The application of diagnostic classification models (DCMs) in the field of educational measurement is getting more attention in recent years. To make a valid inference from the model, it is important to ensure that the model fits the data. The purpose of the present study was to investigate the performance of the limited information goodness-of-fit statistic Mord in the polytomous response DCMs with the presence of hierarchical attribute structures. The first simulation study investigated the empirical Type I error rates of the Mord statistic under the null hypothesis when the model and data were perfectly fitted. The second simulation study explored the empirical rejection rate of M[subscript ord] under different types of misspecifications: model misspecification, attribute hierarchy misspecification, and Q-matrix misspecification. The impact of test length, item quality, attribute structure, marginal/conditional probability of the mastery of attributes, and the number of response categories were investigated. The results indicated that the M[subscript ord] statistic demonstrated well-calibrated Type I error rates under the null conditions with different types of hierarchical attribute structures. When there were model-data misfits, the M[subscript ord] statistic showed high empirical rejection rates in detecting the misspecified sDINA and sDINO but didn't show enough power to detect the sC-RUM. The M[subscript ord] also exhibited high empirical rejection rates when the generating attribute structure was non-strict hierarchical, but the fitted structure was strict hierarchical. Besides, it was sensitive when the sequence of parent and child attributes was reversed. However, the M[subscript ord] statistic couldn't detect the omission of hierarchical attribute connections. When there were Q-matrix misspecifications, the M[subscript ord] statistic showed extremely high empirical rejection rates in the condition of Q-matrix under-specification but was not sensitive to the Q-matrix over-specification. The higher proportion of Q-matrix misspecification led to higher Mord rejection rates. The item quality exhibited a huge influence on the performance of the M[subscript ord] statistic. The M[subscript ord] statistic demonstrated higher empirical rejection rates with higher item quality, longer test length, fewer item response categories, and lower marginal/conditional probability of the mastery of attributes. The types of attribute structure also demonstrated slight influences on the rejection rates of the M[subscript ord] statistics under some circumstances. The performance of the RMSEA[subscript ord] and SRMSR were explored in the present study to assess the degree of misfit and absolute model fit. The results indicated that the frequently used cut-off value of 0.05 was not appropriate in the framework of polytomous response DCMs. The magnitude of RMSEA[subscript ord] and SRMSR values varied in different situations. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://bibliotheek.ehb.be:2222/en-US/products/dissertations/individuals.shtml.]