sequential set of constraints set of tests shadow test simulated simulated annealing simultaneous single test solution standard model subsets target values test length Test Level test specifications test takers test-assembly model test-assembly problem update variance functions weights