Relative and Absolute Fit Evaluation in Cognitive Diagnosis Modeling

As with any psychometric models, the validity of inferences from cognitive diagnosis models (CDMs) determines the extent to which these models can be useful. For inferences from CDMs to be valid, it is crucial that the fit of the model to the data is ascertained. Based on a simulation study, this study investigated the sensitivity of various fit statistics for absolute or relative fit under different CDM settings. The investigation covered various types of model-data misfit that can occur with the misspecifications of the Q-matrix, the CDM, or both. Six fit statistics were considered: -2 log likelihood (-2LL), Akaike's information criterion (AIC), Bayesian information criterion (BIC), and residuals based on the proportion correct of individual items (p), the correlations (r), and the log-odds ratio of item pairs (l). An empirical example involving real data was used to illustrate how the different fit statistics can be employed in conjunction with each other to identify different types of misspecifications. With these statistics and the saturated model serving as the basis, relative and absolute fit evaluation can be integrated to detect misspecification efficiently.