原文鏈接：http://tecdat.cn/?p=10080
Theil-Sen估計器是一種在社會科學中不常用 的簡單線性回歸估計器 。三個步驟：
- 在數據中所有點之間繪制一條線
- 計算每條線的斜率
- 中位數斜率是 回歸斜率
用這種方法計算斜率非常可靠。當誤差呈正態分布且沒有異常值時，斜率與OLS非常相似。
有幾種獲取截距的方法。如果 關心回歸中的截距，那么知道 軟件在做什么是很合理的。
當我對異常值和異方差性有擔憂時，請在上方針對Theil-Sen進行簡單線性回歸的評論 。
我進行了一次 模擬，以了解Theil-Sen如何在異方差下與OLS比較。它是更有效的估計器。
library(simglm)
library(ggplot2)
library(dplyr)
library(WRS)
# Hetero
nRep <- 100
n.s <- c(seq(50, 300, 50), 400, 550, 750, 1000)
samp.dat <- sample((1:(nRep*length(n.s))), 25)
lm.coefs.0 <- matrix(ncol = 3, nrow = nRep*length(n.s))
ts.coefs.0 <- matrix(ncol = 3, nrow = nRep*length(n.s))
lmt.coefs.0 <- matrix(ncol = 3, nrow = nRep*length(n.s))
dat.s <- list()
ggplot(dat.frms.0, aes(x = age, y = sim_data)) +
geom_point(shape = 1, size = .5) +
geom_smooth(method = "lm", se = FALSE) +
facet_wrap(~ random.sample, nrow = 5) +
labs(x = "Predictor", y = "Outcome",
title = "Random sample of 25 datasets from 15000 datasets for simulation",
subtitle = "Heteroscedastic relationships")
ggplot(coefs.0, aes(x = n, colour = Estimator)) +
geom_boxplot(
aes(ymin = q025, lower = q25, middle = q50, upper = q75, ymax = q975), data = summarise(
group_by(coefs.0, n, Estimator), q025 = quantile(Slope, .025),
q25 = quantile(Slope, .25), q50 = quantile(Slope, .5),
q75 = quantile(Slope, .75), q975 = quantile(Slope, .975)), stat = "identity") +
geom_hline(yintercept = 2, linetype = 2) + scale_y_continuous(breaks = seq(1, 3, .05)) +
labs(x = "Sample size", y = "Slope",
title = "Estimation of regression slope in simple linear regression under heteroscedasticity",
subtitle = "1500 replications - Population slope is 2",
caption = paste(
"Boxes are IQR, whiskers are middle 95% of slopes",
"Both estimators are unbiased in the long run, however, OLS has higher variability",
sep = "\n"
))
如果您有任何疑問，請在下面發表評論。