Diagnostic classification models used in conjunction with diagnostic assessments are to classify individual respondents into masters and nonmasters at the level of attributes. Previous researchers (Madison & Bradshaw, 2015) recommended items on the assessment should measure all patterns of attribute combinations to ensure classification accuracy, but in practice, certain attributes may not be measured by themselves. Moreover, the model estimation requires large sample size, but in reality, there could be unanswered items in the data. Therefore, the current study sought to provide suggestions on selecting between two alternative Q-matrix designs when an attribute cannot be measured in isolation and when using maximum likelihood estimation in the presence of missing responses. The factorial ANOVA results of this simulation study indicate that adding items measuring some attributes instead of all attributes is more optimal and that other missing data treatments should be sought if the percent of missing responses is greater than 5%.