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*To*: s185152@student.uq.edu.au*Subject*: Re: ASREML Augmented Designs problem*From*: gilmoua@ornsun.agric.nsw.gov.au (Arthur Gilmour)*Date*: Wed, 19 Nov 1997 12:09:44 +1100*Cc*: asreml@chiswick.anprod.CSIRO.AU*Sender*: owner-asreml

> > 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 > your advice. > > Regards Vince > >

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