The Effects of Q-Matrix Misspecification on Parameter Estimates and Classification Accuracy in the DINA Model

This article reports a study that investigated the effects of Q-matrix misspecifications on parameter estimates and misclassification rates for the deterministic-input, noisy ``and'' gate (DINA) model, which is a restricted latent class model for multiple classifications of respondents that can be useful for cognitively motivated diagnostic assessment. In this study, a Q-matrix for an assessment mapping all 15 possible attribute patterns based on four independent attributes was misspecified by changing one ``0'' or ``1'' for each item. This was done in a way that ensured that certain attribute combinations were completely deleted from the Q-matrix, and certain incorrect dependency relationships between attributes were represented. Results showed clear effects that included an itemspecific overestimation of slipping parameters when attributes were deleted from the Q-matrix, an item-specific overestimation of guessing parameters when attributes were added to the Q-matrix, and high misclassification rates for attribute classes that contained attribute combinations that were deleted from the Q-matrix.