Augmented Designs
Mike Popelka & Jason Morales
What is an augmented design?
• A replicated check experiment augmented by
unreplicated entries.
• Step 1: Start with a field subdivided into plots
What is an augmented design?
• A replicated check experiment augmented by
unreplicated entries.
• Step 2: Divide plots into blocks
What is an augmented design?
• A replicated check experiment augmented by
unreplicated entries.
• Step 3: Randomly place checks in each block
– We now have 6 replicates of a randomized
complete block design (RCBD).
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What is an augmented design?
• A replicated check experiment augmented by
unreplicated entries.
• Step 4: Fill in empty plots with unique entries
(genotypes).
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Purpose of Augmented Designs
• Why use an augmented design?
– Cost effective
– Limited seed quantities or resources
– Increase efficiency of genetic gains
• Goal is to predict the true value of the genotype
by adjusting for spatial effects.
• Spatial effects can include soil fertility, field
gradients, physical soil properties, management
practices, biological competition.
BLUPs
• Best linear unbiased predictors
• Purpose is to estimate the random effects and
provide an adjusted dependent variable.
• In augmented designs, the random effects are
usually related to spatial correction
– Ex: yield = µ + entry(block) + check
• Entry is nested within block and is treated as a random
effect
• Check is treated as a fixed effect and is used to model
and then remove field effects.
Modeling Spatial Effects
• Model 1: See paper, PROC MIXED for Recovering
Both Interblocking and Intervariety Information
• Yield = µ + treatn + rep + block(rep) + treat*new +
Ɛ
• Treatn (fixed) = Individual checks, entries bulked
into one treatment
– i.e. check1, check2, check 3, all non-check entries
• Treat*new (random) = New entries (individually)
Modeling Spatial Effects
• Yield = µ + treatn + rep + block(rep) + treat*new +
Ɛ
• Rep and block(rep) are random effects
Block 1 Block 2 Block 3 Block 4 Block 5 Block 6
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SAS Code
data augbibd;
infile ’augbibd.dat’;
input yield rep block treat;
if (treat > 6) then new = 0 else new = 1;
if (new) then treatn = 999;
else treatn = treat;
proc mixed data = augbibd;
class rep block treat treatn;
model yield = treatn;
random rep block(rep) treat*new / solution;
lsmeans treatn;
make ’solutionr’ out = sr noprint;
run;
proc sort data = sr;
by descending est;
proc print;
run;
Yield
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treatn*
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new*
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Modeling Spatial Effects
• Model 2: See paper, Other Augmented Designs
• Grain weight = µ + WF + treatn + WR + treat*new
Range (Row)
– WF = Orthogonal polynomials treated as fixed
– WR = Orthogonal polynomials treated as random
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Orthogonal Polynomials
• Orthogonal polynomials are used to detect
effects that fit the given polynomial structure.
• Final estimates are corrected using the
covariance of the plot with the effect of the
orthogonal polynomial.
• GLM select is used to identify which
orthogonal polynomials are significant.
SAS Code
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data augmercl;
infile ’augmercl.dat’;
input site col row treat gw cl c2 c3 c4 rl r2 r3 r4; - These are the orthogonal polynomials
if (treat > 120) then new =0 else new = 1;
if (new) then treatn = 999;
else treatn = treat;
ll = rl*cl;
lq = r1"c2;
proc glm data = augmercl;
class row col treat treatn;
modegl w= rl r2 r3 r4 cl c2 c3 c4 ll lq treatn treat*new;
random row col treat*new;
run;
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proc iml;
opnl5 = orpo1(1:15,4);
opnl5[,1] = (1:15)’;
op15 = opnl5;
create opnl5 from opnl5[colname = {’ROW’
’RI’ ’R2’ ’R3’ ’R4’}];
append from opnl5;
close opnl5;
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proc glm data = augmercl;
class row col treat treatn;
model gw = rl r2 r3 r4 cl c2 c3 c4 11 Iq treat;
Ismeans treat / out = Ismeans noprint;
run;
proc sort data = Ismeans;
by descending Ismean;
proc print;
run;