Detection of Q-matrix misspecification using two criteria for validation of cognitive structures under the Least Squares Distance Model

Cognitive Diagnostic Models (CDMs) aim to provide information about the degree to which individuals have mastered specific attributes that underlie the success of these individuals on test items. The Q-matrix is a key element in the application of CDMs, because contains links item-attributes representing the cognitive structure proposed for solve the test. Using a simulation study we investigated the performance of two model-fit statistics (MAD and LSD) to detect misspecifications in the Q-matrix within the least squares distance modeling framework. The manipulated test design factors included the number of respondents (300, 500, 1000), attributes (1, 2, 3, 4), and type of model (conjunctive vs disjunctive). We investigated MAD and LSD behavior under correct Q-matrix specification, with Q-misspecifications and in a real data application. The results shows that the two model-fit indexes were sensitive to Q-misspecifications, consequently, cut points were proposed to use in applied context.