The Use of Reparametrization and Constraints on Linear Models to Parse Qualitative and Quantitative Information for a Set of Predictors

The following study shows how reparameterizations and constraints of the general linear model can serve to parse quantitative and qualitative aspects of predictors. We demonstrate three different approaches. The study uses data from the High School Longitudinal Study of 2009 on mathematics course-taking and achievement as an example. Results show that all mathematics courses are not equally predictive of math achievement. Thus, taking into account qualitative aspects of mathematics courses is useful. The study ends with a justification of quantifying qualitative aspects of predictors relative to a criterion with extensions to other linear models.