Mean-Centering Does Not Alleviate Collinearity Problems in Moderated Multiple Regression Models

The cross-product term in moderated regression may be collinear with its constituent parts, making it difficult to detect main, simple, and interaction effects. The literature shows that mean-centering can reduce the covariance between the linear and the interaction terms, thereby suggesting that it...

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Bibliographic Details
Published inMarketing science (Providence, R.I.) Vol. 26; no. 3; pp. 438 - 445
Main Authors Echambadi, Raj, Hess, James D
Format Journal Article
LanguageEnglish
Published Linthicum INFORMS 01.05.2007
Institute for Operations Research and the Management Sciences (INFORMS)
Institute for Operations Research and the Management Sciences
SeriesMarketing Science
Subjects
Accuracy
Brands
Coefficients
Collinearity
Correlation analysis
Covariance
Data analysis
Estimates
Estimation
Linear programming
Linear regression
Marketing
mean-centering
moderated regression
Multiple regression
Point estimators
Random variables
Regression analysis
Significance tests
Standard error
Studies
Theorems
Variables
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Summary:The cross-product term in moderated regression may be collinear with its constituent parts, making it difficult to detect main, simple, and interaction effects. The literature shows that mean-centering can reduce the covariance between the linear and the interaction terms, thereby suggesting that it reduces collinearity. We analytically prove that mean-centering neither changes the computational precision of parameters, the sampling accuracy of main effects, simple effects, interaction effects, nor the R 2 . We also show that the determinants of the cross product matrix X' X are identical for uncentered and mean-centered data, so the collinearity problem in the moderated regression is unchanged by mean-centering. Many empirical marketing researchers commonly mean-center their moderated regression data hoping that this will improve the precision of estimates from ill conditioned, collinear data, but unfortunately, this hope is futile. Therefore, researchers using moderated regression models should not mean-center in a specious attempt to mitigate collinearity between the linear and the interaction terms. Of course, researchers may wish to mean-center for interpretive purposes and other reasons.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
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ISSN:0732-2399
1526-548X
DOI:10.1287/mksc.1060.0263