Test Assembly for Cognitive Diagnosis Using Mixed-Integer Linear Programming

One purpose of cognitive diagnostic model (CDM) is designed to make inferences about unobserved latent classes based on observed item responses. A heuristic for test construction based on the CDM information index (CDI) proposed by Henson and Douglas (2005) has a far-reaching impact, but there are still many shortcomings. He and other researchers had also proposed new methods to improve or overcome the inherent shortcomings of the CDI test assembly method. In this study, one test assembly method of maximizing the minimum inter-class distance is proposed by using mixed-integer linear programming, which aims to overcome the shortcomings that the CDI method is limited to summarize the discriminating power of each item into a single CDI index while neglecting the discriminating power for each pair of latent classes. The simulation results show that compared with the CDI test assembly and random test assembly, the new test assembly method performs well and has the highest accuracy rate in terms of pattern and attributes correct classification rates. Although the accuracy rate of the new method is not very high under item constraints, it is still higher than the CDI test assembly with the same constraints.