ggplot2：如何在回归线上绘制小高斯密度？

Question

我想以图形方式显示线性（以及后来的其他类型）回归的假设。如何在回归线上添加小高斯密度（或任何类型的密度），如下图所示：

Answer 1

您可以计算沿拟合线的截面残差的经验密度。然后，只需使用geom_path在每个区间中在您选择的位置绘制线条。为了增加理论分布，在每个部分的残差范围内产生一些密度（这里使用正常密度）。对于下面的正常密度，每个部分的标准偏差是根据残差确定的，但您可以选择所有残差的标准偏差，然后使用它。

## Sample data
set.seed(0)
dat <- data.frame(x=(x=runif(100, 0, 50)),
                  y=rnorm(100, 10*x, 100))

## breaks: where you want to compute densities
breaks <- seq(0, max(dat$x), len=5)
dat$section <- cut(dat$x, breaks)

## Get the residuals
dat$res <- residuals(lm(y ~ x, data=dat))

## Compute densities for each section, and flip the axes, and add means of sections
## Note: the densities need to be scaled in relation to the section size (2000 here)
dens <- do.call(rbind, lapply(split(dat, dat$section), function(x) {
    d <- density(x$res, n=50)
    res <- data.frame(x=max(x$x)- d$y*2000, y=d$x+mean(x$y))
    res <- res[order(res$y), ]
    ## Get some data for normal lines as well
    xs <- seq(min(x$res), max(x$res), len=50)
    res <- rbind(res, data.frame(y=xs + mean(x$y),
                                 x=max(x$x) - 2000*dnorm(xs, 0, sd(x$res))))
    res$type <- rep(c("empirical", "normal"), each=50)
    res
}))
dens$section <- rep(levels(dat$section), each=100)

## Plot both empirical and theoretical
ggplot(dat, aes(x, y)) +
  geom_point() +
  geom_smooth(method="lm", fill=NA, lwd=2) +
  geom_path(data=dens, aes(x, y, group=interaction(section,type), color=type), lwd=1.1) +
  theme_bw() +
  geom_vline(xintercept=breaks, lty=2)

或者，只是高斯曲线

## Just normal
ggplot(dat, aes(x, y)) +
  geom_point() +
  geom_smooth(method="lm", fill=NA, lwd=2) +
  geom_path(data=dens[dens$type=="normal",], aes(x, y, group=section), color="salmon", lwd=1.1) +
  theme_bw() +
  geom_vline(xintercept=breaks, lty=2)