Up-and-Down Procedures for Approximating Optimal Designs Using Person-Response Functions

Algorithms developed for item selection in computerized adaptive testing are exclusively from the item response theory perspective, where responses are examined at the item level. They are limited when all item characteristics are not readily known. This paper illustrates an item selection algorithm using person response functions. When targeting a single percentile, median difficulty level can be an estimate of the person’s ability level. Often however, estimating more than one percentile or the entire person response function is desirable. This study considered optimal designs that either minimize the variance of one percentile estimate or a function of the variance-covariance ellipse jointly for all parameter estimates. Due to the problem that an optimal design for nonlinear models depends on unknown parameters, sequential up-and-down designs for approximating optimal designs are considered. Examples are provided to illustrate the efficiency of the procedures.