Re: [S] mixture expt.

Prof Brian Ripley (
Tue, 3 Mar 1998 22:10:39 +0000 (GMT)

Andrew M Kuhn wrote:
> Winson,
> One popular way of graphing contours for mixture designs is the ternary
> plot. With three factors, the graph area resembles a equilateral
> triangle where the axes range form 0 to 1. I don't know that anyone has
> implemented this in splus, but I do kow that sas's JMP product has a
> menu option to create the plot (sorry for the non-Splus plug).

There have been several postings in the past, and there is a ternary plot
function in the on-line exercises & answers to V&R2. The bigger problem
is the contouring. A good contouring algorithm in a triangular coordinate
system will differ from one on a grid. My suggestion would be to map your
points from (x1,x2,x3) to ternary coordinates, use interp to interpolate
to a fine grid, set the results to NA outside the triangle and then use
contour. But this will only work for a smooth surface, and I am not sure
if you have f or Y. If you have Y, you don't want a contouring
algorithm but a smoothing algorithm. Again, in principle the answer
is known, say by first changing coords and using loess.

> Max Kuhn
> Medical College of Virginia
> Virginia Commonwealth University
> On Tue, 3 Mar 1998, Winson Taam wrote:
> > The following question might have been answered in the past.
> > I am trying to construct a contour plot for a response surface from
> > a mixture experiment. That is, Y=f(x1,x2,x3)+e where x1+x2+x3=1.
> > I found no references in Splus help screen, its documentation or
> > MASS book. Any suggestion is welcome.
> >

Brian D. Ripley,        
Professor of Applied Statistics,
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272860 (secr)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595
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