Background: Although research in cognitive psychology suggests refraining from investigating cognitive skills inisolation, many cognitive diagnosis model (CDM) examples do not take hierarchical attribute structures into account. When hierarchical relationships among the attributes are not considered, CDM estimates may be biased. Method: The current study, through simulation and real data analyses, examines the impact of different MMLE-EM approaches on the item and person parameter estimates of the G-DINA, DINA and DINO models when attributes have a hierarchical structure. A number of estimation approaches that can result from modifying either the Q-matrix or prior distribution are proposed. Impact of the proposed approaches on item parameter estimation accuracy and attribute classification are investigated. Results: For the G-DINA model estimation, the Q-matrix type (i.e, explicit vs. implicit) has greater impact than structuring the prior distribution. Specifically, explicit Q-matrices result in better item parameter recovery and higher correct classification rates. In contrast, structuring the prior distribution is more influential on item and person parameter estimates for the reduced models. When prior distribution is structured, the Q-matrix type has almost no influence on item and person parameter estimates of the DINA and DINO models. Conclusion: We can conclude that the Q-matrix type has a significant impact on CDM estimation, especially when the estimating model is G-DINA.