Type 1 Errors of Interaction Effects Due to Collinearity of Primary Terms

Abstract

In this paper we illustrate conditions where, in OLS regression, statistically significant interaction term results may in fact be Type 1 errors. It is known, though not widely considered in practice, that real but omitted quadratic effects of correlated primary variables from an otherwise perfectly specified regression can create Type 1 errors in the form of false interaction effects. We confirm this result and demonstrate that Type 1 errors may occur with primary term correlations as low as 0.2 for samples of 100. If regressions are perfectly specified once quadratic terms are included, the simple solution of including these terms will eliminate most Type 1 errors. However, we demonstrate analytically and via simulation that in many realistic data situations this solution may create the exact problem it attempts to solve: if primary terms are correlated via the presence of an unobservable common factor, including quadratic terms may create a Type 1 interaction term error rather than eliminate it. A single, real quadratic effect may create multiple interaction term Type 1 errors through primary-term correlations. VIF statistics will remain low and ?R2 values will appear high, oblivious to the Type 1 errors. We urge scholars studying interaction effects not to ignore quadratic terms, but to present separate regression results both with and without quadratic terms. We conclude that, if interaction results are of the same sign and statistically significant in both specifications, the results are unlikely to be Type 1 errors. Interaction hypotheses can then be confidently supported.