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Multicollinearity

Part 2. Marketing Research

  1. George R. Franke

Published Online: 15 DEC 2010

DOI: 10.1002/9781444316568.wiem02066

Wiley International Encyclopedia of Marketing

Wiley International Encyclopedia of Marketing

How to Cite

Franke, G. R. 2010. Multicollinearity. Wiley International Encyclopedia of Marketing. 2.

Author Information

  1. University of Alabama, Tuscaloosa, AL, USA

Publication History

  1. Published Online: 15 DEC 2010

Abstract

Predictor variables that are highly correlated provide little independent explanatory ability. This pattern is known as multicollinearity or simply collinearity. Collinearity increases the variances of the regression coefficient, so that they may (i) have theoretically implausible magnitudes or signs; (ii) vary substantially with small changes in the sample of observations or the set of predictors; and (iii) be individually nonsignificant even though they explain significant amounts of variance overall. One indicator of collinearity is correlations of above 0.8 or 0.9 between predictor variables. Another is high R2s from regressing each predictor xi on all the other predictors The inverse of the unexplained variance, inline image, is known as the variance inflation factor (VIF). A VIF ≥10 indicates potentially harmful collinearity. Condition indices (CIs) – functions of eigenvalues of the scaled predictor variables – in combination with the variance proportions of the standard errors of the regression coefficients associated with each CI are especially useful indicators. Treatments include combining or omitting predictors, or constraining coefficients in theoretically justifiable ways. Ridge regression and structural equation modeling may reduce problems that occur with ordinary multiple regression. Model development and data collection procedures are often found to be the best remedy for collinearity problems.

Keywords:

  • regression;
  • correlation;
  • collinearity;
  • variance inflation factor;
  • ridge regression;
  • condition index