Combining regularization and logistic regression model to validate the Q-matrix for cognitive diagnosis model

Abstract

Q-matrix is an important component of most cognitive diagnosis models (CDMs); however, it mainly relies on subject matter experts' judgements in empirical studies, which introduces the possibility of misspecified q-entries. To address this, statistical Q-matrix validation methods have been proposed to aid experts' judgement. A few of these methods, including the multiple logistic regression-based (MLR-B) method and the Hull method, can be applied to general CDMs, but they are either time-consuming or lack accuracy under certain conditions. In this study, we combine the L₁ regularization and MLR model to validate the Q-matrix. Specifically, an L₁ penalty term is imposed on the log-likelihood of the MLR model to select the necessary attributes for each item. A simulation study with various factors was conducted to examine the performance of the new method against the two existing methods. The results show that the regularized MLR-B method (a) produces the highest Q-matrix recovery rate (QRR) and true positive rate (TPR) for most conditions, especially with a small sample size; (b) yields a slightly higher true negative rate (TNR) than either the MLR-B or the Hull method for most conditions; and (c) requires less computation time than the MLR-B method and similar computation time as the Hull method. A real data set is analysed for illustration purposes.