Testing multiplicative models does not require ratio scales

Abstract

A method is outlined to test unambiguously for the presence of interaction when variables are measured on ratio, interval, or ordinal scales. The hierarchical multiple regression methodology is developed with specific reference to the expectancy model of motivation which hypothesizes that motivational force is a function of the product of expectancy (E) and valence (V). The test is shown to be invariant under all linear transformations of the form aX + b of E, V, or both E and V. This invariance is demonstrated with four hypothetical data sets, and is contrasted to the wide fluctuations in zero order correlations between motivational force and the E × V product shown by Schmidt 1973. Several criticisms of hierarchical multiple regression techniques are dealt with. The empirical indistinguishability of alternative formulations of multiplicative models is pointed out, and the interdependence of model testing and measurement is emphasized.