Analysis and application of game theory in estimating variable importance in linear model
10.3724/SP.J.1008.2014.00865
- Author:
Xiao-Xia JIA
1
Author Information
1. Department of Basic Medical Sciences, Zhejiang Pharmaceutical College
- Publication Type:Journal Article
- Keywords:
Game theory;
Linear regression;
Relative importance
- From:
Academic Journal of Second Military Medical University
2014;35(8):865-869
- CountryChina
- Language:Chinese
-
Abstract:
Objective To apply Shapley value analysis of the game theory for evaluating the relative importance of the predictors in the linear regression when colinearity exists, and to provide a new concept of sequential importance partial R2. Methods Shapley value analysis of game theory(proposed by Shapley in 1953) was used to evaluate the influencing factors of hemoglobin(HB) in 757 normal adults, by regressing HB on four predictors including the white blood cell(WBC), red blood cell(RBC), blood platelet(PLT) and hematocrit(HCT); meanwhile, the sequential importance partial R2 was used to analyze its practical significance. Finally the estimated results of Shapley value was compared with others measures including traditional methods and recommended method. Results A succinct set of predictors including RBC, PLT and HCT was identified for establishing a multiply regression, with their relative importance values being 0.355 3, 0.012 4 and 0.553 8, respectively. The results of relative importance were consistent between Shapley value and dominance analysis. Moreover, it was found that the partial R2 of predictors had different marginal contributions in different orders. Conclusion HCT has the largest contribution to HB, followed by RBC, and PLT has the least effect to H.B. The order of contributions is consistent with the correlation matrix, indicating that the relative importance of the predictors in Shapley value is reasonable.
