用回归线法和正态分布叠加法绘制and图

Question

我试图做一个图谋，以显示逻辑(或概率)回归背后的直觉。我怎样才能制作出这样的情节呢？

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(Wolf & Best，“分析和因果推理的智者手册”，2015年，第155页)

实际上，我更愿意做的是，沿着y轴显示一个单一的正态分布，平均值= 0，还有一个特定的方差，这样我就可以画出从线性预测器到y轴的水平线，并且横向正态分布。就像这样：

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这表明(假设我没有误解什么)

。到目前为止我还没有取得多少成功..。

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() 

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Answer 1

我认为这与你给出的第一个例子非常接近。如果这是一件您不需要重复多次的事情，那么最好在绘制之前先计算密度曲线，然后使用单独的数据来绘制这些曲线。

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))

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第二个例子非常接近您的代码。我将您的密度函数简化为标准的正常密度函数，并在stat函数中添加了一些额外参数：

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))

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