Quantile_regression.qmd

---
title: "Quantile regression"
format: html
---

## Quantile regression

分位数回归（Quantile regression, QR回归)，其原理是将数据按因变量进行拆分成多个分位数点，研究不同分位点情况下时的回归影响关系情况。

中位数回归的估计方法与最小二乘法相比，估计结果对离群值（极值）则表现的更加稳健.
分位数回归对误差项不要求“误差项呈正态分布”。因此对于非正态分布而言，分位数回归系数 估计量则更加稳健。




```{r}
library(easystats)
library(quantreg)
```


```{r}
# Model: Quantile Regression
Quan_fit <- quantreg::rq(disp ~ wt, data = mtcars, 
                         tau = 0.5 # f分为数
                         )
Quan_fit
  
# Summary of Model
summary(Quan_fit)

```


```{r}
# Plot
plot(disp ~ wt, data = mtcars, pch = 16, main = "Plot")
abline(lm(disp ~ wt, data = mtcars), col = "red", lty = 2)
abline(rq(disp ~ wt, data = mtcars), col = "blue", lty = 2)
```


```{r}
require(ggplot2)

#create scatterplot with quantile regression line
ggplot(mtcars, aes(wt,disp)) +
  geom_point() + 
  geom_abline(intercept=coef(Quan_fit)[1], slope=coef(Quan_fit)[2]) +
  geom_smooth(method="lm", se=F)
```


```{r}
performance::performance(Quan_fit)
```



```{r}

```