Improved Performance of Model Fit Indices with Small Sample Sizes in Cognitive Diagnostic Models

Selecting an appropriate cognitive diagnostic model (CDM) for data analysis is always challenging. Studies have explored several model fit indices for CDMs. The common results of these studies indicate that Q-matrix misspecifications lead to poor performance of the model fit indices in the context of CDMs. Thus, this study explored whether model fit indices improve performance with a modified Q-matrix. The average class size has reduced to 23 students in Taiwan because of the low birth rate; therefore, the study sought the effect of sample size on the performance of model fit indices. The results showed that Akaike’s information criterion (AIC) was an excellent model fit index in small samples. Model fit indices with the modified Q-matrix presented superior performance.