泊松回归——推荐

1、 # 泊松回归 # # #Median:16.00Mean:33.053rdQu.:36.00Max.:151.00Max.:42.00Max.:302.00泊松回归介绍泊松回归适用于在给定时间内响应变量为事件发生数目的情况，它假设Y服从泊松分布，线性模型的拟合形式为小_aPQY其中人是Y的均值（也等于方差）。此时，连接函数为，概率分布为泊松分布，拟合泊松回归模型如下glm（YX1+X2+X3,family=poisson（link=log）,data=mydata）111glm(YX1+X2+X3,family=poisson(link=log),data=mydata)例使用robust包

2、中的breslow（癫痫数据）数据响应变量为sumy（随机化后八周内癫痫发病数），预测变量为治疗条件（Trt）、年龄（Age）、前八周的基础癫痫发病数（Base）观看基础的癫痫发病数和年龄，对响应变量的潜在影响，最后看下药物治疗能否减少癫痫的发病数data(breslow.dat,package=robust)#导入robust包中的breslow数据names(breslow.dat)#变量名称1IDY1Y2Y3Y4BaseAge叮rtYsumsumYAge1012Base4summary(breslow.datc(6,7,8,10)#获得6、7、8、10的变量数据等同于breslow.da

3、t,c(6,7,8,10)BaseAgeTrtsumYMin.:6.00Min.:18.00placebo:28Min.:0.001stQu.:12.001stQu.:23.00progabide:311stQu.:11.50Median:22.00Median:28.00Mean:31.22Mean:28.343rdQu.:41.003rdQu.:32.00#绘制图形观察基本的情况oparsummary(breslow.datc(6,7,8,10)#获得6、7、8、10的变量数据等同于breslow.dat,c(6,7,8,10)Min.:6.00Min.:18.00placebo:28Mi

4、n.:0.001stQu.:12.001stQu.:23.00progabide:311stQu.:11.50Median:22.00Median:28.00Median:16.0010Mean:31.22Mean:28.34Mean:33.05113rdQu.:41.003rdQu.:32.003rdQu.:36.0012Max.:151.00Max.:42.00Max.:302.00 # # # #1314#绘制图形观察基本的情况15#复制一份图形设置oparpar(mfrow=c(1,2)#修改参数C5C也255placebopiugabideC5C也255placebopiugabid

5、eattach(breslow.dat)1819hist(sumY,breaks=20,xlab=SeizureCount,20+main=DistributionofSeizure)21boxplot(sumYTrt,xlab=Treatment,main=GroupComparisons)22par(opar)还#原原来的设置C5C也255placebopiugabideC5C也255placebopiugabideC5C也255placebopiugabideC5C也255placebopiugabideDistributionofSeizure由o叩ComparisonsC5C也255

6、placebopiugabideC5C也255placebopiugabideC5C也255placebopiugabideC5C也255placebopiugabidecertccC5C也255placebopiugabideC5C也255placebopiugabideC5C也255placebopiugabideC5C也255placebopiugabide因变量的小的均值）。与标准最小二乘法回归不同，泊松回归并不关注方差异质性_c偏倚特性以及可能的离群点，初看图形时，药物治疗下癫痫发病数似乎变小，且方差也变小了（泊松分布中，较小的方差伴随着较7 7 #拟合泊松回归fit|z|)(Int

7、ercept)1.94882590.135619114.3702e-16*Base0.02265170.000509344.4762e-16*Age0.02274010.00402405.6511.59e-08*Trtprogabide-0.15270090.0478051-3.1940.0014*Signif.codes:0*0.001*0.01*0.05.0.11(Dispersionparameterforpoissonfamilytakentobe1)Nulldeviance:2122.73on58degreesoffreedomResidualdeviance:559.44on55d

8、egreesoffreedomAIC:850.71NumberofFisherScoringiterations:5x271#拟合泊松回归2fit|z|)14(Intercept)1.94882590.135619114.3702e-16*15Base0.02265170.000509344.4762e-16*16Age0.02274010.00402405.6511.59e-08*17Trtprogabide-0.15270090.0478051-3.1940.0014*1819Signif.codes:0*0.001*0.01*0.05.0.112021(Dispersionparameterforpoissonfamilytakentobe1)Nulldeviance:2122.73on58degreesoffreedom24R