Addressing Quantitative and Qualitative Hypotheses Using Regression Models with Equality Restrictions and Predictors Measured in Common Units

In regression, some or all of the predictors may be measured in common units: e.g. X ₁ = carbohydrate calories, X₂ = protein calories, X₃ = fat calories. Such predictors can occur in disciplines as diverse as business, economics, education, medicine, nutrition, psychology, sport science, etc. Predictors in common units can lead to unique quantitative and qualitative hypotheses that can be addressed by imposing equality restrictions on the regression weights (e.g. (Formula presented.)). A simple device, total score substitution, is available for constraining regression coefficients to be equal in a variety of regression applications. Applications to linear, moderated linear, and polynomial models are described, but extensions to generalized linear models and multilevel linear models are also possible. Total score substitution in linear and moderated regression is illustrated using high school coursework and mathematics achievement data. Data, code (R, SPSS, SAS), and output are publicly available.