estimation of item parameters, EM algorithm, item analysis, latent trait, dichotomous factor analysis, Law School Aptitude Test (LSAT),

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 quadra-ture 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 & p l u s m n ; 2.5 standard deviations. With the increasing availability of inexpensive ~i~~®~®mp~t~~°s9 adaptive testing of cognitive abilities is fast becoming a practical reality. Many, perhaps most, applications of mental testing will soon benefit from the flexibility and efficiency of computerized adaptive testing. The requisite statistical theory, including realistic item response models (Samejima, 1981) and rigorous methods of item parameter estimation (Bock & Aitkin, 1981; Reiser, 1982; Thissen, 1982), is now available. Production

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A plausible factorial structure for many types of psychological and educational tests exhibits a general factor and one or more group or method factors. This structure can be represented by a bifactor model. The bifactor structure results from the constraint that each item has a nonzero loading on the primary dimension and, at most, one of the group factors. The authors develop estimation procedures for fitting the graded response model when the data follow the bifactor structure. Using maximum marginal likelihood estimation of item parameters, the bifactor restriction leads to a major simplification of the likelihood equations and (a) permits analysis of models with large numbers of group factors, (b) permits conditional dependence within identified subsets of items, and (c) provides more parsimonious factor solutions than an unrestricted full-information item factor analysis in some cases. Analysis of data obtained from 586 chronically mentally ill patients revealed a clear bifactor structure.

Guidelines are proposed for evaluating a computerized adaptive test. Topics include dimensionality, measurement error, validity, estimation of item parameters, item pool characteristics and human factors. Equating CAT and conventional tests is considered and matters of equity are addressed.

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