Computational procedures for probing interactions in OLS and logistic regression: SPSS and SAS implementations

Abstract

924Behavioral science researchers long ago moved beyond the business of theorizing about and testing simple bivariate cause and effect relationships, since few believe that any effects are independent of situational, contextual, or individual-difference factors. Furthermore, we understand some variable's effect on another better when we understand what limits or enhances this relationship, or the boundary conditions of the effect-for whom or under what circumstances the effect exists and where and for whom it does not. Theoretical accounts of an effect can be tested and often are strengthened by the discovery of moderators of that effect. So testing for moderation of effects, also called interaction, is of fundamental importance to the behavioral sciences.A moderated effect of some focal variable F on outcome variable Y is one in which its size or direction depends on the value of a third, moderator variable M. Analytically, moderated effects reveal themselves statistically as an interaction between F and M in a mathematical model of Y. In statistical models such as ordinary least squares (OLS) regression or logistic regression, moderation effects frequently are tested by including the product of the focal independent variable and the moderator as an additional predictor in the model. When an interaction is found, it should be probed in order to better understand the conditions (i.e., the values of the moderator) under which the relationship between the focal predictor and the outcome is strong versus weak, positive versus negative, and so forth.One approach for probing interactions that we have seen used in the literature is the subgroup analysis or separate regressions approach, where the data file is split into various subsets defined by values of the moderator and the analysis is repeated on these subgroups. But this method does not properly represent how the focal predictor variable's effect varies as a function of the moderator, especially when additional variables in the model are used as statistical controls. For details about the problems with this method-a method we do not recommend-see Newsom, Prigerson, Schulz, and Reynolds (2003) and Stone-Romero and Anderson (1994).Fortunately, there are more rigorous and appropriate methods for probing interactions in linear models, two of which we will describe in this article. The first method we discuss, the pick-a-point approach, is one of the more commonly used. This approach involves selecting representative values (e.g., high, moderate, and low) of the moderator variable and then estimating the effect of the focal predictor at those values (see, e.g., Aiken & West, 1991;Cohen, Cohen, West, & Aiken, 2003;Jaccard & Turrisi, 2003). A difficulty with this approach is that, frequently, there are no nonarbitrary guidelines for picking the points at which to probe the interaction. An alternative is the Johnson-Neyman (J-N ) technique (Johnson & Fay, 1950;Johnson & Neyman, 1936;Potthoff, 1964) Researchers often hypothesize moderated effects, in which the effect of ...

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