Scatterplot Showing All Points

On 18 Dec 2007, at 2:42 pm, Duncan Murdoch wrote:

(I must admit to being very surprised that jittering and  
sunflower  plots have been suggested for a dataset of 5000  
points.  Do those who  mentioned these methods have examples on  
that scale where they are  effective?)

Sure.  The original post said there were about 50-60 unique  
locations. This plot:

x <- rbinom(5000, 20, 0.15)
y <- rbinom(5000, 20, 0.15)
plot(x,y)

has a few more unique locations; tune those probabilities if you  
want it closer.  Due to the overlap, the distribution is very  
unclear.  But this plot

plot(jitter(x), jitter(y))

makes the distribution quite clear.

No it doesn't!  It makes it moderately clearer than the plot without  
jittering.  One good alternative here is the fluctuation diagram  
variant of a mosaic plot:

xx<-as.factor(x)
yy<-as.factor(y)
imosaic(xx,yy, type="f")

That plot is better than jittering, but there's the problem in the 
mosaic plot of understanding the scale of the rectangles:  is it area or 
diameter that encodes the count?  With a jittered plot, you lose 
resolution when the number of points gets too high because you just see 
a mess of ink, but at least you only require the viewer to count in 
order to get a close numerical reading from the plot.

I could also claim that while imperfect, at least jittering is widely 
applicable.  For example, if the data were not on a regular grid, 
perhaps because they had been generated like this:

xloc <- rnorm(50)
yloc <- rnorm(50)
index <- sample(1:50, 5000, rep=TRUE, prob = abs(xloc))
x <- xloc[index]
y <- yloc[index]

then jittering still works as well (or as poorly), but the imosaic would 
not work at all.  There are better plots than jittering available, but 
jittering is easy.

(Actually, with this dataset, plot(jitter(x), jitter(y)) is really poor, 
because jitter() chooses a bad amount of jittering.  But with manual 
tuning (e.g.  plot(jitter(x, a=0.1), jitter(y, a=0.1), pch=".")) it's 
not too bad.  So I'd say jittering worked, but the R implementation of 
it may need improvement).

Using jittering for categorical data is really not to be recommended  
and will certainly degrade in performance as the dataset gets bigger.

Yes, I probably wouldn't recommend jittering if there were more than a 
few hundred replications at any point, or more than a few hundred unique 
points.

Duncan Murdoch

P.S. iplots 1.1-1 may have an init problem in Windows: in my first 
attempt, the plot made the boxes too large to fit in their cells, but it 
fixed itself when I resized the window, and the bug doesn't seem to be 
repeatable.

Antony Unwin
Professor of Computer-Oriented Statistics and Data Analysis,
University of Augsburg,
Germany