r - Errorbars in a log scale plot?

Question

So, what is the right way to present error bars when plotting points on a log scale? Because error bars are symetric on the absolute scale, I thought they would be asymmetric on the log scale. However, with the below code, they show up as symmetric on the log scale. My initial question was 'Is the code displaying the error bars properly?' After a little bit of looking I am left a little uncertain.

• I am still not entirely sure it is displaying the error bars properly. However, I am leaning towards the understanding that it is displaying 'relative' error bars, which it thinks are the right error bars to display for logged data.
• Can I display the absolute error bars on the log scale in any simple manner? Is there a parameter I have overlooked that will let me flip this switch?
• Perhaps more generally, why are relative error bars in log space considered 'right'?

library(ggplot2
pde=1.1 #position dodge for error bars
pdp=0.35 #position dodge for points
p<-ggplot(data=mtcars, aes(x=vs, y=mpg, colour=factor(am)))+
  geom_point(position=position_dodge(width=pdp), size=3)+
  stat_summary( fun = "mean", geom="point", size=2,stroke=1.1, position=position_dodge(width=pde))+ 
  stat_summary( fun.data = "mean_se", geom = "errorbar", width=0.15, position=position_dodge(width=pde))+
  scale_y_log10(limits = c(1,150))

Answer 1

The help for coord_trans() explains that scale transformations (e.g., scale_y_log10()) are performed before statistics are calculated, while coordinate transformations (e.g., coord_trans(y="log10")) are performed after statistics are calculated.

In your case, this means that with scale_y_log10 the mean and se are being calculated on the log-transformed data, rather than on the original untransformed data. To calculate the statistics on the untransformed data, remove scale_y_log10() and use coord_trans(y="log10").

The example below shows the values that ggplot is calculating internally and then reproduces those values by direct calculation:

library(tidyverse)

pde=1.1 #position dodge for error bars
pdp=0.35 #position dodge for points

p1 = ggplot(data=mtcars, aes(x=vs, y=mpg, colour=factor(am))) +
  geom_point(position=position_dodge(width=pdp), size=3) +
  stat_summary(fun = "mean", geom="point", size=2, stroke=1.1,
               position=position_dodge(width=pde)) +
  stat_summary( fun.data = "mean_se", geom = "errorbar", 
                width=0.15, position=position_dodge(width=pde)) +
  theme_bw() 

p2 = p1 + scale_y_log10() 

# Get data frames for each set of mean/errorbar layers
#  that ggplot calculates internally 
p1dat = ggplot_build(p1)$data[[3]]
p2dat = ggplot_build(p2)$data[[3]]

p1dat %>% select(y, ymin, ymax)
#>          y     ymin     ymax
#> 1 15.05000 14.24910 15.85090
#> 2 20.74286 19.80888 21.67683
#> 3 19.75000 18.11339 21.38661
#> 4 28.37143 26.57319 30.16967

p2dat %>% select(y, ymin, ymax) %>% 
  mutate(y.trans = 10^y,
         ymax.trans = 10^ymax)
#>          y     ymin     ymax  y.trans ymax.trans
#> 1 1.170219 1.145648 1.194790 14.79853   15.65992
#> 2 1.314225 1.294657 1.333793 20.61699   21.56718
#> 3 1.288104 1.252044 1.324165 19.41353   21.09431
#> 4 1.447286 1.418346 1.476226 28.00826   29.93823

Now reproduce those same values by direct calculation:

mtcars %>% 
  group_by(am, vs) %>% 
  summarise(mean = mean(mpg),
            mean.log = mean(log10(mpg)),
            mean.log.trans = 10^mean.log,
            mean.plus.se = mean + sqrt(var(mpg)/length(mpg)),
            se.log = sqrt(var(log10(mpg))/length(mpg)),
            mean.log.plus.se = mean.log + se.log,
            mean.log.plus.se.trans = 10^mean.log.plus.se)

#>   am vs     mean mean.log mean.log.trans mean.plus.se     se.log
#> 1  0  0 15.05000 1.170219       14.79853     15.85090 0.02457101
#> 2  0  1 20.74286 1.314225       20.61699     21.67683 0.01956814
#> 3  1  0 19.75000 1.288104       19.41353     21.38661 0.03606088
#> 4  1  1 28.37143 1.447286       28.00826     30.16967 0.02893993
#>   mean.log.plus.se mean.log.plus.se.trans
#> 1         1.194790               15.65992
#> 2         1.333793               21.56718
#> 3         1.324165               21.09431
#> 4         1.476226               29.93823

And we can also see that coord_trans(y="log10") calculates means and error bars before the log transformation:

p3 = p1 + coord_trans(y="log10")
p3dat = ggplot_build(p3)$data[[3]]

p3dat %>% select(y, ymin, ymax)
#>          y     ymin     ymax
#> 1 15.05000 14.24910 15.85090
#> 2 20.74286 19.80888 21.67683
#> 3 19.75000 18.11339 21.38661
#> 4 28.37143 26.57319 30.16967