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Do not adjust coefficients in Shapley value regression. (English) Zbl 1223.62118

For linear regression applications with severely correlated regressors, S. Lipovetsky and M. Conklin [Appl. Stoch. Models Bus. Ind. 17, No. 4, 319–330 (2001; Zbl 1008.62041)] proposed a method, which they call Shapley value regression. The Shapley value regression consists of two steps. First, each regressor’s importance in the model is assessed based on averaging \(R^2\) increases over all orderings of the regressors. Second, the coefficients in the model are adjusted to match the regressor importance assessment, using another metric for the \(R^2\) decomposition.
This paper argues that the second step of Shapley value regression, namely the coefficient adjustment, is not useful and should be omitted. It is demonstrated that coefficient adjustment yields misleading conclusions in cases of an artificial example of Lord’s paradox as well as in a real data example that exhibits suppressions. An alternative procedure is proposed for situations for which the coefficients are requested to have a certain sign.

MSC:

62J05 Linear regression; mixed models
65C60 Computational problems in statistics (MSC2010)

Citations:

Zbl 1008.62041

Software:

R; relaimpo
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Full Text: DOI

References:

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