R语言中quantile()函数的用法说明

> data <- c(1,2,3,4,5,6,7,8,9,10)
> quantile(data,0.5)
50% 
5.5 
> quantile(data,c(0.25,0.75))
 25%  75% 
3.25 7.75 

> quantile(data,seq(0.1,1,0.1))
 10%  20%  30%  40%  50%  60%  70%  80%  90% 100% 
 1.9  2.8  3.7  4.6  5.5  6.4  7.3  8.2  9.1 10.0 

> unname(quantile(data,seq(0.1,1,0.1)))
 [1]  1.9  2.8  3.7  4.6  5.5  6.4  7.3  8.2  9.1 10.0

#导入分位数回归的包
library(quantreg)                         
# 引入数据
data(engel)
#查看数据格式
mode(engel)
[1] "list"
#查看变量名
names(engel)
[1] "income"  "foodexp"
#查看格式
class(engel)
[1] "data.frame"
#查看数据的前五行
head(engel)
income  foodexp
1 420.1577 255.8394
2 541.4117 310.9587
3 901.1575 485.6800
4 639.0802 402.9974
5 750.8756 495.5608
6 945.7989 633.7978
#画个散点图看看数据
plot(engel$income, engel$foodexp, xlab='income', ylab='foodexp')

#查看foodexp的变化范围
boxplot(engel$foodexp, xlab='foodexp')
#简单验证一下因变量foodexp是否服从正态分布
qqnorm(engel$foodexp, main='QQ plot')
qqline(engel$foodexp, col='red', lwd=2)

#可以直接调用数据框里变量
attach(engel)
#设置0.05, 0.25, 0.5, 0.75, 0.95五个分位点，并且进行分位数回归，这样可以得到五条分位数回归线
rq_result <- rq(foodexp ~ income, tau=c(0.05, 0.25, 0.5, 0.75, 0.95))
summary(rq_result)
Call: rq(formula = foodexp ~ income, tau = c(0.05, 0.25, 0.5, 0.75, 
    0.95))
tau: [1] 0.05
Coefficients:
            coefficients lower bd  upper bd 
(Intercept) 124.88004     98.30212 130.51695
income        0.34336      0.34333   0.38975
Call: rq(formula = foodexp ~ income, tau = c(0.05, 0.25, 0.5, 0.75, 
    0.95))
tau: [1] 0.25
Coefficients:
            coefficients lower bd  upper bd 
(Intercept)  95.48354     73.78608 120.09847
income        0.47410      0.42033   0.49433
Call: rq(formula = foodexp ~ income, tau = c(0.05, 0.25, 0.5, 0.75, 
    0.95))
tau: [1] 0.5
Coefficients:
            coefficients lower bd  upper bd 
(Intercept)  81.48225     53.25915 114.01156
income        0.56018      0.48702   0.60199
Call: rq(formula = foodexp ~ income, tau = c(0.05, 0.25, 0.5, 0.75, 
    0.95))
tau: [1] 0.75
Coefficients:
            coefficients lower bd  upper bd 
(Intercept)  62.39659     32.74488 107.31362
income        0.64401      0.58016   0.69041
Call: rq(formula = foodexp ~ income, tau = c(0.05, 0.25, 0.5, 0.75, 
    0.95))
tau: [1] 0.95
Coefficients:
            coefficients lower bd upper bd
(Intercept) 64.10396     46.26495 83.57896
income       0.70907      0.67390  0.73444
#上面就是没条回归线的回归系数，我们做个图看一下
plot(income, foodexp, cex=0.25, type='n', xlab='income', ylab='foodexp')
points(income, foodexp, cex=0.5, col='blue')
#加中位数数回归的直线
abline(rq(foodexp~income, tau=0.5), col='blue')
#加均值回归的五条直线
abline(lm(foodexp~income), lty=2, col='red')
#将分位数回归的五条线加上去
taus <- c(0.05, 0.1, 0.25, 0.75, 0.9, 0.95)
#
for (i in 1:length(taus)){
  abline(rq(foodexp~income, tau=taus[i]), col='gray')
}