The major purpose of this study is to describe a conceptual framework for examining differential item functioning (DIF) and differential person functioning (DPF) as types of model-data misfit within the context of assessing students with disabilities. Specifically, DIF and DPF can be viewed through the lens of residual analyses. Residual analyses can be used to explore DIF (item fit) as well as extended to explore DPF (person fit). One of the advantages of this conceptual framework is that the size of the subgroups can be quite small with interpretable results produced even for individuals. To illustrate this conceptual framework, Rasch measurement theory is used as the item response theory model. Methodological and theoretical issues are discussed. Data from a high-stakes assessment in mathematics in Georgia (Grade 7, geometry items) are used to illustrate the conceptual framework for students with disabilities. The substantive research questions used to illustrate the conceptual framework addresses whether modifications in test administration (use of resource guides or calculators) influence item functioning for students with disabilities (DIF analyses) and whether students with various disabilities differentially benefit from these modifications (DPF analyses). (Contains 2 figures and 5 tables.)