R语言-泊松回归

当通过一系列连续型和或类别型预测变量的预测计数型结果变量时，泊松回归是非常有用的工具。利用robust包学习和理解泊松回归。

遭受轻微或严重间歇性癫痫的病人的年龄和癫痫发病数收集了数据，包含病人被随机分配到药物组或者安慰剂组前八周和随机 分配后八周内两种情况。响应变量为sumY( 随机后八周内癫痫发病次数)，预测变量为治疗条件 (Trt)、年龄(Age)和前八周内的基础癫痫发病次数(Base)。接下来研究药物治疗是否能够减少癫痫发病次数。

> data(breslow.dat,package="robust")

> library(robust)

载入需要的程辑包：fit.models

> names(breslow.dat)

[1] "ID" "Y1" "Y2" "Y3" "Y4" "Base" "Age" "Trt" "Ysum" "sumY" "Age10" #共有12个变量

[12] "Base4"

> summary(breslow.dat[c(6,7,8,10)])#仅描述Base、Age等

Base Age Trt sumY

Min. : 6.00 Min. :18.00 placebo :28 Min. : 0.00

1st Qu.: 12.00 1st Qu.:23.00 progabide:31 1st Qu.: 11.50

Median : 22.00 Median :28.00 Median : 16.00

Mean : 31.22 Mean :28.34 Mean : 33.05

3rd Qu.: 41.00 3rd Qu.:32.00 3rd Qu.: 36.00

Max. :151.00 Max. :42.00 Max. :302.00

> opar <- par(no.readonly = TRUEr)

> par(mfrow=c(1,2))

> attach(breslow.dat)

> hist(sumY,breaks =20,xlab="Seazure Count",main="Distribution of Seizures")

> boxplot(sumY ~ Trt,xlab="Trearment",main="Group Comparisons")

> par(opar)

> fit <- glm(sumY ~ Base + Age + Trt,data = breslow.dat,family = poisson())

> summary(fit)

Call:

glm(formula = sumY ~ Base + Age + Trt, family = poisson(), data = breslow.dat)

Deviance Residuals:

Min 1Q Median 3Q Max

-6.0569 -2.0433 -0.9397 0.7929 11.0061

Coefficients:

Estimate Std. Error z value Pr(>|z|)

(Intercept) 1.9488259 0.1356191 14.370 < 2e-16 ***

Base 0.0226517 0.0005093 44.476 < 2e-16 ***

Age 0.0227401 0.0040240 5.651 1.59e-08 ***

Trtprogabide -0.1527009 0.0478051 -3.194 0.0014 **

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for poisson family taken to be 1)

Null deviance: 2122.73 on 58 degrees of freedom

Residual deviance: 559.44 on 55 degrees of freedom

AIC: 850.71

Number of Fisher Scoring iterations: 5

运行过程中产生的图片：

#解释参数：

> coef(fit)

(Intercept) Base Age Trtprogabide

1.94882593 0.02265174 0.02274013 -0.15270095

> exp(coef(fit))

(Intercept) Base Age Trtprogabide

7.0204403 1.0229102 1.0230007 0.8583864