Re: Continuous variables in 3 dimensions
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Re: Continuous variables in 3 dimensions

Dear Geoff,

Your idea of splitting the 2 dependent variables into say a 5 x 5 grid
has merit in that you can see how good the coverage is as well as
what the means are within each cell.

If there is evidence a response serface you can then use the tensor
spline approach.

A simple spline is fitted in ASREML as

   D = mu  I1 !r  spl(I1)
   maybe with a fac(I1) added if there is replication.
Generalising this to 2 dimensions

   D = mu I1 I2 I1*I2 !r spl(I1) spl(I2) I1.spl(I2) I2.spl(I1) spl(I1).spl(I2)
   maybe with  fac(I1).fac(I2)  for the lack of fit.
As I understand it, the tensor spline imposes equal
variance on the 5 random terms but this is scale dependent
[i.e. changing units from gms to kg would give a different fit
so I am uncomfortable with imposing that constraint.

Used with the  !SCALE qualifier,    
   equating the components for spl(I1) and spl(I2),
                   and for I1.spl(I2) and I2.spl(I1)
                   does not create a scale dependent model.
   Of course there are many variants of this involving setting knot points etc.
   PS I'll be in Norway, UK and Israel over the next 7 weeks so
   am unlikely to keep up with my email.
> X-Authentication-Warning: petidomo set sender to using -f
> From: "Pollott, Geoffrey E" <>
> To:
> Subject: Continuous variables in 3 dimensions
> Date: Thu, 27 Sep 2001 08:33:02 +0100
> MIME-Version: 1.0
> Dear All
> I have had several situations recently where I am interested in analysing a
> dependent variable (D) and two independent varaibles (I1 and I2) in the same
> model, all three being continuous, normally distributed etc. 
> D = a + b(I1) + c(I2) + ........
> The plot of this relationship is of course three dimensional and a flat
> surface.
> If I suspect that the response surface is not flat:
> a) Has anyone got any ideas for a left hand side that could explore the
> curvature of the response surface?
> b) Has anyone got any good software for plotting such a surface in 3D.
> My 'simple' solution is to divide each independent variable into a number of
> classes and then estimate the interaction least-squares means for each
> sub-class. These can be plotted. However, this seems rather a 'cop out' way
> of solving the problem.
> Any ideas please?
> Thanks
> Geoff
> _____________________________________________________ 
> Dr Geoff Pollott 
> Senior Lecturer in Animal Breeding and Production 
> Department of Agricultural Sciences 
> Imperial College at Wye 
> Ashford 
> Kent 
> TN25 5AH 
> UK 
> Tel: +44 (0)20 759 42707 
> Fax: +44 (0)20 759 42919 
> __________________________________________________ 

Arthur Gilmour PhD        
Principal Research Scientist (Biometrics)            fax: <61> 2 6391 3899
NSW Agriculture                                           <61> 2 6391 3922
Orange Agricultural Institute             telephone work: <61> 2 6391 3815
Forest Rd, ORANGE, 2800, AUSTRALIA                  home: <61> 2 6362 0046
                                                   Cargo: <61> 2 6364 3288
I havn't finished building my house at Cargo but am back at work.

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