Moderated Hierarchical Multiple Regression (MHMR) is typically used to test for the presence of interactions. When an interaction term is composed of correlated variables, linearity and additivity become confounded. The result of this confounding is that an interaction term in MHMR may be statistically significant only because of its overlap with unmeasured nonlinear terms. I recommend that squared terms be used as covariates 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.
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