Attribute structure is an explicit way of presenting the relationship between attributes in diagnostic measurement. The specification of attribute structures directly affects the classification accuracy resulted from psychometric modeling. This study provides a conceptual framework for understanding misspecifications of attribute structures. Under the framework, each attribute structure can be represented through an external shape and an internal organization. A simulation study and an application example were used to investigate how misspecification of external shapes and internal organizations affects model fit and item fit assessments, and respondent classification. The proposed framework and simulation results aim to support using attribute structures to (a) develop better diagnostic assessments and (b) inform theories of constructs.