D-Optimal Sequential Sampling Designs for Item Response Theory Models

Abstract

The selection of optimal designs in IRT models encounters at least two problems. The first problem is that Fisher’s information matrix is generally not independent of the values of the IRT parameters, and the second problem is that the design points are unknown parameters and have to be estimated together with the other parameters. In this study, these two problems are taken care of by a sequential design procedure. This procedure is a modification of a D-optimality procedure proposed by Wynn (1970) . The results show that this algorithm leads to consistent estimates and that errors in selecting the abilities generally do not affect optimality very much.