# NOT RUN {
#!___________________________
#! Qualitative Factor(s) (QL)
#!___________________________
#! Completely Randomized Design (CRD)
#! 1 factor - CRD - QLF
# Nonsense(experimental error = 0)
# Yi = mu + fe + e
r <- 2 # (repet. number)
fln <- 3 # (factor levels number)
crd00 <- gexp(mu=0,
r=r,
fe=list(f1=c(1, 2, 3)),
err=matrix(0,
nrow=r*fln),
round=0)
crd00
print(crd00)
str(crd00)
summary(crd00)
#! 1 factor - CRD - QL
# Nonsense(error is 0)
# Yi = mu + fe + e
r <- 3 # (repet. number)
fln <- 5 # (factor levels number)
crd01 <- gexp(mu=1,
r=r,
fe=list(f1=c(0, 2, 4, 6, 8)),
err=matrix(0,
nrow=r*fln),
round=2)
summary(crd01)
#! 1 factor - CRD - QL
# Default error: rmvnorm(sigma = diag(ncol(as.matrix([[fe]]))))
crd_1f <- gexp(mu=1,
r=3,
fe=list(f1=c(1, 1, 5, 1, 1)),
fl=list(Treat=LETTERS[1:5]),
round=2)
summary(crd_1f)
#! Binomial error - CRD - QL
e_binom <- as.matrix(rbinom(n=15,
size=5,
prob=0.1))
crd_bin <- gexp(mu=20,
err=e_binom,
r=5,
fe=list(f1=c(1, 4, 1)))
summary(crd_bin)
mod <- aov(Y1 ~ X1,
data=crd_bin$dfm)
shapiro.test(mod$res)
#! Factorial Experiment (FE) - CRD - QL
crd_fe <- gexp(mu=0,
r=2,
fe=list(f1=c(1, 1, 5),
f2=c(1, 1),
f3=c(2, 2, 1)),
fl=list(A=paste('a',
1:3,
sep=''),
B=paste('b',
1:2,
sep=''),
C=paste('c',
1:3,
sep='')),
inte = rep(1,39),
round=0,
type = 'FE')
summary(crd_fe)
#! Factorial Experiment (FE) - Multivariated - CRD - QL
# Error = 0 - Nonsense (you can easily undertand the effects)
crd_femn <- gexp(mu=c(0, 0),
r=1,
err=mvtnorm::rmvnorm(n=3^1 * 2^1 * 1,
sigma=matrix(c(0, 0,
0, 0),
ncol=2)),
#Y1 Y2
fe=list(f1=matrix(c(0, 3, #X1 X1
1, 4, #X2 X2
2, 5), #X3 X3
ncol=2,
byrow=TRUE),
#Y1 Y2
f2=matrix(c(0, 2, #X1 X1
1, 3), #X2 X2
ncol=2,
byrow=TRUE)),
round=1)
summary(crd_femn)
#! Factorial Experiment (FE) - Multivariated - CRD - QL
# Using default error
set.seed(30)
crd_femd <- gexp(mu=c(0, 2),
r=3,
fe=list(f1=matrix(c(1, 1,
5, 1,
1, 1),
ncol=2,
byrow=TRUE),
f2=matrix(c(1, 3,
2, 2),
ncol=2,
byrow=TRUE)),
round=1)
summary(crd_femd)
set.seed(30)
crd_femi <- gexp(mu=c(0, 2),
err=mvtnorm::rmvnorm(n=3^1 * 2^1 * 3,
sigma=matrix(c(1, 0, # The same that the default error
0, 1),
ncol=2)),
r=3,
fe=list(f1=matrix(c(1, 1,
5, 1,
1, 1),
ncol=2,
byrow=TRUE),
f2=matrix(c(1, 3,
2, 2),
ncol=2,
byrow=TRUE)),
round=1)
summary(crd_femi)
crd_femd$dfm[, 4:5] # Use of the dafault error
crd_femi$dfm[, 4:5] # Use of the user error (same as the default!)
crd_femd$dfm[, 4:5] == crd_femi$dfm[, 4:5]
#! Factorial Experiment (FE) - With interaction - CRD - QL
fe_crd <- gexp(mu=30,
fe=list(f1=c(1, 1, 3),
f2=c(1, 1)),
fl=list(A=paste('a',
1:3,
sep=''),
B=paste('b',
1:2,
sep='')),
inte=c(3, 1, 1, 1, 1, 5),
round=1,
type='FE')
summary(fe_crd)
#! Split-plot Experiment (SPE) - CRD - QL
split_crd <- gexp(mu=30,
fe=list(f1=c(1, 1),
f2=c(2, 3)),
fl=list(P=paste('p',
1:2,
sep=''),
SP=paste('sp',
1:2,
sep='')),
inte=c(1, 15, 1, 1),
round=1,
type='SPE')
summary(split_crd)
#! Randomized Complete Block Design (RCBD) - QL
# 1 factor, 3 blocks
rcbd <- gexp(mu=0,
fe=list(f1=c(5, 1, 1)),
fl=list(TR=LETTERS[1:3]),
blke=c(1, 2, 3),
blkl=list(BLK=paste('B',
1:3,
sep='')),
round=1,
type='RCBD')
summary(rcbd)
#! Factorial Experiment (FE) - RCBD - QL
fe_rcbd <- gexp(mu=30,
fe=list(f1=c(1, 1, 1),
f2=c(2, 3)),
blke=c(1, 3),
inte=c(1, 15, 1, 1, 5, 1),
round=1,
type='FE')
summary(fe_rcbd)
#! Multivariated - RCBD - QL
rcbd_m <- gexp(mu=c(0, 2),
fe=list(f1= matrix(c(1, 1,
5, 1,
1, 1),
ncol=2,
byrow=TRUE)),
blke=matrix(c(2, 1,
1, 2,
1, 1),
ncol=2,
byrow=TRUE),
round=1,
type='RCBD')
summary(rcbd_m)
#! Split-plot Experiment (SPE) - RCBD - QL
split_rcbd <- gexp(mu=30,
fe=list(f1=c(1, 1),
f2=c(2, 3),
f3=c(1, 1, 1)),
fl=list(A=paste('a',
1:2,
sep=''),
B=paste('b',
1:2,
sep=''),
C=paste('c',
1:3,
sep='')),
blke=c(1, 2),
blkl=list(BLK=paste('B',
1:2,
sep='')),
inte=c(1, 15, 1, 1, 1, 3, 4, 2, 1, 1, 4, 1,
1, 2, 1, 1,
1, 1, 1, 1, 1, 1,
1, 1, 3, 3, 3, 3),
round=1,
type='SPE')
summary(split_rcbd)
#! Latin Square Design (LSD) - QL
lsd <- gexp(mu=30,
fe=list(f1=c(1, 1, 10)),
rowe=c(1, 1, 1),
cole=c(1, 1, 1),
rowl=list(Row=paste('r',
1:3,
sep='')),
coll=list(Col=paste('c',
1:3,
sep='')),
round=1,
type='LSD')
summary(lsd)
#! Factorial Experiment (FE) - LSD - QL
fe_lsd <- gexp(mu=30,
fe=list(f1=c(1, 1),
f2=c(2, 3)),
rowe=c(1, 3, 2, 1),
cole=c(2, 2, 1, 1),
rowl=list(Row=paste('r',
1:4,
sep='')),
coll=list(Col=paste('c',
1:4,
sep='')),
inte=c(1, 15, 1, 1),
round=1,
type='FE')
summary(fe_lsd)
#! Split-plot Experiment (SPE) - LSD - QL
split_lsd <- gexp(mu=30,
fe=list(f1=c(1, 1, 2),
f2=c(2, 3, 1)),
fl=list(P=paste('p',
1:3,
sep=''),
SP=paste('sp',
1:3,
sep='')),
inte=c(1, 15, 1, 1, 1, 1, 1, 1, 1),
rowe = c(1, 1, 1),
cole = c(1, 1, 1),
rowl=list(Row=paste('r',
1:3,
sep='')),
coll=list(Col=paste('c',
1:3,
sep='')),
round=1,
type='SPE')
summary(split_lsd)
#!___________________________
#! Quantitative Factor(s) (QT)
#!___________________________
# CRD - Orthogonal polynomials
level <- c(0, 10, 20, 30)
cont_crd <- contr.poly(length(level))
# Linear effect
crd_lo <- gexp(mu=NULL,
r=4,
# B0 B1 B2 B3 Linear only
fe=list(f1=c(2, 5, 0, 0)),
fl=list(Dose=ordered(level)),
contrasts=list(f1=cont_crd))
summary(crd_lo)
plot(Y1 ~ Dose,
crd_lo$dfm)
# Quadratic effect
crd_qo <- gexp(mu=NULL,
r=4,
# B0 B1 B2 B3 quadratic
fe=list(f1=c(2, 0, 5, 0)),
fl=list(Dose=ordered(c(0, 10, 20, 30))),
contrasts=list(f1=cont_crd))
summary(crd_qo)
plot(Y1 ~ Dose,
crd_qo$dfm)
# Cubic effect
crd_co <- gexp(mu=NULL,
r=4,
# B0 B1 B2 B3 cubic
fe=list(f1=c(2, 0, 0, 5)),
fl=list(Dose=ordered(c(0, 10, 20, 30))),
contrasts=list(f1=cont_crd))
summary(crd_co)
plot(Y1 ~ Dose,
crd_co$dfm)
# Not orthogonal polynomials
# Linear
cont_crd <- matrix(c(level,
level^2,
level^3),
ncol=3)
crd_l <- gexp(mu=NULL,
r=4,
fe=list(f1=c(2, 10, 0, 0)),
fl=list(Dose=ordered(c(0, 10, 20, 30))),
contrasts=list(f1=cont_crd))
summary(crd_l)
plot(Y1 ~ Dose,
crd_l$dfm)
reg <- lm(Y1 ~ Dose + I(Dose^2) + I(Dose^3),
data=crd_l$dfm)
summary(reg)
# Linear and quadratic
# When has two or more factor, to inform only Beta0 to first factor.
crd_lq <- gexp(mu=NULL,
r=3,
fe=list(f1=c(0, 10, 0, 0), #linear
f2=c(0, 3, 4, 0)), #quadratic
fl=list(P=ordered(level),
N=ordered(1:4)),
contrasts=list(f1=cont_crd,
f2=cont_crd))
summary(crd_lq)
with(crd_lq$dfm,
plot(Y1 ~ P))
with(crd_lq$dfm,
plot(Y1 ~ N))
# Multivariated!
crd_m <- gexp(mu=NULL,
r=4, #L Q
fe=list(f1=matrix(c( 2, 2,
10, 0,
0, 10,
0, 0),
ncol=2,
byrow=TRUE)),
fl=list(Dose=ordered(level)),
contrasts=list(f1=cont_crd))
with(crd_m$dfm,
plot(Y1 ~ Dose))
with(crd_m$dfm,
plot(Y2 ~ Dose))
# Orthogonal polynomios - RCBD
cont_rcbd <- contr.poly(4)
rcbd <- gexp(mu=NULL,
fe=list(f1=c(1, 3, 0, 0)),
blke=c(1, 2, 3),
r=2,
fl=list(Dose=ordered(c(0, 2, 4, 6))),
blkl=list(Blk=c('B1', 'B2', 'B3')),
contrasts=list(f1=cont_rcbd,
Blk=diag(3)),
type='RCBD')
summary(rcbd)
#! Hibrid: qualitative and quantitative factors in the same experiment - hb
# CRD
r <- 2
(error <- matrix(rep(0,
4^1*3^1*r),
ncol=1))
crd_hb <- gexp(mu=NULL,
err=error,
r=r,
fe=list(f1=c(0, 1, 0), # Qualitative
f2=c(2, 1, 0, 0)), # Quantitative linear
fl=list(Var=LETTERS[1:3],
Dose=ordered(level)),
contrasts=list(f1=diag(3),
f2=cont_crd))
summary(crd_hb)
# RCBD
r <- 2
blke <- c(1, 2)
(error <- matrix(rep(0,
4^1*3^1*r*length(blke)),
ncol=1))
rcbd_hb <- gexp(mu=NULL,
err=error,
r=r,
fe=list(f1=c(0, 1, 0), # Qualitative
f2=c(2, 1, 0, 0)), # Quantitative linear
fl=list(Var=LETTERS[1:3],
Dose=ordered(level)),
blke=blke,
blkl=list(Blk=c('B1', 'B2')),
contrasts=list(f1=diag(3),
f2=cont_crd,
Blk=diag(2)),
type='RCBD')
summary(rcbd_hb)
# }
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