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我正在使用ggplot/easyGgplot2创建两组的密度图。我想要一个度量或指示两条曲线之间有多少交叉点。我什至可以使用没有曲线的任何其他解决方案，只要它允许我衡量哪些组更不同（几个不同的数据组）。

在 R 中有没有简单的方法来做到这一点？

例如使用这个样本，它生成这个图

在此处输入图像描述

我如何估计两者共有的面积百分比？

ggplot2.density(data=weight, xName='weight', groupName='sex',
    legendPosition="top",
    alpha=0.5, fillGroupDensity=TRUE )
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2 回答 2

6

首先，制作一些数据以供使用。在这里，我们将从内置iris数据集中查看两种植物的花瓣宽度。

## Some sample data from iris
dat <- droplevels(with(iris, iris[Species %in% c("versicolor", "virginica"), ]))

## make a similar graph
library(ggplot2)
ggplot(dat, aes(Petal.Width, fill=Species)) +
  geom_density(alpha=0.5)

在此处输入图像描述

要找到交点的面积，您可以使用approxfun描述重叠的函数来近似。然后，将其整合到获取区域。由于这些是密度曲线，它们的面积为 1（ish），因此积分将是重叠百分比。

## Get density curves for each species
ps <- lapply(split(dat, dat$Species), function(x) {
    dens <- density(x$Petal.Width)
    data.frame(x=dens$x, y=dens$y)
})

## Approximate the functions and find intersection
fs <- sapply(ps, function(x) approxfun(x$x, x$y, yleft=0, yright=0))
f <- function(x) fs[[1]](x) - fs[[2]](x)   # function to minimize (difference b/w curves)
meet <- uniroot(f, interval=c(1, 2))$root  # intersection of the two curves

## Find overlapping x, y values
ps1 <- is.na(cut(ps[[1]]$x, c(-Inf, meet)))
ps2 <- is.na(cut(ps[[2]]$x, c(Inf, meet)))
shared <- rbind(ps[[1]][ps1,], ps[[2]][ps2,])

## Approximate function of intersection
f <- with(shared, approxfun(x, y, yleft=0, yright=0))

## have a look
xs <- seq(0, 3, len=1000)
plot(xs, f(xs), type="l", col="blue", ylim=c(0, 2))

points(ps[[1]], col="red", type="l", lty=2, lwd=2)
points(ps[[2]], col="blue", type="l", lty=2, lwd=2)

polygon(c(xs, rev(xs)), y=c(f(xs), rep(0, length(xs))), col="orange", density=40)

在此处输入图像描述

## Integrate it to get the value
integrate(f, lower=0, upper=3)$value
# [1] 0.1548127
于 2015-07-22T23:40:59.337 回答
3

我喜欢上一个答案，但这可能更直观一点，我也确保使用公共带宽：

library ( "caTools" )

# Extract common bandwidth
Bw <- ( density ( iris$Petal.Width ))$bw

# Get iris data
Sample <- with ( iris, split ( Petal.Width, Species ))[ 2:3 ]

# Estimate kernel densities using common bandwidth
Densities <- lapply ( Sample, density,
                      bw = bw,
                      n = 512,
                      from = -1,
                      to = 3 )

# Plot
plot( Densities [[ 1 ]], xlim = c ( -1, 3 ),
      col = "steelblue",
      main = "" )
lines ( Densities [[ 2 ]], col = "orange" )

# Overlap
X <- Densities [[ 1 ]]$x
Y1 <- Densities [[ 1 ]]$y
Y2 <- Densities [[ 2 ]]$y

Overlap <- pmin ( Y1, Y2 )
polygon ( c ( X, X [ 1 ]), c ( Overlap, Overlap [ 1 ]),
    lwd = 2, col = "hotpink", border = "n", density = 20) 

# Integrate
Total <- trapz ( X, Y1 ) + trapz ( X, Y2 )
(Surface <- trapz ( X, Overlap ) / Total)
SText <- paste ( sprintf ( "%.3f", 100*Surface ), "%" )
text ( X [ which.max ( Overlap )], 1.2 * max ( Overlap ), SText )

杂色和弗吉尼亚花瓣宽度的密度重叠

于 2015-07-24T06:32:34.943 回答