# NOT RUN {
## For optimum results, the number of searches may need to be increased in practice.
## Designs should be rebuilt repeatedly to check that a near-optimum design has been found.
## 3 replicates of 48 treatments with 3 replicate blocks of size 48,
## 18 nested sub-blocks of size 8 (sub1), 36 nested sub-sub-blocks of
## size 4 (sub2) and 72 nested sub-sub-sub-blocks of size two (sub3)
treatments=factor(1:48)
reps=factor(rep(1:3,each=48))
sub1=factor(rep(1:18,each=8))
sub2=factor(rep(1:36,each=4))
sub3=factor(rep(1:72,each=2))
blocks=data.frame(reps,sub1,sub2,sub3)
design(treatments,blocks,searches=1)
## 48 treatments in 2 replicate blocks of size 4 x 12 with 2 main rows and 3 main columns
treatments=factor(1:48)
replicates=factor(rep(1:2,each=48))
rows=factor(rep(rep(1:2,each=24),2))
cols=factor(rep(rep(1:3,each=4),8))
blocks=data.frame(replicates,rows,cols)
design(treatments,blocks,searches=1)
## 4 replicates of 12 treatments with 16 nested blocks of size 3
treatments = factor(1:12)
Blocks = factor(rep(1:4,each=12))
subBlocks = factor(rep(1:16,each=3))
blocks = data.frame(Blocks,subBlocks)
design(treatments,blocks)$blocks_model
## 4 x 12 design for 4 replicates of 12 treatments with 16 nested blocks of size 3
## only the intermediate weighting will give an optimal Trojan design
treatments = factor(1:12)
MainCols = factor(rep(rep(1:4,each=3),4))
MainRows = factor(rep(1:4,each=12))
Columns = factor(rep(1:12,4))
blocks = data.frame(MainCols,MainRows,Columns)
# }
# NOT RUN {
design(treatments,blocks,searches=100,weighting=0)$blocks_model
design(treatments,blocks,searches=100)$blocks_model
design(treatments,blocks,searches=100,weighting=1)$blocks_model
# }
# NOT RUN {
## 4 x 13 Row-and-column design for 4 replicates of 13 treatments
## Youden design Plan 13.5 Cochran and Cox (1957).
treatments=factor(1:13)
Rows =factor(rep(1:4,each=13))
Cols =factor(rep(1:13,4))
blocks =data.frame(Rows,Cols)
# }
# NOT RUN {
design(treatments,blocks,searches=500)
# }
# NOT RUN {
## Durban - 272 treatments in a 16 x 34 design with nested rows-and-columns
data(durban)
durban=durban[c(3,1,2,4,5)]
durban=durban[ do.call(order, durban), ]
treatments=data.frame(gen=durban$gen)
Reps = factor(rep(1:2,each=272))
Rows = factor(rep(1:16,each=34))
Col1 = factor(rep(rep(1:4,c(9,8,8,9)),16))
Col2 = factor(rep(rep(1:8,c(5,4,4,4,4,4,4,5)),16))
Col3 = factor(rep(1:34,16))
blocks = data.frame(Reps,Rows,Col1,Col2,Col3)
## D-efficiency factors assuming best design found by sequential optimization
# }
# NOT RUN {
## Optimises the assumed post-blocked design
design(treatments,blocks,searches=1)$blocks_model
## Finds post-blocked efficiency factors of the original design
blockEfficiencies(treatments,blocks)
# }
# NOT RUN {
## differential replication including single replicate treatments
treatments=factor(c(rep(1:12,2), rep(13:24,1)))
Main=factor(rep(1:2,each=18))
Sub =factor(rep(1:6,each=6))
blocks =data.frame(Main,Sub)
design(treatments,blocks,searches=5)
## Factorial treatment designs defined by a treatments data frame and a factorial model equation.
## Main effects of five 2-level factors in a half-fraction of a 2/2/2 nested blocks design
treatments = expand.grid(F1=factor(1:2),F2=factor(1:2),F3=factor(1:2),F4=factor(1:2),F5=factor(1:2))
blocks=data.frame(b1=factor(rep(1:2,each=8)),b2=factor(rep(1:4,each=4)),b3=factor(rep(1:8,each=2)))
treatments_model="F1 + F2 + F3 + F4 + F5"
design(treatments,blocks,treatments_model,searches=5)
# Second-order model for five qualitative 2-level factors in 4 randomized blocks
treatments=expand.grid(F1=factor(1:2),F2=factor(1:2),F3=factor(1:2),F4=factor(1:2),F5=factor(1:2))
blocks=factor(rep(1:4,each=8))
treatments_model="(F1+F2+F3+F4+F5)^2"
design(treatments,blocks,treatments_model,searches=5)
# Main effects of five 2-level factors in a half-fraction of a 4 x 4 row-and column design.
treatments = expand.grid(F1=factor(1:2),F2=factor(1:2),F3=factor(1:2),F4=factor(1:2),
F5=factor(1:2))
blocks=data.frame( rows=factor(rep(1:4,each=4)), cols=factor(rep(1:4,4)))
treatments_model="~ F1+F2+F3+F4+F5"
design(treatments,blocks,treatments_model,searches=20)
# Quadratic regression for one 6-level numeric factor in 2 randomized
# blocks assuming 10/6 fraction
treatments=expand.grid(X=1:6)
blocks=factor(rep(1:2,each=5))
treatments_model=" ~ poly(X,2)"
design(treatments,blocks,treatments_model,searches=5)
# First-order model for 1/3rd fraction of four qualitative 3-level factors in 3 blocks
treatments=expand.grid(F1=factor(1:3),F2=factor(1:3),F3=factor(1:3),F4=factor(1:3))
blocks=factor(rep(1:3,each=9))
treatments_model=" ~ F1+F2+F3+F4"
design(treatments,blocks,treatments_model,searches=5)
# Second-order model for a 1/3rd fraction of five qualitative 3-level factors in 3 blocks
treatments=expand.grid( F1=factor(1:3), F2=factor(1:3), F3=factor(1:3), F4=factor(1:3),
F5=factor(1:3))
blocks=factor(rep(1:3,each=27))
treatments_model=" ~ (F1+F2+F3+F4+F5)^2"
# }
# NOT RUN {
design(treatments,blocks,treatments_model,searches=500)
# }
# NOT RUN {
# Second-order model for two qualitative and two quantitative level factors in 4 randomized blocks
treatments=expand.grid(F1=factor(1:2),F2=factor(1:3),V1=1:3,V2=1:4)
blocks=factor(rep(1:4,each=18))
treatments_model = " ~ F1 + F2 + poly(V1,2) + poly(V2,2) + (poly(V1,1)+F1+F2):(poly(V2,1)+F1+F2) "
# }
# NOT RUN {
design(treatments,blocks,treatments_model,searches=5)
# }
# NOT RUN {
# Plackett and Burman design for eleven 2-level factors in 12 runs (needs large number of searches)
GF=expand.grid(F1=factor(1:2),F2=factor(1:2),F3=factor(1:2),F4=factor(1:2),F5=factor(1:2),
F6=factor(1:2),F7=factor(1:2),F8=factor(1:2),F9=factor(1:2),F10=factor(1:2),F11=factor(1:2))
blocks=factor(rep(1,12))
model=model="~ F1+F2+F3+F4+F5+F6+F7+F8+F9+F10+F11"
# }
# NOT RUN {
design(GF,blocks,model,searches=25)
# }
# NOT RUN {
# }
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