While the SAT-Math test is designed to measure one “construct” – i.e. overall mathematical aptitude at the High School level, – it surely could be analyzed to reveal different abilities for algebra and geometry, for example. When analyzing a semester-long course, one would naturally expect different abilities on different topics (e.g. energy vs. momentum); on different types of problems (e.g. conceptual vs. calculational), or within one lesson (e.g. Newton’s 2^{nd} law vs Newton’s 3^{rd} law). Hence RELATE has done considerable work on multi-dimensional analyses like factor analysis, or generalizations of IRT where the discriminations or questions and the abilities of students are multidimensional.

BRS12 *Multidimensional Student Skill with Collaborative Filtering*. Y. Bergner, S. Rayyan, D. T. Seaton, and D. E. Pritchard, Physics Education Research Conference 2012, Philadelphia, PA

PSD 19 *Mining Students Pre-instruction Beliefs for Improved Learning* Angel Perez-Lemonche, John Stewart, Byron Drury, Rachael Henderson, Alex Shconski, and David E Pritchard LAS 2019 Proceedings

PCP18 *Mining Student Misconceptions from Pre- and Post-Test Data*. Angel Perez-Lemonche, Byron Coffin Drury, David Pritchard *EDM Proceedings 2018* KE Boyer and M Yudelson eds p 449 (2018)

*SDW21* *Examining the relation of correct knowledge and misconceptions using the nominal response model* John Stewart , Byron Drury, James Wells, Aaron Adair, Rachel Henderson, Yunfei Ma, Ángel P´erez-Lemonche, and David Pritchard PHYSICAL REVIEW PHYSICS EDUCATION RESEARCH 17,010122 (2021)