| As cognitive diagnostic models (CDMs) become increasingly popular in modern educational measurement, it is important to develop a person fit index that examines the appropriateness of a CDM for each individual examinee. The purpose of this study is to propose a new person fit index, the hierarchy misfit index (HMI), for CDMs, and test the power and type 1 error of the HMI at detecting misfitting item response vectors using a simulation study. The results of the simulation study showed that the HMI had high powers and acceptable type 1 errors when a test consisted of highly discriminating items. But when a test consisted of low discriminating items, the HMI's type 1 errors were too high to be acceptable. A comparison was also made with a previously developed person fit index, the hierarchical consistency index, (HCI). The results showed that the HMI performed better in high item discrimination conditions. |
