Interaction Effects: Centering, Variance Inflation Factor, and Interpretation Issues

Research hypotheses that include interaction effects should be of more interest to educational researchers, especially since issues related to centering and interpretation of the variance inflation factor have been introduced. The purpose of this paper was to examine interaction effects in the context of centered versus uncentered variables and the variance inflation factor, especially upon the interpretation of interaction effects. Results indicated that centering of variables was required when examining interaction effects, uncentered variables impacted the variance inflation factor values, and separate regression equations have important interpretation outcomes in the presence of non-significant interaction effects. istorically, hypotheses that specify testing interaction effects before examining main effects have appeared under the framework of analysis of variance. In the 1960’s with the emergence of multiple regression, coding for interaction effects was introduced. Faculty who taught multiple regression therefore usually included instruction on dummy coding to obtain a test of interaction effects (Fox, 1997). Today, depending upon the textbook used, analysis of variance with A x B interaction effect may be covered without any corresponding interaction effect presentation given for multiple regression (Hinkle, Wiersma, & Jurs, 1998). Much of the published research literature seems to only examine main effects or linear effects. In practice, A x B interactions are only found in a few published journal articles, A x B x C interactions, are less common, and A x B x C x D interactions are even more scarce. Only a few 5-way interactions have ever been published. The reason is that such higher level interaction effects are extremely difficult to interpret. Interaction effects that are categorical in nature, involve multiplicative continuous variables, or hypothesize quadratic or cubic terms are rare (Schumacker & Marcoulides, 1998). Research hypotheses that include interaction effects should be of more interest to educational researchers, especially since issues related to centering (Aiken & West, 1991) and interpretation of the variance inflation factor (Freund, Littell, and Creighton, 2003) have been introduced. The purpose of this paper is to examine interaction effects in the context of centered versus uncentered variables and the variance inflation factor, especially upon the interpretation of interaction results. Theoretical Framework The effects of predictor scaling on coefficients of regression equations (centered versus uncentered solutions and higher order interaction effects (3-way interactions; categorical by continuous effects) has thoughtfully been covered by Aiken and West (1991). Their example illustrates that considerable multicollinearity is introduced into a regression equation with an interaction term when the variables are not centered. The variance inflation factor should detect the degree of multicollinearity when variables are uncentered (Freund, Little, & Creighton, 2003). The variance inflation factor as a measure of the degree of multicollinearity however has not been examined in context with centered versus uncentered variables in a regression equation containing interaction effects. Centering Centering is defined as subtracting the mean (a constant) from each score, X, yielding a centered score. Aiken & West (1991) demonstrated that using other transformations, additive constant, or uncentered scores can have a profound effect on interaction results. Regression with higher order terms has covariance between interaction terms (XZ) and each component (X and Z) depends in part upon the means of the individual predictors. Rescaling, changes the means, thus changes the predictor covariance, yielding different regression weights for the predictors in the higher order function. Centering is therefore an important step when testing interaction effects in multiple regression to obtain a meaningful interpretation of results. Centering the variables places the intercept at the means of all the variables. A regression equation with an intercept is often misunderstood in the context of multicollinearity. The intercept is an estimate of the response at the origin where all independent variables are zero, thus inclusion of the intercept in the

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