*--------
*-4.1.4.4 R2 的分解: 解释变量对 R2 的贡献度 (Self-reading)
help shapley2
*-Israeli, O., 2007
* A Shapley-based decomposition of the R-Square of a linear regression.
* Journal of Economic Inequality, 5(2):199-212.
shellout "$path\Refs\OLS_Shapley_R2.pdf" //pp.202
*-目的: 对 R2 进行分解, 分析每个变量对 R2 的贡献;
*-示例:
sysuse auto, clear
pwcorr price weight length //相关系数
reg price weight length
shapley2, stat(r2)
*-原理: 如何得到 R2_weight = 0.22559 ?
*-weight 对 R2 的边际贡献有两种衡量方法：
*-m1: R2(y c x1 x2) - R2(y c x2) = R2_m1
rename (price weight length) (y x1 x2)
qui reg y x1 x2
local R2_all = e(r2)
qui reg y x2
local R2_x2 = e(r2)
local R2_m1_x1 = `R2_all'-`R2_x2'
*-m2: R2(y c x1) - R2(y c) = R2_m2
qui reg y x1
local R2_x1 = e(r2)
qui reg y
local R2_0 = e(r2)
local R2_m2_x1 = `R2_x1'-`R2_0'
*-Sharpley value = (R1_m1+R2_m2)/2
local R2_x1_Sharp = (`R2_m1_x1'+`R2_m2_x1')/2
dis "Shapley value of weight = " in g %6.5f `R2_x1_Sharp'
*-多变量情形
sysuse nlsw88, clear
reg wage age hours tenure married
shapley2, stat(r2)
*-分组分析
tab race, gen(dum)
reg wage age hours tenure married dum2 dum3
shapley2, stat(r2) group(age hours tenure married, dum2 dum3)
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