Graphics for Statistics - figures with ggplot2 - chapter 5 quantile-quantile plots

Table of Contents

• 1. Keen Chapter 5
  
  • 1.1. Figure 5.1 normal quantile-quantile plot
  • 1.2. Figure 5.2 normal quantile-quantile plot
  • 1.3. Figure 5.3 normal quantile-quantile plot
  • 1.4. Figure 5.4 gamma quantile-quantile plot
  • 1.5. Figure 5.5 normal quantile-quantile plot
  • 1.6. Figure 5.6 normal quantile-quantile plot
  • 1.7. Figure 5.7 gamma quantile-quantile plot

1 Keen Chapter 5

1.1 Figure 5.1 normal quantile-quantile plot

• first set up the data vector
  
• then we use a point layer with the quantile-quantile stat and change the size of the points: geom_point(stat="qq",shape=1,size=3.5)
  

require(ggplot2)
require(grid)
mass<-c(5.9,32.0,40.0,51.5,70.0,100.0,78.0,80.0,85.0,85.0,
              110.0,115.0,125.0,130.0,120.0,120.0,130.0,135.0,110.0,130.0,
              150.0,145.0,150.0,170.0,225.0,145.0,188.0,180.0,197.0,218.0,
              300.0,260.0,265.0,250.0,250.0,300.0,320.0,514.0,556.0,840.0,
              685.0,700.0,700.0,690.0,900.0,650.0,820.0,850.0,900.0,1015.0,
              820.0,1100.0,1000.0,1100.0,1000.0,1000.0)
df <- data.frame(y=mass)

ggplot(df,aes(sample=mass)) +
    geom_point(stat="qq",shape=1,size=3.5) +
    scale_x_continuous(limits=c(-3,3),breaks=-3:3,expand=c(0,0.1)) +
    scale_y_continuous(limits=c(0,1200),breaks=seq(0,1200,by=200),expand=c(0,20)) +
    xlab("Standard Normal Quantiles") +
    ylab("Mass (g)") +
          theme(
          panel.background=element_blank(),
          axis.line=element_line(colour="black"),
          axis.text=element_text(colour="black",size=14),
          axis.title=element_text(colour="black",size=14),
          axis.ticks=element_line(colour="black"),
          axis.ticks.length=unit(3,"mm")
          )

1.2 Figure 5.2 normal quantile-quantile plot

• only use coord_flip() on the previous plot
  

ggplot(df,aes(sample=mass)) +
    geom_point(stat="qq",shape=1,size=3.5) +
    scale_x_continuous(limits=c(-3,3),breaks=-2:2,expand=c(0,0.5)) +
    scale_y_continuous(limits=c(0,1200),breaks=seq(0,1200,by=200),expand=c(0,20)) +
    xlab("Standard Normal Quantiles") +
    ylab("Mass (g)") +
    coord_flip() +
          theme(
          panel.background=element_blank(),
          axis.line=element_line(colour="black"),
          axis.text=element_text(colour="black",size=14),
          axis.title=element_text(colour="black",size=14),
          axis.ticks=element_line(colour="black"),
          axis.ticks.length=unit(3,"mm")
          )

1.3 Figure 5.3 normal quantile-quantile plot

• only add geom_abline() with intercept=mean(mass) and slope=sd(mass) (the line goes through the point defined by the mean of both, x and y values which is (mean(standard normal dist)=0,mean(mass)) therefore mean(mass) is the intercept; the sd of the norm is one so the slope is sd(mass)/sd(standard normal dist)=sd(mass))
  

ggplot(df,aes(sample=mass)) +
    geom_point(stat="qq",shape=1,size=3.5) +
    geom_abline(intercept=mean(mass),slope=sd(mass)) + 
    scale_x_continuous(limits=c(-3,3),breaks=-3:3,expand=c(0,0.1)) +
    scale_y_continuous(limits=c(0,1200),breaks=seq(0,1200,by=200),expand=c(0,20)) +
    xlab("Standard Normal Quantiles") +
    ylab("Mass (g)") +
          theme(
          panel.background=element_blank(),
          axis.line=element_line(colour="black"),
          axis.text=element_text(colour="black",size=14),
          axis.title=element_text(colour="black",size=14),
          axis.ticks=element_line(colour="black"),
          axis.ticks.length=unit(3,"mm")
          )

1.4 Figure 5.4 gamma quantile-quantile plot

• first we calculate the estimates of the scale and shape parameter of the gamma dist
  
• then we only change the dist to qgamma (distribution="qgamma") and set the parameters as list (dparams=list(shape=sshape,scale=sscale))
  
• last adjust the x-axis (limits and breaks)
  

sshape<-(mean(mass)/sd(mass))**2
sscale<-var(mass)/mean(mass)

ggplot(df,aes(sample=mass)) +
    geom_point(stat="qq",distribution="qgamma",dparams=list(shape=sshape,scale=sscale),shape=1,size=3.5) +
    scale_x_continuous(limits=c(0,1500),breaks=seq(0,1500,by=500),expand=c(0,20)) +
    scale_y_continuous(limits=c(0,1200),breaks=seq(0,1200,by=200),expand=c(0,20)) +
    xlab("Gamma Quantiles") +
    ylab("Mass (g)") +
          theme(
          panel.background=element_blank(),
          axis.line=element_line(colour="black"),
          axis.text=element_text(colour="black",size=14),
          axis.title=element_text(colour="black",size=14),
          axis.ticks=element_line(colour="black"),
          axis.ticks.length=unit(3,"mm")
          )

1.5 Figure 5.5 normal quantile-quantile plot

• we only have to change the x-axis of plot 5.1
  
• so set the limits to c(-4,4) and the breaks to the required x-values by using the qnorm() function and change the labels appropriately
  
• finally change to title of the x-axis
  

ggplot(df,aes(sample=mass)) +
    geom_point(stat="qq",shape=1,size=3.5) +
    scale_x_continuous(limits=c(-4,4),
                       breaks=qnorm(c(0.0001,.01,.05,.25,.50,.75,.95,.99,.9999)),
                       labels=c(0.01,1,5,25,50,75,95,99,99.99),
                       expand=c(0,0.1)) +
    scale_y_continuous(limits=c(0,1200),breaks=seq(0,1200,by=200),expand=c(0,20)) +
    xlab("Normal Percentiles") +
    ylab("Mass (g)") +
          theme(
          panel.background=element_blank(),
          axis.line=element_line(colour="black"),
          axis.text=element_text(colour="black",size=14),
          axis.title=element_text(colour="black",size=14),
          axis.ticks=element_line(colour="black"),
          axis.ticks.length=unit(3,"mm")
          )

1.6 Figure 5.6 normal quantile-quantile plot

• it is the same like plot 5.5 - only add coord_flip()
  

ggplot(df,aes(sample=mass)) +
    geom_point(stat="qq",shape=1,size=3.5) +
    scale_x_continuous(limits=c(-4,4),
                       breaks=qnorm(c(0.0001,.01,.05,.25,.50,.75,.95,.99,.9999)),
                       labels=c(0.01,1,5,25,50,75,95,99,99.99),
                       expand=c(0,0.1)) +
    scale_y_continuous(limits=c(0,1200),breaks=seq(0,1200,by=200),expand=c(0,20)) +
    xlab("Normal Percentiles") +
    ylab("Mass (g)") +
    coord_flip() +
          theme(
          panel.background=element_blank(),
          axis.line=element_line(colour="black"),
          axis.text=element_text(colour="black",size=14),
          axis.title=element_text(colour="black",size=14),
          axis.ticks=element_line(colour="black"),
          axis.ticks.length=unit(3,"mm")
          )

1.7 Figure 5.7 gamma quantile-quantile plot

• from figure 5.4 we have to change the axis and flip the coordinates:
  
• to calculate the breaks we use qgamma() with the appropriate values and the shape and scale parameter
  
• then we change the labels accordingly
  
• add coord_flip()
  

sshape<-(mean(mass)/sd(mass))**2
sscale<-var(mass)/mean(mass)

ggplot(df,aes(sample=mass)) +
    geom_point(stat="qq",distribution="qgamma",dparams=list(shape=sshape,scale=sscale),shape=1,size=3.5) +
    scale_x_continuous(limits=c(0,2400),
                       breaks=qgamma(c(0.01,.25,.50,.75,.95,.99,.999),shape=sshape,scale=sscale),
                       labels=c(1,25,50,75,95,99,99.9),expand=c(0,20)) +
    scale_y_continuous(limits=c(0,1200),breaks=seq(0,1200,by=200),expand=c(0,20)) +
    xlab("Gamma Quantiles") +
    ylab("Mass (g)") +
    coord_flip() +
          theme(
          panel.background=element_blank(),
          axis.line=element_line(colour="black"),
          axis.text=element_text(colour="black",size=14),
          axis.title=element_text(colour="black",size=14),
          axis.ticks=element_line(colour="black"),
          axis.ticks.length=unit(3,"mm")
          )