A Binary Programming Approach to Automated Test Assembly for Cognitive Diagnosis Models

Automated test assembly (ATA) has been an area of prolific psychometric research. Although ATA methodology is well developed for unidimensional models, its application alongside cognitive diagnosis models (CDMs) is a burgeoning topic. Two suggested procedures for combining ATA and CDMs are to maximize the cognitive diagnostic index and to use a genetic algorithm. Each of these procedures has a disadvantage: The cognitive diagnostic index cannot control attribute-level information and the genetic algorithm is computationally intensive. The goal of this article is to solve both problems by using binary programming, together with the item discrimination indexes of Henson et al., for performing ATA with CDMs. The three procedures are compared in simulation. Advantages and disadvantages of each are discussed.