Item Selection Algorithms in Computerized Adaptive Test Comparison Using Items Modeled with Nonparametric Isotonic Model

Abstract

A computerized adaptive test (CAT) is used in this paper where the item bank is calibrated by using the nonparametric isotonic model proposed by Luzardo and Rodriguez (Quantitative psychology research. Springer International Publishing, Switzerland, pp. 99-108, 2015). The model is based on the estimation of the inverse of the item characteristic curves (ICC), and it uses a two-stage process. First, it uses the Ramsay nonparametric estimator of the ICC (Ramsay In Psychometrika 56:611–630, 1991) and then it estimates the density function of the inverse ICC by using Ramsay’s estimator. By integrating the density function and then symmetrizing it, we obtain the result. Xu and Douglas (Psychometrika 71:121–137, 2006) studied the possibility of using Ramsay’s nonparametric model in a CAT. They explored the possible methods of item selection but they did not use Fisher’s maximum information method because the derivatives of the ICC may not be estimated well. We present, for the isotonic model, a suitable way to estimate the derivatives of the ICCs and obtain a formula for item information that allows us to use the maximum information criterion. This work focuses on comparing three methods for selecting items in the CAT: random selection, the maximum Fisher information criterion with the isotonic model, and the Kullback-Leibler information criterion.