Diagnostic classification models (DCMs) are statistical models that provide diagnostic information about the mastery state of examinees’ knowledge component or attributes. DCMs classify examinees based on these specified attributes, providing fine-grained and multidimensional diagnostic information. This information can be used by educators in designing targeted instructional interventions to enhance student performance. In DCMs, the inclusion of DIF analysis and effect size measures holds significant importance. DIF analysis enables the identification of potential biases and ensures test fairness in diagnostic assessments by detecting items that function differently across different groups. This process enhances the accuracy of diagnostic classifications by identifying items that may unfairly advantage or disadvantage certain groups. Furthermore, the incorporation of effect size measures in DIF analysis provides valuable insight into the practical significance of DIF. The effect size measures facilitate the interpretation of DIF results and aid in decision-making regarding the treatment of DIF items. This dissertation consists of two studies that address DIF analysis in a general DCM framework. The first study focuses on evaluating the performance of the Wald DIF detection method using the LCDM as a general framework under various conditions. Through simulation conditions, we investigate the performance of Wald DIF under the LCDM model and compare its performance with the likelihood ratio test (LRT) for DIF detection. In the second study, we investigate the practical significance of DIF in DCMs. We examine criteria based on the degree to which DIF items impact DCM classifications and reliability. A simulation study is conducted to investigate the effects of DIF on classifications, and the results are compared with the unsigned area (UA) effect size measure to provide guidelines for flagging DIF items.
