Re: ASREML Augmented Designs problem

# Re: ASREML Augmented Designs problem

```> > From: Vincenzo Matassa <s185152@student.uq.edu.au>
> To: Arthur Gilmour <gilmoua@ornsun.agric.nsw.gov.au>
> Subject: ASREML Augmented Designs problem
>
> Dear Asremlers,
> 	I am baffled in another problem of mine. Pretend we have an
> Augmented randomised complete block experiment. That is a randomised
> complete block design with unreplicated genotypes augmenetd in the
> design. For instance:
>
> 		Rep1	Rep2
>
>                 check   5
> 		1       check
> 		2       6
> 		3       7
> 		4       check
> 		check   8
>
> Now if we think of the linear model;
>
> 	Yield= grand_mean + Block effects + Genotype +Check + Error    (1)
>
> were all main effects are considered fixed.
>
> The Fitted value for say Genotype (1) should be;
>
>         Yield(1)=rep1 effect + raw genotype(1) yield value        (2)
>
> If I fit
>
> 	Yield ~ mu rep check  genotype                   (3)
>
> in ASREML.The fitted value for Genotypoe (1) say is just the raw yield
> value. I believe it should be the form given in eq.(2).
>

QUESTION 1: how is 'genotype' coded in the CHECK plots?
If we assume genotype is 0 for check plots
and CHECK is coded a particular value for all TEST plots.

Without constraints or random effects
rep_1 effect is zero;
check_1 effect is zero and
genotype_1 effect is zero

However; if CHECK is coded 0 for all TEST plots,
then NO singularity occures in the GENOTYPE factor
so  Genotype_1 will be the deviation from the mean.

X matrix becomes
mu r1 r2  C g1 g2 g3 g4 g5 g6 g7 g8
1  1  0  1  0  0  0  0  0  0  0  0
1  1  0  0  1  0  0  0  0  0  0  0
1  1  0  0  0  1  0  0  0  0  0  0
1  1  0  0  0  0  1  0  0  0  0  0
1  1  0  0  0  0  0  1  0  0  0  0
1  1  0  1  0  0  0  0  0  0  0  0

1  0  1  0  0  0  0  0  1  0  0  0
1  0  1  1  0  0  0  0  0  0  0  0
1  0  1  0  0  0  0  0  0  1  0  0
1  0  1  0  0  0  0  0  0  0  1  0
1  0  1  1  0  0  0  0  0  0  0  0
1  0  1  0  0  0  0  0  0  0  0  1

S        S
Here, the first REP effect is singular and the first genotype will
be singular becasue the Check and Genotype combine to make MU

If terms were fitted in a different order in ASREML; so that MU and
REP_1 were singular, then  you would get the effect you describe.

CHeck the .sln file to see what is singular.

Arthur
> I am most grateful for this discussion group. I thank you, once again for