INTERACTION, NONLINEARITY, AND MULTICOLLINEARITY - IMPLICATIONS FOR MULTIPLE-REGRESSION

Moderated Hierarchical Multiple Regression (MHMR) is typically used to test for the presence of interactions. When an interaction term is co mposed of correlated variables, linearity and additivity become confou nded. The result of this confounding is that an interaction term in MH MR may be statistically significant only because of its overlap with u nmeasured nonlinear terms. I recommend that squared terms be used as c ovariates in such situations and show that the resulting loss of power with respect to the test of significance for the interaction term is limited to that associated with the loss of degrees of freedom and is therefore negligible if it exists at all.