7

我需要将下图中置信带之外的数据点与带内的数据点着色不同。我是否应该在我的数据集中添加一个单独的列来记录数据点是否在置信区间内？你能提供一个例子吗？

用置信带绘图

示例数据集：

## Dataset from http://www.apsnet.org/education/advancedplantpath/topics/RModules/doc1/04_Linear_regression.html

## Disease severity as a function of temperature

# Response variable, disease severity
diseasesev<-c(1.9,3.1,3.3,4.8,5.3,6.1,6.4,7.6,9.8,12.4)

# Predictor variable, (Centigrade)
temperature<-c(2,1,5,5,20,20,23,10,30,25)

## For convenience, the data may be formatted into a dataframe
severity <- as.data.frame(cbind(diseasesev,temperature))

## Fit a linear model for the data and summarize the output from function lm()
severity.lm <- lm(diseasesev~temperature,data=severity)

# Take a look at the data
plot(
  diseasesev~temperature,
  data=severity,
  xlab="Temperature",
  ylab="% Disease Severity",
  pch=16,
  pty="s",
  xlim=c(0,30),
  ylim=c(0,30)
)
title(main="Graph of % Disease Severity vs Temperature")
par(new=TRUE) # don't start a new plot

## Get datapoints predicted by best fit line and confidence bands
## at every 0.01 interval
xRange=data.frame(temperature=seq(min(temperature),max(temperature),0.01))
pred4plot <- predict(
                        lm(diseasesev~temperature),
                        xRange,
                        level=0.95,
                        interval="confidence"
                    )

## Plot lines derrived from best fit line and confidence band datapoints
matplot(
  xRange,
  pred4plot,
  lty=c(1,2,2),   #vector of line types and widths
  type="l",       #type of plot for each column of y
  xlim=c(0,30),
  ylim=c(0,30),
  xlab="",
  ylab=""
)
4

3 回答 3

10

好吧，我认为使用 ggplot2 会很容易，但现在我意识到我不知道如何计算 stat_smooth/geom_smooth 的置信限。

考虑以下：

library(ggplot2)
pred <- as.data.frame(predict(severity.lm,level=0.95,interval="confidence"))
dat <- data.frame(diseasesev,temperature, 
    in_interval = diseasesev <=pred$upr & diseasesev >=pred$lwr ,pred)
ggplot(dat,aes(y=diseasesev,x=temperature)) +
stat_smooth(method='lm')  + geom_point(aes(colour=in_interval)) +
    geom_line(aes(y=lwr),colour=I('red')) + geom_line(aes(y=upr),colour=I('red'))

这会产生： 替代文本 http://ifellows.ucsd.edu/pmwiki/uploads/Main/strangeplot.jpg

我不明白为什么 stat_smooth 计算的置信带与直接从 predict 计算的带不一致（即红线）。任何人都可以对此有所了解吗？

编辑：

弄清楚了。ggplot2 使用 1.96 * 标准误差来绘制所有平滑方法的间隔。

pred <- as.data.frame(predict(severity.lm,se.fit=TRUE,
        level=0.95,interval="confidence"))
dat <- data.frame(diseasesev,temperature, 
    in_interval = diseasesev <=pred$fit.upr & diseasesev >=pred$fit.lwr ,pred)
ggplot(dat,aes(y=diseasesev,x=temperature)) +
    stat_smooth(method='lm')  + 
    geom_point(aes(colour=in_interval)) +
    geom_line(aes(y=fit.lwr),colour=I('red')) + 
    geom_line(aes(y=fit.upr),colour=I('red')) +
    geom_line(aes(y=fit.fit-1.96*se.fit),colour=I('green')) + 
    geom_line(aes(y=fit.fit+1.96*se.fit),colour=I('green'))
于 2010-04-22T00:50:01.553 回答
6

最简单的方法可能是计算一个TRUE/FALSE值向量，指示数据点是否在置信区间内。我将稍微重新调整您的示例，以便在执行绘图命令之前完成所有计算 - 这在程序逻辑中提供了一个干净的分离，如果您要将其中的一些打包到一个函数中，可以利用它.

第一部分几乎相同，除了我用变量替换了对 inside 的额外调用——当lm()我们已经存储了线性模型时，不需要使用额外的计算资源来重新计算线性模型：predict()severity.lm

## Dataset from 
#  apsnet.org/education/advancedplantpath/topics/
#    RModules/doc1/04_Linear_regression.html

## Disease severity as a function of temperature

# Response variable, disease severity
diseasesev<-c(1.9,3.1,3.3,4.8,5.3,6.1,6.4,7.6,9.8,12.4)

# Predictor variable, (Centigrade)
temperature<-c(2,1,5,5,20,20,23,10,30,25)

## For convenience, the data may be formatted into a dataframe
severity <- as.data.frame(cbind(diseasesev,temperature))

## Fit a linear model for the data and summarize the output from function lm()
severity.lm <- lm(diseasesev~temperature,data=severity)

## Get datapoints predicted by best fit line and confidence bands
## at every 0.01 interval
xRange=data.frame(temperature=seq(min(temperature),max(temperature),0.01))
pred4plot <- predict(
  severity.lm,
  xRange,
  level=0.95,
  interval="confidence"
)

现在，我们将计算原始数据点的置信区间并运行测试以查看这些点是否在区间内：

modelConfInt <- predict(
  severity.lm,
  level = 0.95,
  interval = "confidence"
)

insideInterval <- modelConfInt[,'lwr'] < severity[['diseasesev']] &
  severity[['diseasesev']] < modelConfInt[,'upr']

然后我们将进行绘图-首先是高级绘图函数plot()，正如您在示例中使用的那样，但我们只会绘制区间内的点。然后我们将跟进低级函数points()，它将以不同的颜色绘制区间外的所有点。最后，matplot()将用于填写您使用时的置信区间。par(new=TRUE)但是，我宁愿将参数传递给高级函数，而不是调用add=TRUE，以使它们像低级函数一样工作。

使用par(new=TRUE)绘图功能就像玩肮脏的把戏 - 这可能会产生无法预料的后果。该add参数由许多函数提供，以使它们向绘图添加信息而不是重绘它 - 我建议尽可能利用此参数，并将par()操作作为最后的手段。

# Take a look at the data- those points inside the interval
plot(
  diseasesev~temperature,
  data=severity[ insideInterval,],
  xlab="Temperature",
  ylab="% Disease Severity",
  pch=16,
  pty="s",
  xlim=c(0,30),
  ylim=c(0,30)
)
title(main="Graph of % Disease Severity vs Temperature")

# Add points outside the interval, color differently
points(
  diseasesev~temperature,
  pch = 16,
  col = 'red',
  data = severity[ !insideInterval,]
)

# Add regression line and confidence intervals
matplot(
  xRange,
  pred4plot,
  lty=c(1,2,2),   #vector of line types and widths
  type="l",       #type of plot for each column of y
  add = TRUE
)
于 2010-04-22T00:55:03.590 回答
4

我喜欢这个想法并尝试为此创建一个功能。当然，它远非完美。欢迎您的意见

diseasesev<-c(1.9,3.1,3.3,4.8,5.3,6.1,6.4,7.6,9.8,12.4)
# Predictor variable, (Centigrade)
temperature<-c(2,1,5,5,20,20,23,10,30,25)

## For convenience, the data may be formatted into a dataframe
severity <- as.data.frame(cbind(diseasesev,temperature))

## Fit a linear model for the data and summarize the output from function lm()
severity.lm <- lm(diseasesev~temperature,data=severity)

# Function to plot the linear regression and overlay the confidence intervals   
ci.lines<-function(model,conf= .95 ,interval = "confidence"){
  x <- model[[12]][[2]]
  y <- model[[12]][[1]]
  xm<-mean(x)
  n<-length(x)
  ssx<- sum((x - mean(x))^2)
  s.t<- qt(1-(1-conf)/2,(n-2))
  xv<-seq(min(x),max(x),(max(x) - min(x))/100)
  yv<- coef(model)[1]+coef(model)[2]*xv

  se <- switch(interval,
        confidence = summary(model)[[6]] * sqrt(1/n+(xv-xm)^2/ssx),
        prediction = summary(model)[[6]] * sqrt(1+1/n+(xv-xm)^2/ssx)
              )
  # summary(model)[[6]] = 'sigma'

  ci<-s.t*se
  uyv<-yv+ci
  lyv<-yv-ci
  limits1 <- min(c(x,y))
  limits2 <- max(c(x,y))

  predictions <- predict(model, level = conf, interval = interval)

  insideCI <- predictions[,'lwr'] < y & y < predictions[,'upr']

  x_name <- rownames(attr(model[[11]],"factors"))[2]
  y_name <- rownames(attr(model[[11]],"factors"))[1]

  plot(x[insideCI],y[insideCI],
  pch=16,pty="s",xlim=c(limits1,limits2),ylim=c(limits1,limits2),
  xlab=x_name,
  ylab=y_name,
  main=paste("Graph of ", y_name, " vs ", x_name,sep=""))

  abline(model)

  points(x[!insideCI],y[!insideCI], pch = 16, col = 'red')

  lines(xv,uyv,lty=2,col=3)
  lines(xv,lyv,lty=2,col=3)
}

像这样使用它：

ci.lines(severity.lm, conf= .95 , interval = "confidence")
ci.lines(severity.lm, conf= .85 , interval = "prediction")
于 2010-04-22T12:08:59.873 回答