Browsing by Author "Bock, R. Darrell"
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Item Adaptive EAP estimation of ability in a microcomputer environment(1982) Bock, R. Darrell; Mislevy, Robert J.Expected a posteriori (EAP) estimation of ability, based on numerical evaluation of the mean and variance of the posterior distribution, is shown to have unusually good properties for computerized adaptive testing. The calculations are not complex, precede noniteratively by simple summation of log likelihoods as items are added, and require only values of the response function obtainable from precalculated tables at a limited number of quadrature points. Simulation studies are reported showing the near equivalence of the posterior standard deviation and the standard error of measurement. When the adaptive testings terminate at a fixed posterior standard deviation criterion of .90 or better, the regression of the EAP estimator on true ability is virtually linear with slope equal to the reliability, and the measurement error homogeneous, in the range +- 2.5 standard deviations.Item Full-information item factor analysis(1988) Bock, R. Darrell; Gibbons, Robert; Muraki, EijiA method of item factor analysis based on Thurstone’s multiple-factor model and implemented by marginal maximum likelihood estimation and the EM algorithm is described. Statistical significance of successive factors added to the model is tested by the likelihood ratio criterion. Provisions for effects of guessing on multiple-choice items, and for omitted and not-reached items, are included. Bayes constraints on the factor loadings are found to be necessary to suppress Heywood cases. Numerous applications to simulated and real data are presented to substantiate the accuracy and practical utility of the method. Index terms: Armed Services Vocational Aptitude Battery, Beta prior, E M algorithm, Item factor analysis, TESTFACT, Tetrachoric correlation.