R语言中的Theil-Sen回归分析

Theil-Sen估计器是一种在社会科学中不常用的简单线性回归估计器。三个步骤：

用这种方法计算斜率非常可靠。当误差呈正态分布且没有异常值时，斜率与OLS非常相似。

可下载资源

完整代码、数据和文档（word）

在数据中所有点之间绘制一条线
计算每条线的斜率
中位数斜率是回归斜率

有几种获取截距的方法。如果关心回归中的截距，那么知道软件在做什么是很合理的。

当我对异常值和异方差性有担忧时，请在上方针对Theil-Sen进行简单线性回归的评论。

我进行了一次模拟，以了解Theil-Sen如何在异方差下与OLS比较。它是更有效的估计器。

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"
       ))