Assessments built on a theory of learning progressions are promising formative tools to support learning and teaching. The quality and usefulness of those assessments depend, in large part, on the validity of the theory-informed inferences about student learning made from the assessment results. In this study, we introduced an approach to address an important challenge related to examining theorized level links across progressions. We adopted the method to analyze response data for three learning progressions: Equality and Variable, Functions and Linear Functions, and Proportional Reasoning in middle-school mathematics . Multidimensional item response theory models were fit to the data to evaluate the postulated learning levels and level links. Our findings supported the theoretical hypotheses for Functions and Linear Functions, and Proportional Reasoning. Thus, items measuring these progressions can be used to develop formative assessment tasks, and assist instructional practices. Our findings did not support the theory underlying Equality and Variable. Implications for assessment developers and users, and future directions for research were discussed.