On Thu, 13 May 1999, Arthur Gilmour wrote:
Hi Hans,
I have added a few more comments,
>
>
> >
> > Dear Arthur,
> >
> > I am trying to fit three-way models, using US and FA structures. The
> > following is an example. It works well with US (only a few seconds! great!
> > With MIXED, it takes hours! While writing this, MIXED has not converged on
> > the same data set).
> >
> > Unfortunately, I am having some problems with the FA starcture.
> >
> > Questions:
> >
> > (1) Do I need to specify !S2==1 also with the G.L and G.Y structures
> > (G-matrices), as in the R-matrix structures? If I do, I get some strange
> > error messages with some models. With US, the last variance parameter is
> > fixed at 1, so it seems I should not be using "S2==1 with G structures. But
> > why with the R-matrix and not with the G-matrix?
>
> It is a matter of fixing the overall scale. Essentially the Variance
> Structure is S2(R+ZGZ') .
This is clearly a problem with the ASREML syntax. Users shouldn't have to
be confused by this. It seems to me that all variance models should be
defined by the users in terms of variance components. ASREML should then
be able to internally decide whether a scale parameters ie $\sigma^2_e$
can be extracted sensibly. Ie in the analysis of an MET one-stage there
is no sensible way of extracting this scale parameter.
>
> If R is a correlation matrix (e.g. ARxAR as in the spatial analysis,
> I as in a simple mixed model - say incomplete block analysis) then S2 is
> needed. So the default for a univariate analysis at one site is to
> estimate S2 and assume R is a correlation. I suppose ASREML could work it out
> but it doesn't at the moment and the default is the most common case.
> G is then parameterized in terms of Gammas (Variance ratios)
>
> However, in your case R is a variance matrix 9it includes a scaling
> parameter. The choice is then to fix S2 (at say 1 but it could be
> any value) or to fix an element in R (which is possible). G is then
> placed on the same scale. It is important then that G always include
> a scale parameter.
>
> >
> > (2) When I replace the first US (R-matrix) by FA in the code below, ASREML
> > aborts with the error message "AIGETR FA 2". How can this be fixed?
> >
> yield ~ mu !r L.G Y.G !f G mv
> 1 3 2 !step 0.01
> L L !S2==1
> Y Y !S2==1
> G G US !GP !+10
> 2
> 1 2
> 1 1 2
> 1 1 1 2
>
>
> First S2 should only be specified once
>
> Secondly, The order of G (4) is not big enough to sustain 2 factors.
> 2 factor FA of 4 levels involves 12 parameters but a full US only has 10.
> Since I overwrite the initial US with the FA parameters, there is
> not enough room.
>
> Thirdly, we hqve often had dificulty getting FA 2 and higher working
> without using good starting values. So a better way of setting it up
> is
>
> G G FA !G5PZ4P5P !A !V2 !+15 # Assuming 5 levels
> 5*.7
> 5*.1
> 5*2
there is much to do in this area, Arthur has given you the basis but our
simulations have indicated that the average information algorithm is
unreliable for fa(2) models, even with good starting values and a corner
point constraint as he has used in the above
>
> > (3) When I replace the second US by FA/FACV, thr program runs, but I get 2
> > strange variances in the output:
> >
> > Variance 400 319 0.00000 0.00000 0.00 0 F
> > Variance 400 319 0.00000 0.00000 0.00 0 F
> >
> > Funnily, this does not happen, if I replace (only) the third US by FA/FACV.
> > What is wrong here?
>
> These lines should not be printed.
>
> ASREML reads in the 10 parameters for the US layout and then
> reparameterizes to the 8 parameters of the FA1 layout. This leaves
> 2 unused positions which are set to zero. I'll look for the reason
> they appear but the should not. Ignore them.
>
> >
> > (4) I thought, using !V2 on the FA structure, i.e.
> >
> > G 0 FACV !V2 !GP !+10 ,
> >
> > I would be fitting 2 factors, but I end up with only one term and the same
> > fit as when not using !V2. What am I missing?
>
> You need at least 5 levels in G to fit FA 2 as explained above.
> I realise you couuld define an FA2 putting an appropriate constraint
> to reduce the free parameters from 12 to 10 but I do not allow that
> (probably even if you put the vectors in directly).
yes, see alison's phd, chapter 6 for a more complete discussion
best wishes
brian
...............................................................................
Brian Cullis Tel: 02 6938 1855
NSW Agriculture Fax: 02 6938 1809
Wagga Agricultural Institute email: brian.cullis@agric.nsw.gov.au
Pine Gully Rd
WAGGA WAGGA NSW 2650
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