Estimators of Relative Importance in Linear Regression Based on Variance Decomposition

By Ulrike Grömping. 2007

619 citations recorded by the source corpus.

Subfields: Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/d2875bbe455ba8aa21c0f06f6f1ee42c7269d7ad

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In Management Science and Operations Research

In Statistics and Probability

Citations in the corpus

The consecutive disparity index, D : a measure of temporal variability in ecological studies (2018, methodology): “The proportional marginal variance decomposition (PMVD) metric (Gr€omping 2007) is also shown as a measure of the explained variance (R2).”
Confronting collinearity: comparing methods for disentangling the effects of habitat loss and fragmentation (2009, background): “HVP is one of a number of closely related metrics of relative importance that are more commonly applied in the social sciences (Kruskal 1987; Gromping 2007 ).”
Similarities and differences when building trust: the role of cultures (2010, positive): “…to reporting p values and confidence intervals we include the proportional marginal value decomposition (short, pmvd) as a measure of how much each variable contributes to the variance of our dependent variable . pmvd was proposed by Feldman (2005), we use the implementation of Grömping (2007).”
Work motivation and public service motivation: disentangling varieties of motivation and job satisfaction (2018, methodology): “We used the R2 decomposition approach suggested by Grömping (2007), which assesses each independent variable contribution to the models’ R2 fit.”
Synoptic and meteorological drivers of extreme ozone concentrations over Europe (2016, methodology): “In the case of linear regression methods, the main important predictors of the ozone are estimated using the coefficient of determination R2, which is partitioned by averaging over orders, according to the method proposed by Lindeman et al (1980) (Grömping 2007).”
Estimation of tropical forest structure from SPOT-5 satellite images (2010, methodology): “The statistic called LMG (the initials of the three authors who first proposed the method) averages the sum of sequential squares for all possible arrangements of the variables in the model (Grömping 2006, 2007).”
Childhood maltreatment is associated with reduced volume in the hippocampal subfields CA3, dentate gyrus, and subiculum (2012, methodology): “1 shows the percent variance (s(2)) in subfield volume accounted for by degree of maltreatment, as assessed using variance decomposition (40, 41).”
Axiomatic arguments for decomposing goodness of fit according to Shapley and Owen values (2012, background): “Grömping [7] discusses this point and suggests that this property may be reasonable in many practical settings where causal relationships are not obvious.”
How to explain and predict the shape parameter of the generalized extreme value distribution of streamflow extremes using a big dataset (2018, methodology): “Ranking the relative importance of the predictor variables in the linear model is crucial for understanding how the predictor variables affect the dependent variable (Grömping 2007a).”
Quantitative Models of Sovereign Debt Crises (2016, positive): “Specifically, we construct a variance decomposition following the algorithm of Lindeman, Merenda, and Gold (1980) as outlined by Gromping (2007). This procedure constructs the average marginal R(2) in the case of correlated regressors by assuming a uniform distribution over all possible permutations”
The many Shapley values for model explanation (2019, methodology): “[5, 6]) that uses the Shapley value to attribute the goodness of fit (R2) of a linear regression model to its features by retraining the model on different feature sets.”
Fungible Weights in Multiple Regression (2008, background): “Numerous researchers have reminded us that coefficient size is an unreliable index of parameter importance in multiple regression (e.g., Budescu, 1993; Darlington, 1968; Green, Carroll, & DeSarbo, 1978; Gromping, 2007; Johnson, 2000).”