使用回归线和正态分布叠加制作ggplot

Question

我试图绘制一个图以显示逻辑（或概率）回归背后的直觉。我将如何在ggplot中绘制出类似以下内容的图？

（Wolf＆Best，《贤者回归分析和因果推断手册》，2015年，第155页）

实际上，我更愿意做的是沿y轴显示一个均值= 0的正态分布，并具有特定的方差，以便我可以绘制从线性预测器到y轴并横向的水平线正态分布。像这样：

应该显示的内容是（假设我没有误解）。到目前为止，我还没有取得太大的成就...

library(ggplot2)

x <- seq(1, 11, 1)
y <- x*0.5

x <- x - mean(x)
y <- y - mean(y)

df <- data.frame(x, y)

# Probability density function of a normal logistic distribution 
pdfDeltaFun <- function(x) {
  prob = (exp(x)/(1 + exp(x))^2)
  return(prob)
}

# Tried switching the x and y to be able to turn the 
# distribution overlay 90 degrees with coord_flip()
ggplot(df, aes(x = y, y = x)) + 
  geom_point() + 
  geom_line() + 
  stat_function(fun = pdfDeltaFun)+ 
  coord_flip() 

Answer 1

我认为这与您提供的第一个插图非常接近。如果您不需要重复很多次，最好在绘制图形之前先计算密度曲线，然后使用单独的数据框进行绘制。

library(ggplot2)

x <- seq(1, 11, 1)
y <- x*0.5

x <- x - mean(x)
y <- y - mean(y)

df <- data.frame(x, y)

# For every row in `df`, compute a rotated normal density centered at `y` and shifted by `x`
curves <- lapply(seq_len(NROW(df)), function(i) {
  mu <- df$y[i]
  range <- mu + c(-3, 3)
  seq <- seq(range[1], range[2], length.out = 100)
  data.frame(
    x = -1 * dnorm(seq, mean = mu) + df$x[i],
    y = seq,
    grp = i
  )
})
# Combine above densities in one data.frame
curves <- do.call(rbind, curves)


ggplot(df, aes(x, y)) +
  geom_point() +
  geom_line() +
  # The path draws the curve
  geom_path(data = curves, aes(group = grp)) +
  # The polygon does the shading. We can use `oob_squish()` to set a range.
  geom_polygon(data = curves, aes(y = scales::oob_squish(y, c(0, Inf)),group = grp))

第二个插图非常接近您的代码。我通过标准的普通密度函数简化了密度函数，并向stat函数添加了一些额外的参数：

library(ggplot2)

x <- seq(1, 11, 1)
y <- x*0.5

x <- x - mean(x)
y <- y - mean(y)

df <- data.frame(x, y)

ggplot(df, aes(x, y)) +
  geom_point() +
  geom_line() +
  stat_function(fun = dnorm,
                aes(x = after_stat(-y * 4 - 5), y = after_stat(x)),
                xlim = range(df$y)) +
  # We fill with a polygon, squishing the y-range
  stat_function(fun = dnorm, geom = "polygon",
                aes(x = after_stat(-y * 4 - 5), 
                    y = after_stat(scales::oob_squish(x, c(-Inf, -1)))),
                xlim = range(df$y))