Theoretical and mathematical issues related to the study of interaction effects are discussed. Constraints imposed by the theoretical expectation of ordinal or monotone interactions are defined by the general concept of inversion values. The mathematical constraints implied by these values are demonstrated by the derivation of a general formula. Further definitions related to this general formula are discussed for qualitative and quantitative variables. It is argued that interaction effects of substantial magnitude may not be routinely detected in behavioral science because many interactive theories may be implicitly ordinal. Levels of predictability common to behavioral science make such effects mathematically nonexistent, and thus impossible to detect. To have strong ordinal moderation, there must be a strong effect to be moderated.
Rogers, William M., "Theoretical and Mathematical Constraints of Interactive Regression Models" (2002). Peer Reviewed Articles. 6.