Robust Graphical Methods For Group Comparisons (v. 0.2.1)
The rogme
R package provides graphical tools and robust statistical
methods to compare groups of continous and pseudo-continuous
observations. The goal is to illustrate and quantify how and by how much
groups differ. The current version of the package is limited to
comparing two groups (though multiple pairs of groups can be compared in
one go). Future developments will extend the tools to deal with multiple
groups, interactions and hierarchical designs.
NEW: a hierarchical shift function to compare two dependent conditions from one group is now available. It has parametric and bootstrap versions. The approach is described in Rousselet & Wilcox, 2019.
The package can be installed using these commands:
install.packages("devtools")
devtools::install_github("GRousselet/rogme")
The approach behind the package can be summarised in one figure:
How two independent distributions differ. Left: standard but misleading bar graphs of mean values. Right: detailed graphical methods. A. Stripcharts of marginal distributions. Vertical lines mark the deciles, with a thicker line for the median. B. Kernel density representation and rug plot of the distribution of difference scores. Vertical lines mark the deciles, with a thicker line for the median. C. Shift function. Group 1 - Group 2 is plotted along the y-axis for each decile (white disk), as a function of Group 1 deciles. The vertical lines indicate 95% bootstrap confidence intervals. The shift function can be sparser or denser by changing the quantiles. D. Difference asymmetry function with 95% bootstrap confidence intervals.
The approach is also described in these articles:
A few simple steps to improve the description of group results in neuroscience
Beyond differences in means: robust graphical methods to compare two
groups in
neuroscience.
[Reproducibility package using
rogme
]
rogme
uses ggplot2
for graphical representations, and the main
statistical functions were developed by Rand Wilcox, as part of his
WRS
package.
The main tool in rogme
is the shift
function. A
shift function shows the difference between the quantiles of two groups
as a function of the quantiles of one group. For inferences, the
function returns an uncertainty interval for each quantile difference.
By default, the deciles are used. Currently, confidence intervals are
computed using one of two percentile bootstrap techniques. Highest
density intervals and Bayesian
bootstrap intervals will be
available eventually.
All the main functions rely on the Harrell-Davis quantile
estimator,
computed by the hd()
function.
In the WRS
package, the shift function can be calculated using:
shifthd()
or qcomhd()
for independent groupsshiftdhd()
or Dqcomhd()
for dependent groupsThese functions can also produce non-ggplot figures.
In rogme
, the shift function can be calculated using:
shifthd()
or shifthd_pbci()
for independent groupsshiftdhd()
or shiftdhd_pbci()
for dependent groupsIllustrations of the results is handled separately by plot_sf()
.
You can see the shift function in action for instance in these publications:
Sex Differences in the Adult Human Brain: Evidence from 5216 UK Biobank Participants
Manipulation of contact network structure and the impact on foot-and-mouth disease transmission
No evidence that frontal eye field tDCS affects latency or accuracy of prosaccades
The difference asymmetry function is another powerful graphical and
inferential tool. In the WRS
package it is calculated using:
qwmwhd()
for independent groupsdifQpci()
for dependent groupsIn rogme
, these functions have been renamed:
asymhd()
for independent groupsasymdhd()
for dependent groupsplot_diff_asym()
to plot the resultsYou can see the difference asymmetry function in action in this blog post and in this review article.
Detailed illustration of the shift function using two distributions that differ in spread. The observations are in arbitrary units (a.u.).
#> generate data
set.seed(21)
g1 <- rnorm(1000) + 6
g2 <- rnorm(1000) * 1.5 + 6
#> make tibble
df <- mkt2(g1, g2)
First, we generate 1D scatterplots for the two groups.
#> scatterplots alone
ps <- plot_scat2(data = df,
formula = obs ~ gr,
xlabel = "",
ylabel = "Scores (a.u.)",
alpha = 1,
shape = 21,
colour = "grey10",
fill = "grey90") #> scatterplots
ps <- ps + coord_flip()
ps
Second, we compute the shift function and then plot it.
#> compute shift function
sf <- shifthd(data = df, formula = obs ~ gr, nboot = 200)
#> sf <- shifthd_pbci(data = df, formula = obs ~ gr, nboot = 200, q = c(.1,.25,.5,.75,.9))
#> plot shift function
psf <- plot_sf(sf, plot_theme = 2)
#> Warning: Using alpha for a discrete variable is not advised.
#> Warning: Using alpha for a discrete variable is not advised.
#> add labels for deciles 1 & 9
psf <- add_sf_lab(psf, sf,
y_lab_nudge = .1,
text_size = 4)
#> change axis labels
psf[[1]] <- psf[[1]] + labs(x = "Group 1 quantiles of scores (a.u.)",
y = "Group 1 - group 2 \nquantile differences (a.u.)")
psf[[1]]
Third, we make 1D scatterplots with deciles and colour coded differences.
p <- plot_scat2(df,
xlabel = "",
ylabel = "Scores (a.u.)",
alpha = .3,
shape = 21,
colour = "grey10",
fill = "grey90") #> scatterplots
p <- plot_hd_links(p, sf[[1]],
q_size = 1,
md_size = 1.5,
add_rect = TRUE,
rect_alpha = 0.1,
rect_col = "grey50",
add_lab = TRUE,
text_size = 5) #> superimposed deciles + rectangle
p <- p + coord_flip() #> flip axes
p
Finally, we combine the three plots into one figure.
library(cowplot)
cowplot::plot_grid(ps, p, psf[[1]], labels=c("A", "B", "C"), ncol = 1, nrow = 3,
rel_heights = c(1, 1, 1), label_size = 20, hjust = -0.5, scale=.95)
Panel A illustrates two distributions, both n = 1000, that differ in
spread. The observations in the scatterplots were jittered based on
their local density, as implemented in ggbeeswarm::geom_quasirandom
.
Panel B illustrates the same data from panel A. The dark vertical lines mark the deciles of the distributions. The thicker vertical line in each distribution is the median. Between distributions, the matching deciles are joined by coloured lined. If the decile difference between group 1 and group 2 is positive, the line is orange; if it is negative, the line is purple. The values of the differences for deciles 1 and 9 are indicated in the superimposed labels.
Panel C focuses on the portion of the x-axis marked by the grey shaded area at the bottom of panel B. It shows the deciles of group 1 on the x-axis – the same values that are shown for group 1 in panel B. The y-axis shows the differences between deciles: the difference is large and positive for decile 1; it then progressively decreases to reach almost zero for decile 5 (the median); it becomes progressively more negative for higher deciles. Thus, for each decile the shift function illustrates by how much one distribution needs to be shifted to match another one. In our example, we illustrate by how much we need to shift deciles from group 2 to match deciles from group 1.
More generally, a shift function shows quantile differences as a function of quantiles in one group. It estimates how and by how much two distributions differ. It is thus a powerful alternative to the traditional t-test on means, which focuses on only one, non-robust, quantity. Quantiles are robust, intuitive and informative.
The shift function can also be computed for all pairs of groups in a
data frame in one call by using the argument doall = TRUE
.
set.seed(21) # generate data
n <- 100 # sample size
library(tibble)
df <- tibble(gr = factor(c(rep("group1",n),rep("group2",n),rep("group3",n))),
obs= c(rnorm(n), rnorm(n)+1, rnorm(n)*5)) # make tibble
out <- shifthd(df, doall = TRUE) # compute all comparisons
Plot all shift functions in one call of plot_sf
.
plist <- plot_sf(out)
The plots can then be combined using the packages gridExtra or cowplot.
library(gridExtra)
do.call("grid.arrange", c(plist, ncol=2))
To extract one object and for instance change a label:
p <- plist[[1]]
p + labs(y = "Difference")
New group plot with different y labels and titles:
for(sub in 1:length(plist)){
plist[[sub]] <- plist[[sub]] + labs(y = "Difference", title = names(out)[sub]) + theme(plot.title = element_text(size = 20, face = "bold.italic"))
}
do.call("grid.arrange", c(plist, ncol=2))
To understand what’s going on, here are the marginal distributions:
p <- plot_scat2(df,
xlabel = "",
ylabel = "Scores (a.u.)",
alpha = .5,
shape = 21,
colour = "grey10",
fill = "grey90") #> scatterplots
p + coord_flip() #> flip axes
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.