Determining targets for multi-stage adaptive tests using integer programming

This paper considers a multi-stage adaptive test (MST) where the testlets at each stage are determined prior to the administration. The assembly of a MST requires target information and target response functions for the MST design. The targets are chosen to create tests with accurate scoring and high utilization of items in an operational pool. Forcing all MSTs to have information and response function plots to be within an interval about the targets will yield parallel MSTs, in the sense that standardized paper-and-pencil tests are considered parallel. The objective of this paper is to present a method to determine targets for the MST design based on an item pool and an assumed distribution of examinee ability. The approach is applied to a Skills Readiness Inventory test designed to identify logical reasoning deficiencies of examinees. This method can be applied to obtain item response theory targets for a linear test as this is a special case of a MST.