泊松回歸——推薦

1、 # 泊松回歸 # # #Median:16.00Mean:33.053rdQu.:36.00Max.:151.00Max.:42.00Max.:302.00泊松回歸介紹泊松回歸適用于在給定時間內(nèi)響應變量為事件發(fā)生數(shù)目的情況，它假設Y服從泊松分布，線性模型的擬合形式為小_aPQY其中人是Y的均值（也等于方差）。此時，連接函數(shù)為，概率分布為泊松分布，擬合泊松回歸模型如下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（癲癇數(shù)據(jù)）數(shù)據(jù)響應變量為sumy（隨機化后八周內(nèi)癲癇發(fā)病數(shù)），預測變量為治療條件（Trt）、年齡（Age）、前八周的基礎(chǔ)癲癇發(fā)病數(shù)（Base）觀看基礎(chǔ)的癲癇發(fā)病數(shù)和年齡，對響應變量的潛在影響，最后看下藥物治療能否減少癲癇的發(fā)病數(shù)data(breslow.dat,package=robust)#導入robust包中的breslow數(shù)據(jù)names(breslow.dat)#變量名稱1IDY1Y2Y3Y4BaseAge叮rtYsumsumYAge1012Base4summary(breslow.datc(6,7,8,10)#獲得6、7、8、10的變量數(shù)據(jù)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#繪制圖形觀察基本的情況oparsummary(breslow.datc(6,7,8,10)#獲得6、7、8、10的變量數(shù)據(jù)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#繪制圖形觀察基本的情況15#復制一份圖形設置oparpar(mfrow=c(1,2)#修改參數(shù)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)還#原原來的設置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因變量的小的均值）。與標準最小二乘法回歸不同，泊松回歸并不關(guān)注方差異質(zhì)性_c偏倚特性以及可能的離群點，初看圖形時，藥物治療下癲癇發(fā)病數(shù)似乎變小，且方差也變小了（泊松分布中，較小的方差伴隨著較7 7 #擬合泊松回歸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#擬合泊松回歸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