稳健线性回归.docx

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1、稳健（robust）线性回归稳健线性回归适用于普通线性回归的任何情况，当做回归诊断时，可能发现数据存在一些异常值，而且没有理由去除这些异常值进行分析，此时可用稳健线性回归。回归方程中预测值和实际观测值的差值是残差，应变量Y异常的值残差比较大，自变量X异常的值表现为其离均值较远。此时做稳健线性回归时，系统将根据变量值残差大小赋予不同的权重，残差越大，权重越小。例：DEMO数据对SBP进行稳健回归输入界面如下：其中研究对象编号是用来识别有异常值的观测记录。输出结果：结果变量:SystolicBP,mmhg变量分布与联系函数:gaussian模型:SB

2、P~AGE+HEIGHT+WEIGHT+SEX+SMOKE+ALH+OCCU.NEW+factor(EDU.NEW)稳健回归(迭代重加权最小二乘法)ValueStd.Errortvalue95%CIlow95%CIupp(Intercept)142.749521.18156.7393101.2337184.2652AGE0.65610.051712.68430.55470.7575HEIGHT-21.666913.5887-1.5945-48.30074.9668WEIGHT0.2330.10632.1920.02470.4413SEX-6.52

3、312.1123-3.0881-10.6631-2.383SMOKE-3.11071.6938-1.8365-6.43060.2092ALH-3.06371.8783-1.6311-6.74510.6178OCCU.NEW-4.38841.2538-3.5001-6.8458-1.931factor(EDU.NEW)20.28671.64380.1744-2.93513.5085factor(EDU.NEW)31.23381.97490.6247-2.6375.1045LogLikelihood:-3455.6405,df=11sigma:14.

4、6848Numberofobservationsused:784普通最小二乘回归EstimateStd.ErrortvaluePr(>

5、t

6、)95%CIlow95%CIupp(Intercept)147.838324.9445.9268098.948196.7286AGE0.80570.060913.227800.68630.9251HEIGHT-29.594116.0024-1.84930.0648-60.95891.7707WEIGHT0.30880.12522.4670.01380.06350.5541SEX-6.51382.4875-2.

7、61860.009-11.3893-1.6383SMOKE-3.50551.9947-1.75740.0792-7.41520.4042ALH-1.84262.2119-0.8330.4051-6.1782.4928OCCU.NEW-4.37171.4765-2.96090.0032-7.2656-1.4778factor(EDU.NEW)20.31921.93580.16490.8691-3.47494.1133factor(EDU.NEW)30.52882.32570.22740.8202-4.02955.0871sigma:19.7411L

8、ogLikelihood:-3445.8529,df=11R-squared:0.2417Adj.r-squared:0.2329Numberofobservationsused:784被分配权重最小的10条记录Cooks.distancestd.residualweightSBPAGEHEIGHTWEIGHTSEXSMOKEALHOCCU.NEWEDU.NEWSUBJ0.03963770277910324.901655287946030.19019523965630325568.61.4653.5200113780.02722843725625

9、174.487828882855210.21275674294498823460.51.6655110225080.03350207553727334.09048600372930.22894978094731722663.91.7258111222890.02505052969537443.610907658380180.26022436872760722059.41.6759.5100217430.01033553282969513.607326830526250.26103669175782721054.41.484220021520.01

10、345984885283943.49832247957970.26462069493358521963.71.4840200111170