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Augmented Designs

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?.

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Augmented Designs

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  1. Augmented Designs Mike Popelka & Jason Morales

  2. What is an augmented design? • A replicated check experiment augmented by unreplicated entries. • Step 1: Start with a field subdivided into plots

  3. What is an augmented design? • A replicated check experiment augmented by unreplicated entries. • Step 2: Divide plots into blocks

  4. 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).

  5. What is an augmented design? • A replicated check experiment augmented by unreplicated entries. • Step 4: Fill in empty plots with unique entries (genotypes).

  6. 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.

  7. 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.

  8. 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)

  9. 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 Rep 1 Rep 2 Rep 3

  10. 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; procmixed data = augbibd; class rep block treat treatn; model yield = treatn; random rep block(rep) treat*new / solution; lsmeanstreatn; make ’solutionr’ out = srnoprint; run; proc sort data = sr; by descending est; proc print; run;

  11. Modeling Spatial Effects • Model 2: See paper, Other Augmented Designs • Grain weight = µ + WF + treatn + WR+treat*new • WF = Orthogonal polynomials treated as fixed • WR= Orthogonal polynomials treated as random

  12. 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.

  13. SAS Code • data augmercl; • infile ’augmercl.dat’; • input site col row treat gwcl 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; • procglm data = augmercl; • class row col treat treatn; • modegl w= rl r2 r3 r4 cl c2 c3 c4 lllqtreatn treat*new; • random row col treat*new; • run; • prociml; • 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; • procglm data = augmercl; • class row col treat treatn; • model gw = rl r2 r3 r4 cl c2 c3 c4 11 Iq treat; • Ismeans treat / out = Ismeansnoprint; • run; • proc sort data = Ismeans; • by descending Ismean; • proc print; • run;

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