Estimators of Relative Importance in Linear Regression Based on Variance Decomposition

2007/04/01 by Ulrike Grömping · 606 citations
Decision Sciences · Mathematics · #Advanced Statistical Methods and Models #Computer science #Decomposition #Econometrics #Economics #Estimator #Key (lock) #Linear model #Linear regression #Mathematics #Multi-Criteria Decision Making #Set (abstract data type) #Statistical Methods and Inference #Statistics #Variance (accounting) #Variance decomposition of forecast errors

paper · doi:10.1198/000313007x188252

published in The American Statistician 61(2), 139-147 (Taylor & Francis)

openalex publication_date 2007/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

Assigning shares of “relative importance” to each of a set of regressors is one of the key goals of researchers applying linear regression, particularly in sciences that work with observational data. Although the topic is quite old, advances in computational capabilities have led to increased applications of computer-intensive methods like averaging over orderings that enable a reasonable decomposition of the model variance. This article serves two purposes: to reconcile the large and somewhat fragmented body of recent literature on relative importance and to investigate the theoretical and empirical properties of the key competitors for decomposition of model variance.

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