5Grouping Property and Decomposition of Explained Variance in Linear Regression

The quantification of the relative importance of predictors on a response variable has been an active subject of research for many years. Regression analysis may be used for that purpose but estimating importance of predictors via (standardized) regression coefficients is not adequate in the presence of correlations between these variables. Therefore, alternative methods have been considered. Grouping property is respected when estimators of importance tend to equate for highly correlated predictors. We will analyze the respect of grouping property for several methods used to quantify the relative importance of predictors through decomposition of the explained variance in linear regression. After being criticized by several authors, Correlation-Adjusted marginal coRrelation (CAR) scores have been recommended again as estimators of importance of predictors and presented with respect to the grouping property. We will show that CAR scores actually do not respect this property. We will explain, in turn, why some other variance decomposition methods do respect grouping property and we will formulate recommendations for quantifying the relative importance of predictors.

5.1. Introduction

The quantification of relative importance of predictors on a response variable has been a subject of research in biostatistics, psychology, economics or market research. Many methods have been investigated, sometimes ...

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