A Deterministic Learning Algorithm Estimating the Q-Matrix for Cognitive Diagnosis Models

Abstract

The goal of an exam in cognitive diagnostic assessment is to uncover whether an examinee has mastered certain attributes. Different cognitive diagnosis models (CDMs) have been developed for this purpose. The core of these CDMs is the Q-matrix, which is an item-to-attribute mapping, traditionally designed by domain experts. An expert designed Q-matrix is not without issues. For example, domain experts might neglect some attributes or have different opinions about the inclusion of some entries in the Q-matrix. It is therefore of practical importance to develop an automated method to estimate the Q-matrix. This research proposes a deterministic learning algorithm for estimating the Q-matrix. To obtain a sensible binary Q-matrix, a dichotomizing method is also devised. Results from the simulation study shows that the proposed method for estimating the Q-matrix is useful. The empirical study analyzes the ECPE data. The estimated Q-matrix is compared with the expert-designed one. All analyses in this research are carried out in R.

Approximate Invariance Testing in Diagnostic Classification Models in the Presence of Attribute Hierarchies: A Bayesian Network Approach

“…In this paper, we assumed that the entries in the Q-matrix are known; however, see, for instance, Refs. [23][24][25][26] for data-driven approaches for learning the structure of the Q-matrix.…”

Approximate Invariance Testing in Diagnostic Classification Models in the Presence of Attribute Hierarchies: A Bayesian Network Approach

“…Construction of the Q-matrix is generally informed by theory or by domain experts (e.g., Templin & Hoffman, 2013). In this paper, we assume that the entries in the Q-matrix are known, however, see, for instance, Chen et al (2021), Chung (2014), and Culpepper (2019 for data-driven approaches for learning the structure of the Q-matrix.…”