MATLAB: How to create variability charts

jmpStatistics and Machine Learning Toolboxvariability

I'm trying to find a way to recreate JMP-style variability charts using MATLAB.
I've tried looking through the Stats Toolbox and the File Exchange, and can't find anything that would do the trick. Anyone have an idea?
Thanks!

Best Answer

EDIT: file added to MATLAB File Exchange. Share and enjoy!
Based on your comment above, boxplot with nominal grouping variables will do it:
x = randn(400,1);
y1 = nominal(round(rand(400,1)),{'little','lots'});
y2 = nominal(round(rand(400,1)),{'large','small'});
y3 = nominal(round(rand(400,1)),{'gourmet','plain'});
boxplot(x,[y1,y2,y3])
Hopefully this is basically how your data is already arranged. x contains all 400 observations of the response variable. y1, y2, and y3 are nominal arrays that record each observation's status for the three categories.
The boxplot labeling doesn't emphasize the hierarchy, but the results are correct.
EDIT TO ADD Oops, I got the grouping variables backward. Anyway, this is getting close to what you posted:
boxplot(x,[y3,y2,y1],...
  'plotstyle','compact','labelorientation','horizontal',...
  'factorseparator',[1,2])
The only problem is that the vertical arrangement of the group labels is backwards, for showing the hierarchy. This can be hacked, though, if you need:
h = findobj(get(gca,'children'),'type','text');
tl = get(h,'position');
tl = cat(1,tl{:});
tl(:,2) = flipud(tl(:,2));
for k = 1:length(h)
   set(h(k),'position',tl(k,:))
end
EDIT TO ADD (2): Not pretty, but here's a function that does a reasonable job of approximating the graphic:
function variabilityplot(x,y)
n = size(y,2);
numgrps = zeros(1,n);
for k = 1:n
    numgrps(k) = numel(unique(y(:,k)));
end
numgrps = cumprod(numgrps);
N = numgrps(n);
y = fliplr(y);
boxplot(x,y,...
    'plotstyle','compact','labelorientation','horizontal',...
    'factorseparator',1:n);
hbxplt = get(gca,'children');
hall = get(hbxplt,'children');
halltype = get(hall,'type');
hsepln = hall(end-n+1:end);
htxt = hall(strcmpi('text',halltype));
set(htxt,'units','data')
txtpos = get(htxt,'position');
txtpos = cat(1,txtpos{:});
txtpos(:,2) = flipud(txtpos(:,2));
x = reshape(txtpos(:,1),N,n);
for k = 2:n
    m = numgrps(k-1);
    for j = 1:N
        ii = floor((j-1)/m);
        i1 = 1 + m*ii;
        i2 = m*(1+ii);
        x(j,k) = mean(x(i1:i2,1));
    end
end
txtpos(:,1) = x(:);
for k = 1:length(htxt)
    set(htxt(k),'position',txtpos(k,:))
end
tlcol = 0.5*[1,1,1];
txtpos = get(htxt,'extent');
txtpos = cat(1,txtpos{:});
xl = xlim;
yl = ylim;
y1 = min(yl);
y2 = min(txtpos(:,2));
y = linspace(y1,y2,n+1);
for k = 2:(n+1)
    line(xl,[y(k),y(k)],'parent',gca,'clipping','off','color',tlcol)
end
line(xl(1)*[1,1],[y1,y2],'parent',gca,'clipping','off','color',tlcol)
line(xl(2)*[1,1],[y1,y2],'parent',gca,'clipping','off','color',tlcol)
for j = 1:n
    newy = get(hsepln(j),'YData');
    newy(newy==yl(2)) = y(j+1);
    line(get(hsepln(j),'XData'),newy,'parent',gca,'clipping','off','color',tlcol)
end
delete(hsepln(1))
Trying it out:
x = randn(400,1);
y1 = nominal(randi(2,400,1),{'little','lots'});
y2 = nominal(randi(3,400,1),{'large','medium','small'});
y3 = nominal(randi(2,400,1),{'gourmet','plain','aardvark','potato'},[1,2,3,4]);
y = [y1,y2,y3];
variabilityplot(x,y)
If you think it's useful, I'll clean it up a bit and put it on the File Exchange soon.
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