Using Explained Variance Allocation to analyse Importance of Predictors

Using applications of linear regression, Market Research practitioners want to determine a ranking of predictors or a quantification of their respective importance for a desired outcome. As predictors are often correlated, regression coefficients can be difficult to use directly because they can be instable across samples and have negative values that are counterintuitive. To overcome these difficulties other methods have been proposed in the industry using squared semi partial correlation coefficients, squared zero order correlation coefficients or methods such as Shapley Value decomposition or decomposition via orthogonalisation in the space of predictors. The proximity between the results obtained by different Variance Decomposition methods has led some authors to conclude that they are a fully valid approach. This paper will highlight theoretical reasons why these methods present similarities, offer a simple alternative new way to decompose variance but will also show the flaws and risks of relaying on Variance Decomposition for quantification of importance of predictors and why a Game Theory approach like Shapley Value can lead to misinterpretations. It will also present additional methods developed to compute β coefficients using Variance Decomposition as an intermediate step and propose recommendations for driver analysis.