Distinguishing between moderator and quadratic effects in multiple regression. [article]. - MacCallum, Robert C.
Moderated regression analysis is commonly used to test for multiplicative influences of independent variables in regression models. D. Lubinski and L. G. Humphreys (1990) have shown that significant moderator effects can exist even when stronger quadratic effects are present. They recommend comparing effect sizes associated with both effect types and selecting the model that yields the strongest effect. The authors show that this procedure of comparing effect sizes is biased in favor of the moderated model when multicollinearity is high because of the differential reliability of the quadratic and multiplicative terms in the regression models. Fortunately, levels of multicollinearity under which this bias is most problematic may be outside the range encountered in many empirical studies. The authors discuss causes and implications of this phenomenon as well as alternative procedures for evaluating structural relationships among variables. -- (from the author)