On Regression Standardization for Moments

Polynomial regression models can be used to standardize means of endogenous variables for moments of exogenous variables. In other words, standardized means obtained from polynomial models adjust for group differences in location and shape parameters that characterize distributions of exogenous variables. The suggested approach is a natural extension of the conventional method of regression standardization for means (or first moments) of exogenous variables, and it is a more direct analogue to standardization methods used in demography. We also give simple methods that can be used to test the significance of various components of a difference between two means.