An exploratory discrete factor loading method for q-matrix specification in cognitive diagnostic models

Abstract

The Q-matrix is usually unknown for many existing tests. If the Q-matrix is specified by subject matter experts but contains a large amount of misspecification, it will be difficult for the recovery of a high-quality Q-matrix through a validation method, because the performance of the validation method relies on the quality of a provisional Q-matrix. Under these two situations above, an exploratory technique is necessary. The purpose of this study is to explore a simple method for Q-matrix specification, called a discretized factor loading (DFL) method, in which exploratory factor analysis regarding latent attributes as latent factors is used to estimate a factor loading matrix after which a discretization process is employed on the factor loading matrix to obtain a binary Q-matrix. A series of simulation studies were conducted to investigate the performance of the DFL method under various conditions. The simulation results showed that the DFL method can provide a high-quality provisional Q-matrix.