Clarifying the role of mean centring in multicollinearity of interaction effects

Abstract

Moderated multiple regression (MMR) is frequently employed to analyse interaction effects between continuous predictor variables. The procedure of mean centring is commonly recommended to mitigate the potential threat of multicollinearity between predictor variables and the constructed cross-product term. Also, centring does typically provide more straightforward interpretation of the lower-order terms. This paper attempts to clarify two methodological issues of potential confusion. First, the positive and negative effects of mean centring on multicollinearity diagnostics are explored. It is illustrated that the mean centring method is, depending on the characteristics of the data, capable of either increasing or decreasing various measures of multicollinearity. Second, the exact reason why mean centring does not affect the detection of interaction effects is given. The explication shows the symmetrical influence of mean centring on the corrected sum of squares and variance inflation factor of the product variable while maintaining the equivalence between the two residual sums of squares for the regression of the product term on the two predictor variables. Thus the resulting test statistic remains unchanged regardless of the obvious modification of multicollinearity with mean centring. These findings provide a clear understanding and demonstration on the diverse impact of mean centring in MMR applications.

Knowledge, Attitudes, and Practice about Evidence-Based Practice: A Jordanian Study

“…Predictor variables with significant correlation (pvalue<0.1) were selected for further analyses and added to the multiple regression model. Multicollinearity was not a problem as VIF values were less than three [21]. To answer research question number two and three, ANOVA with post hoc analysis was done.…”

Mean centering helps alleviate “micro” but not “macro” multicollinearity

“…Allison, 1977;Dalal & Zickar, 2012;Kromrey & Foster-Johnson, 1998;Shieh, 2011Shieh, , 2010Shieh, , 2009Smith & Sasaki, 1979). Furthermore, most researchers concur that mean centering X 1 and X 2 will reduce their correlations with the product term X 1 X 2 .…”

“…We note that the literature we just reviewed briefly also considers other related issues, including multicollinearity that arises due to power terms (e.g., X 2 ), not just product terms (Bradley & Srivastava, 1979), and the effects of non-normality and analogous effects on three-way interactions (Shieh, 2010). Some articles contain equations and proofs, and some offer demonstrations with very small data sets or simulations (e.g., Allison, 1977;Shieh, 2011). In our investigations that follow, we use all of these methods to offer a more comprehensive view of the micro and macro issues.…”

“…Figure 2 shows the average over the 1,000 pairs of regressions for the β 1 (or β 2 ) estimates (given that the strength of the relationship between X 1 and Y was the same as that between X 2 and Y, both main effect βs were equal, for simplicity). As we mentioned previously, it is known that a linear transformation like mean centering will not affect the highest order term in a model, in this case, the X 1 X 2 interaction term (Allison, 1977;Dalal & Zickar, 2012;Kromrey & Foster-Johnson, 1998;Shieh, 2011Shieh, , 2010Shieh, , 2009Smith & Sasaki, 1979), thus we focus on the results for the main effect predictors. Much like the plot in Fig.…”

Multicollinearity is a red herring in the search for moderator variables: A guide to interpreting moderated multiple regression models and a critique of Iacobucci, Schneider, Popovich, and Bakamitsos (2016)

“…I have debunked the myth that mean centering of X and M is necessary prior to the estimation of a model with an interaction between X and M. I cannot take credit for this, however, as this myth and it corollaries have been repeatedly debunked in the methodology literature yet doggedly persist in spite of that literature (see e.g., Cronbach, 1987;Echambadi & Hess, 2007;Edwards, 2009;Friedrich, 1982;Hayes et al, 2012;Irwin & McClelland, 2001;Kam & Franzese, 2007;Kromrey & Foster-Johnson, 1998;Shieh, 2011;Whisman & McClelland, 2005). To be sure, there are interpretational advantages associated with mean centering, but the differences in model coefficients and standard errors have nothing to do with reduced multicollinearity that results from mean centering.…”