Usually there is agreement on facts, but there exist disagreements regarding the assessments of those facts.įor example, looking at the results of a moderated multiple regression of the form Y = b 0 + b 1 X 1 + b 2 X 2 + b 3 X 1 X 2 + ϵ from the “micro” perspective, that is, examining the individual predictors and regression coefficients, researchers agree that mean centering X 1 and X 2 has no effect on the product term X 1 X 2, nor the power with which the moderator effect may be detected (cf. No researchers believe that mean centering affects essential multicollinearity, and they differ on whether they believe that mean centering reduces nonessential multicollinearity.īeyond those basic points, there is less consistency among researchers’ points of view. “Essential” multicollinearity describes correlations between variables for constructs that are very likely to be correlated Aiken and West ( 1991, p.36) give the example of a likely correlation “between the age of a child and his/her developmental stage.” In contrast, “nonessential” multicollinearity describes correlations that arise due to issues of measurement or in the moderated multiple regression context, the fact that X 1 and X 2 are likely correlated with their product term X 1 X 2 because, of course, they are contained within it. The terms are not great, given that they are somewhat value-laden, but these terms are used in this literature (cf., Bradley & Srivastava, 1979 Dalal & Zickar, 2012 Shieh, 2010). Third, Aiken and West ( 1991) attribute to Marquardt ( 1980) the terminology of distinguishing “essential” and “nonessential” multicollinearity. Researchers of both camps mention the variables’ measurement properties as a plausible and defensible reason for mean centering (Dalal & Zickar, 2012 Echambadi & Hess, 2007 Irwin & McClelland, 2001 Jaccard, Wan, & Turrisi, 1990 Kromrey & Foster-Johnson, 1998). ![]() Researchers who do not believe the mean centering helps have no argument against mean centering per se for example, if researchers are working with variables whose measurements include arbitrary zeros, then it may be fruitful to mean center a variable such that results are interpretable with respect to the variable’s mean rather than to an arbitrary point of zero. Second, researchers who believe that mean centering will help clarify the regression results will obviously recommend that the variables X 1 and X 2 be mean centered before the product term is computed. Some researchers see this as a problem and others do not, and we will show that these different positions are largely a function of which results are under consideration however, researchers do not disagree that, empirically, the high correlations are likely. Let us begin with three points on which these scholars agree.įirst, when multiple regression models are expanded from a supposition of two main effects, Y = b 0 + b 1 X 1 + b 2 X 2 + ϵ, to a model in which there exists a multiplicative term to capture the interaction, Y = b 0 + b 1 X 1 + b 2 X 2 + b 3 X 1 X 2 + ϵ, the main effect variables (both X 1 and X 2) are often highly correlated with their composite product term ( X 1 X 2). We hope to contribute to the literature by clarifying the issues, reconciling the two perspectives, and quelling the current confusion regarding whether and how mean centering can be a useful practice.Ī number of scholars have considered issues related to mean centering with regard to the inclusion of product terms in a multiple regression model to test for moderators. To do so, we use proofs, an illustrative dataset, and a Monte Carlo simulation to show the precise effects of mean centering on both individual correlation coefficients as well as overall model indices. ![]() We distinguish between “micro” and “macro” definitions of multicollinearity and show how both sides of such a debate can be correct. In this article, we clarify the issues and reconcile the discrepancy. Adding to the confusion is the fact that there is also a perspective in the literature that mean centering does not reduce multicollinearity. Many researchers use mean centered variables because they believe it’s the thing to do or because reviewers ask them to, without quite understanding why. There seems to be confusion among researchers regarding whether it is good practice to center variables at their means prior to calculating a product term to estimate an interaction in a multiple regression model.
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