Scatterplot Showing All Points

On 18 Dec 2007, at 4:49 pm, Duncan Murdoch wrote:

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?

Area is used.

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.

If someone needs a count, they should be given a table.   Graphics  
are for qualitative conclusions not details.  Anyway, counting will  
only work for really small datasets.

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.

That's right and that's (almost) the sort of example I was thinking  
of.  For a limited number of locations like this a bubble plot would  
be best (which has already been suggested in this thread, I think).   
For many locations and few replications I would still go for varying  
pointsize and transparency.

Incidentally, to check your suggestion I ran your code and discovered  
that the transparency in iplot does not seem to like replications.   
Very strange, we'll have to check why.  I then looked closely at the  
numbers of replications generated and discovered that case 25 was  
picked 325 times and case 40 only once.  Rather too extreme for my  
liking!  Running it again gave very similar results, though not  
exactly the same: this time it was 325 times for case 25 and case 40  
was not picked at all.  Other numbers varied slightly.  This is not  
what I expected, any ideas?

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.

Thanks.  This happens occasionally on the Mac too.  Refreshing solves  
it in practice, but we need to find out why it can happen (and stop  
it happening!).

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