"Effect Equations" or "Effect Coefficients": A Note on the Visual and Verbal Presentation of Multiple Regression Interactions

Abstract

Multiple regression interaction terms are appearing with increasing frequency in sociologi- cal literature but the verbal and diagrammatic procedures for presenting interactions remain rela- tively unknown. The precise interpretation of multiplicative interactions as partial derivatives pro- vides a background for a simple factoring procedure which is applicable to the most prevalent usage of interactions. Both correct and incorrect methods for diagramming interactions are discussed. An extended example illustrates how the incorrect interpretation of a product term as a real variable can lead one to provide erroneous indirect effect interpretations and how this can also tempt one to make the more serious error of estimating improper equations.