Using commonality analysis in multiple regressions: a tool to decompose regression effects in the face of multicollinearity



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.