Examining Parameter Invariance in a General Diagnostic Classification Model

The present study aimed at investigating invariance of a diagnostic classification model (DCM) for reading comprehension across gender. In contrast to models with continuous traits, diagnostic classification models inform mastery of a finite set of latent attributes, e.g., vocabulary or syntax in the reading context, and allow to provide fine grained feedback to learners and instructors. The generalized deterministic, noisy "and" gate (G-DINA) model was fit to item responses of 1000 male and female individuals to a high-stakes reading comprehension test. Use of the G-DINA model allowed for minimal assumption on the relationship of latent attribute profiles and item-specific response probabilities, i.e., the G-DINA model can represent compensatory or non-compensatory relationships of latent attributes and response probabilities. Item parameters were compared across the two samples, and only a small number of item parameters were statistically different between the two groups, corroborating the result of a formal measurement invariance test based on the multigroup G-DINA model. Neither correlations between latent attributes were significantly different across the two groups, nor mastery probabilities for any of the attributes. Model selection at item level showed that from among the 18 items that required multiple attributes, 16 items picked different rules (DCMs) across the groups. While this seems to suggest that the relationship among the attributes of reading comprehension differs across the two groups, a closer inspection of the rules picked by the items showed that almost in all cases the relationships were very similar. If a compensatory DCM was suggested by the G-DINA framework for an item in the female group, a model belonging to the same family resulted for the male group.