Using commonality analysis in multiple regressions: a tool to decompose regression effects in the face of multicollinearity
Article first published online: 20 MAR 2014
© 2014 The Authors. Methods in Ecology and Evolution © 2014 British Ecological Society
Methods in Ecology and Evolution
Volume 5, Issue 4, pages 320–328, April 2014
How to Cite
Ray-Mukherjee, J., Nimon, K., Mukherjee, S., Morris, D. W., Slotow, R., Hamer, M. (2014), Using commonality analysis in multiple regressions: a tool to decompose regression effects in the face of multicollinearity. Methods in Ecology and Evolution, 5: 320–328. doi: 10.1111/2041-210X.12166
- Issue published online: 9 APR 2014
- Article first published online: 20 MAR 2014
- Accepted manuscript online: 28 JAN 2014 01:57AM EST
- Manuscript Accepted: 20 JAN 2014
- Manuscript Received: 23 MAY 2013
- stepwise regression;
- hierarchical regression;
- structure coefficients;
- standardized partial regression coefficient;
- suppressor variable;
- habitat selection
1. In the face of natural complexities and multicollinearity, model selection and predictions using multiple regression may be ambiguous and risky. Confounding effects of predictors often cloud researchers’ assessment and interpretation of the single best ‘magic model’. The shortcomings of stepwise regression have been extensively described in statistical literature, yet it is still widely used in ecological literature. Similarly, hierarchical regression which is thought to be an improvement of the stepwise procedure, fails to address multicollinearity.
2. We propose that regression commonality analysis (CA), a technique more commonly used in psychology and education research will be helpful in interpreting the typical multiple regression analyses conducted on ecological data.
3. CA decomposes the variance of R2 into unique and common (or shared) variance (or effects) of predictors, and hence, it can significantly improve exploratory capabilities in studies where multiple regressions are widely used, particularly when predictors are correlated. CA can explicitly identify the magnitude and location of multicollinearity and suppression in a regression model.
In this paper, using a simulated (from a correlation matrix) and an empirical dataset (human habitat selection, migration of Canadians across cities), we demonstrate how CA can be used with correlated predictors in multiple regression to improve our understanding and interpretation of data. We strongly encourage the use of CA in ecological research as a follow-on analysis from multiple regressions.