A Model for Optimal Constrained Adaptive Testing

Abstract

A model for constrained computerized adaptive testing is proposed in which the information in the test at the trait level (0) estimate is maximized subject to a number of possible constraints on the content of the test. At each item-selection step, a full test is assembled to have maximum information at the current 0 estimate, fixing the items already administered. Then the item with maximum in-formation is selected. All test assembly is optimal because a linear programming (LP) model is used that automatically updates to allow for the attributes of the items already administered and the new value of the 0 estimator. The LP model also guarantees that each adaptive test always meets the entire set of constraints. A simulation study using a bank of 753 items from the Law School Admission Test showed that the 0 estimator for adaptive tests of realistic lengths did not suffer any loss of efficiency from the presence of 433 constraints on the item selection process.