A mathematical setting based on a statistical sampling probability mechanism is described. In this setting, a mathematical meaning is given for the information function; and it becomes possible to study the relative merits of various ability-estimating procedures. The maximum likelihood estimation procedure under the one-, two-, three-parameter…

Single sample approximations are considered for the cross-validation coefficient in the analysis of covariance structures. Results of a random sampling experiment--using data from ability tests administered to high school students (sample sizes 100, 400, and 800)--illustrate the coefficient and adjustment for predictive validity. (SLD)

Computerized adaptive testing procedures (CATPs) based on the graded response method (GRM) of F. Samejima (1969) and the partial credit model (PCM) of G. Masters (1982) were developed and compared. Both programs used maximum likelihood estimation of ability, and item selection was conducted on the basis of information. Two simulated data sets, one…

This study developed a hybrid of item response theory (IRT) models and latent class models, which combined the strengths of each type of model. The primary motivation for developing the new model is to describe characteristics of examinees' knowledge at the time of the examination. Hence, the application of the model lies mainly in so-called…

Two modification formulas are presented for the test information function in order to provide better measures of local accuracies of the estimation of "theta" when maximum likelihood estimation is used to provide the estimate of ability "theta." A minimum bound of any estimator, biased or unbiased, is considered; and Formula 1…

The conventional method of measuring ability--based on items with assumed true parameter values obtained from a pretest--is compared to a Bayesian method that deals with the uncertainties of such items. Data from a 1987 American College Testing Program mathematics test indicate that maximum likelihood/Bayesian techniques underestimate uncertainty.…

Several models for optimizing incomplete sample designs with respect to information on the item parameters are presented. The following cases are considered: (1) known ability parameters; (2) unknown ability parameters; (3) item sets with multiple ability scales; and (4) response models with multiple item parameters. The models are able to cope…

Dichotomous search strategies (DSSs) for computerized adaptive testing are similar to golden section search strategies (GSSSs). Each middle point of successive search regions is a testing point. After each item is administered, the subject's obtained score is compared with the expected score at successive testing points. If the subject's obtained…