Sun X, Zhang T, Nie C, Song N, Xin T. Combining regularization and logistic regression model to validate the Q-matrix for cognitive diagnosis model.
THE BRITISH JOURNAL OF MATHEMATICAL AND STATISTICAL PSYCHOLOGY 2024. [PMID:
38646968 DOI:
10.1111/bmsp.12346]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/04/2023] [Revised: 12/17/2023] [Accepted: 04/03/2024] [Indexed: 04/25/2024]
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.
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