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With the availability of various CDM parameterizations that are different in nature, the potential and consequence to incorrectly specify the CDM cannot be ignored. Based on simulation study, this research extended previous simulation studies to consider different percentages of CDM misspecification and parameter values that were close to practical situations. We also evaluated the selected fit measures at both the test and item levels. It turned out that these added factors were not only challengeable to the simulation study but also influential on previous findings substantially. An empirical example with real data was used to illustrate how these fit measures can be employed to detect CDM misspecifications at both the test and item levels in practice.