orthog polynomials and splines
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orthog polynomials and splines




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> Hi,

> Three questions related to random regressions:

> How are constructed the orthogonal polynomials in ASREML (or what is de family 
> of polynomials that Arthur used for the program)?

   The orthogonal polynomial coefficients are print in the .asl file
   if you use the -DL command line option.  I have list track of the
   source of the subroutine but I think it was given me by Brian Coote
   over 20 years ago.   

> If the polynomials are really orthogonal I think the variance matrix of the > 
> polynomial coefficients should be a diagonal, but checking in the .res file > 
> after fitting a DIAG matrix shows covariance terms different from 0.  However, 
> if I try to fit a US matrix, the program does not converge (and it is just > > 
> jumping from one value to other).  Should I just assume that they are zero?

The coefficients are orthogonal when taken as a single replicate.
More likely you have unequal replication of the X values so that
across the data file, they will not be orthogonal.  

If you take as starting values, those from the .res file after fitting DIAG,
I would have thought you should be able to get to convergence.
I would use !STEP 0.1 if it failed to converge initially.\

COnvergence may be difficult to achieve when there are other random factors
in the model which might use some of the variation.

> If I include something like subject.spl(age) as part of my model (to use a > > 
> random regression) how is the G matrix specified for that term?
> e.g. y~spl(age) !r subject.spl(age) etc...
...
> subject.spl(age) 2
> subject 0
> spl(age) 0 ?


I wouldbe looking at adding a few more terms: (I presume spl(age) as a fixed 
effect
is a typo!

Try
   y ~ mu lin(age) !r spl(age) subject subject.age subject.spl(age) dev(age)
   ...
   
   For this model, you do not need to specify a G structure for any terms
   [but you may want to allow a covariance between slope and intercept
   
   subject 2
   2 0 US .1 -.01 .1
   subject
   
   
   I would build up to this though - first fitting the simpler model
   so as to get reasonable starting values.
   
   
   Arthur
Thanks a lot,


Luis

&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~>
Luis Apiolaza
Palmerston North, New Zealand
Web:	http://www.geocities.com/Yosemite/Gorge/3063/
Email:	cronopio@altavista.net
"Quote me as saying I was misquoted" - Groucho Marx
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~>




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Arthur Gilmour PhD                    email: Arthur.Gilmour@agric.nsw.gov.au
Senior Research Scientist (Biometrics)                 fax: <61> 2 6391 3899
NSW Agriculture                                             <61> 2 6391 3922
Orange Agricultural Institute               telephone work: <61> 2 6391 3815
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