Optimization of Classical Reliability in Test Construction

Abstract

This article considers the problem of generating a test from an item bank using a criterion based on classical test theory parameters. A mathematical programming model is formulated that maximizes the reliability coefficient α, subject to logical constraints on the choice of items. The special structure of the problem is exploited with network theory and Lagrangian relaxation techniques. An empirical study shows that the method produces tests with high coefficient a subject to various practicable item constraints.