Up-and-Down Procedures for Approximating Optimal Designs

Computerized adaptive testing has many advantages over the traditional paper-and-pencil tests. Algorithms developed for item selections focus on exclusively item response functions. However, person-response functions are more desirable when not all item characteristics are known. When targeting a single percentile, median difficulty level is an estimate of the person’s ability level. Often however, estimating more than one percentile or the entire person-response curve is desirable. This study considers optimal designs that either minimize the variance of one percentile estimate or a function of the variance-covariance eclipse 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.