143 – New Ideas in Advanced Undergraduate Courses
Making Use of Atypical Regression Models for Theory Building
Ernest Davenport Jr., PhD
University of Minnesota College of Education & Human Development
Haijiang Kuang, PhD
Pearson
Mark Davison, PhD
University of Minnesota College of Education & Human Development
Kyle Nickodem
University of Minnesota College of Education & Human Development
Qinjun Wang
University of Minnesota College of Education & Human Development
While investigators typically use one regression model to ascertain information regarding a theory, this presentation gives six equivalent regression models (for a 2-predictor model) with predictors and/or their mutual residuals as predictors that can lead to richer theory building. While each model is equivalent in significance and variance accounted for, the mix of raw and residual score predictors provide for testing different aspects of a theory. We have named the approach Total Information Regression Analysis (TIRA). We demonstrate the approach with data from the 2001 edition of Baccalaureate and Beyond. Undergraduate GPA is the criterion. For simplicity we use only two predictors, SATM and SATV (and their errors), but the approach is readily adaptable to more predictors (which will increase the number of potential equivalent models). We also give a geometric rationale for our procedure. The geometric rationale is especially helpful as half of the models presented are not obviously equivalent.