Test-level and Item-level Model Fit Comparison of General vs. Specific Diagnostic Classification Models: A Case of True DCM

The current study compared the model fit indices, skill mastery probabilities, and classification accuracy of six Diagnostic Classification Models (DCMs): a general model (G-DINA) against five specific models (LLM, RRUM, ACDM, DINA, and DINO). To do so, the response data to the grammar and vocabulary sections of a General English Achievement Test, designed specifically for cognitive diagnostic purposes from scratch, was analyzed. The results of the test-level-model fit values obtained strong evidence in supporting the G-DINA and LLM models possessing the best model fit. In addition, the ACDM and RRUM were almost very identical to that of the G-DINA. The value indices of the DINO and DINA models were very close to each other but larger than those of the G-DINA and LLM. The model fit was also investigated at the item level, and the results revealed that model selection should be performed at the item level rather than the test level, and most of the specific models might perform well for the test. The findings of this study suggested that the relationships among the attributes of grammar and vocabulary are not ‘either-or’ compensatory or non-compensatory but a combination of both.