Adaptive EAP estimation of ability in a microcomputer environment

Abstract

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.