问题

我有一个包含N个观测值和两个不重叠边界（一个更高，另一个更低）的数据集。我想要分析我的观测值相对于这些边界：看看有多少观测值（1）高于两个边界，（2）在两个边界之间，以及（3）低于两个边界。

这里是我的数据的简化版本。

data_line1 <- data.frame(line = "1", x = c(0, round(runif(18,0,10), 2), 10), y = round(runif(20,40,60), 2))
data_line2 <- data.frame(line = "2", x = c(0, round(runif(18,0,10), 2), 10), y = round(runif(20,0,39), 2))
data_dots <- data.frame(x = round(runif(200,0,10), 2), y = round(runif(100,0,60), 2))

plot <- ggplot()+
  geom_line(data = data_line1, aes(x,y), color = "black")+
  geom_line(data = data_line2, aes(x,y), color = "red")+
  geom_point(data = data_dots, aes(x,y), color = "deepskyblue")

我相当确信这个问题应该有一个优雅的解决方案，但在尝试R之前，我甚至没有能够在纸上想出任何东西（我对R也相对陌生）。

data_line1 <- data.frame(line = "1", x = c(0, round(runif(18,0,10), 2), 10), y = round(runif(20,40,60), 2))
data_line2 <- data.frame(line = "2", x = c(0, round(runif(18,0,10), 2), 10), y = round(runif(20,0,39), 2))
data_dots <- data.frame(x = round(runif(200,0,10), 2), y = round(runif(100,0,60), 2))

plot <- ggplot()+
  geom_line(data = data_line1, aes(x,y), color = "black")+
  geom_line(data = data_line2, aes(x,y), color = "red")+
  geom_point(data = data_dots, aes(x,y), color = "deepskyblue")

答案1

得分: 3

对于data_dots中的每个点，您需要找出y值是否高于相应x值处的每条线。为了做到这一点，您需要对构成每条线的点进行插值。我们可以使用approxfun来实现：

data_dots$line1_value <- approxfun(data_line1$x, data_line1$y)(data_dots$x)
data_dots$line2_value <- approxfun(data_line2$x, data_line2$y)(data_dots$x)
data_dots$group <- with(data_dots, 1 + (y > line2_value) + (y > line1_value))

现在，我们可以根据它们是否在每条线的上方或下方为每个组分配适当的标签：

data_dots$group <- c('below', 'between', 'above')[data_dots$group]

为了展示这一过程的效果，让我们根据它们的组来绘制点：

ggplot(data = data_line1, aes(x, y)) +
  geom_point(data = data_dots, aes(colour = group)) +
  geom_line() +
  geom_line(data = data_line2) 

要获取每个组中的实际数字，我们可以简单地使用table：

table(data_dots$group)
#> above   below between 
#>    35      59     106 

data_dots$line1_value <- approxfun(data_line1$x, data_line1$y)(data_dots$x)
data_dots$line2_value <- approxfun(data_line2$x, data_line2$y)(data_dots$x)
data_dots$group <- with(data_dots, 1 + (y > line2_value) + (y > line1_value))

data_dots$group <- c('below', 'between', 'above')[data_dots$group]

ggplot(data = data_line1, aes(x, y)) +
  geom_point(data = data_dots, aes(colour = group)) +
  geom_line() +
  geom_line(data = data_line2) 

table(data_dots$group)
#> above   below between 
#>    35      59     106 

答案2

得分: 2

你可以使用 approxfun 来定义插值函数，分别用于下界和上界，然后使用给定的 x 和来自 data_dots 的数据检查 y 是否在两个边界之间，例如，

fu <- with(data_line1, approxfun(x, y))
fl <- with(data_line2, approxfun(x, y))
with(data_dots, sum(y >= fl(x) & y <= fu(x)))

这将计算在边界内的点的数量。

对于可视化，你可以尝试以下代码：

fu <- with(data_line1, approxfun(x, y))
fl <- with(data_line2, approxfun(x, y))
idx <- with(data_dots, y >= fl(x) & y <= fu(x))

plot +
    geom_point(data = data_dots[idx, ], aes(x, y), color = "purple", size = 5)

<details>
<summary>英文:</summary>

You can use `approxfun` to define interpolation functions for both lower and upper bounds, and then check if `y` is in between two bounds with given `x` for data from `data_dots`, e.g.,

fu <- with(data_line1, approxfun(x, y))
fl <- with(data_line2, approxfun(x, y))
with(data_dots, sum(y >= fl(x) & y <= fu(x)))

which counts the number of points within bounds.

----------------------------------

For the visualization, you can try

fu <- with(data_line1, approxfun(x, y))
fl <- with(data_line2, approxfun(x, y))
idx <- with(data_dots, y >= fl(x) & y <= fu(x))

plot +
geom_point(data = data_dots[idx, ], aes(x, y), color = "purple", size = 5)

[![enter image description here][1]][1]


  [1]: https://i.stack.imgur.com/mOxVa.png

</details>