#setwd(choose.dir()) ## set working directory
source("S1 ANOVA-Venn Diagrams.r")
source("S2 multichoose.r")

library(lsr)

#table 1
(m3=createUnbalancedMatrix12(10))

# dataset reproduced from Shaw & Mitchell-Olds (1993) Ecology 74(6), pp. 1638-1645
height = y <- c( 50, 57, 57, 71, 85, 91, 94, 102, 110, 105, 120 ) #height
treatment <- c( rep( "0control", 2 ), rep( "1removal", 3 ), rep( "0control", 4 ), rep( "1removal", 2 ) )
initial.size <- c( rep( "0small", 2 ), rep( "0small", 3 ), rep( "1large", 4 ), rep( "1large", 2 ))
# Shaw.MitchellOlds <- data.frame( height, treatment, initial.size )
# tapply( height, list(initial.size, treatment), mean ) # cell means
# model.matrix(lm(height~treatment*initial.size, data=Shaw.MitchellOlds)) #check model matrix
# Anova(lm(height~treatment*initial.size, data=Shaw.MitchellOlds), type=3)  # wrong results
# summary(lm(height~treatment*initial.size, data=Shaw.MitchellOlds))


#SS table 2
a=as.numeric(factor(treatment))-1    # use 0,1 coding for analysis
b=as.numeric(factor(initial.size))-1
lmres= lm(y~a+b+a:b)
anova(lmres) # type IA
anova(lm(y~b+a+a:b)) # type IB
Anova(lmres, type = 2) # type II
Anova(lmres, type = 3) # type III


#Figure 1
(comp=SSComp_A2xB2(y, a, b))
AnovaVenn_A2xB2(comp)


#Table 3
a2 = 2*a - 1  # use -1,1 coding for analysis
b2 = 2*b - 1
lmres= lm(y~a2+b2+a2:b2)
anova(lmres) # type IA
anova(lm(y~b2+a2+a2:b2)) # type IB
Anova(lmres, type = 2) # type II
Anova(lmres, type = 3) # type III

#Figure 2
(comp2=SSComp_A2xB2(y, a2, b2))
AnovaVenn_A2xB2(comp2)

# table 4
# run a simulation
set.seed(12)
sim=1000
# 0, 1 coding
A1 = c(rep(0,500), rep(1,500))
B1= c(rep(0,250), rep(1,250), rep(0,250), rep(1,250))
# -1, +1 coding
A2 = c(rep(-1,500), rep(1,500))
B2 = c(rep(-1,250), rep(1,250), rep(-1,250), rep(1,250))
lm1 = matrix(0, 1000, 5)
lm2 = matrix(0, 1000, 5)
lm3 = matrix(0, 1000, 5)
lm4 = matrix(0, 1000, 5)
an1=matrix(0, 1000, 4)
an2=matrix(0, 1000, 4)
an3=matrix(0, 1000, 4)
an4=matrix(0, 1000, 4)

for (i in 1:sim){

  error = rnorm(1000,sd=10)
  Y1 = 10+4*A1+4*B1+4*A1*B1+error
  Y2 = 10+4*A2+4*B2+4*A2*B2+error

  # linear regression
  lm=lm(Y1~A1*B1)
  lm1[i,1:4] = lm$coefficients
  lm1[i,5]=summary(lm)$sigma
  an1[i,1:4]=anova(lm)$"Sum Sq"
  lm=lm(Y1~A2*B2)
  lm2[i,1:4] = lm$coefficients
  lm2[i,5]=summary(lm)$sigma
  an2[i,1:4]=anova(lm)$"Sum Sq"
  lm=lm(Y2~A1*B1)
  lm3[i,1:4] = lm$coefficients
  lm3[i,5]=summary(lm)$sigma
  an3[i,1:4]=anova(lm)$"Sum Sq"
  lm=lm(Y2~A2*B2)
  lm4[i,1:4] = lm$coefficients
  lm4[i,5]=summary(lm)$sigma
  an4[i,1:4]=anova(lm)$"Sum Sq"

}
round(colMeans(lm1),1)
round(colMeans(an1),0)
round(colMeans(lm2),1)
round(colMeans(an2),0)
round(colMeans(lm3),1)
round(colMeans(an3),0)
round(colMeans(lm4),1)
round(colMeans(an4),0)

#code01=F # please choose F (congruous) or T (incongruous)
code01=F  # choose simulation method 0,1 or -1,1.
docentralize=F # choose to centralize dependent variable (or not) after simulation
filename = ifelse(!docentralize,
                  ifelse(code01,"S6 simdata01.txt" , "S7 simdata-11.txt") ,
                  ifelse(code01,"S8 simdata01c.txt" , "S9 simdata-11c.txt"))
simdata = read.table(filename, header=T) # cells are identified as X00, X01, X10 and X11
table(simdata$I)
#colnames(simdata)

# Table 5 (code01=F, docentralize=F) and Table 7 (code01=T, docentralize=F) 
# and Table XX (code01=T, docentralize=T) (not in manuscript)
# centralizing the dependent varaible does not solve anything; the results are
# similar to the uncentralized version.)
# percentages of H0 rejections
effects=c("effAb1","effBb1","effABb1","effAu2","effBu2","effABu2","effAu3","effBu3","effABu3")
rbind(round(colMeans(simdata[(simdata$I==0),effects]),3),
      round(colMeans(simdata[(simdata$I==4),effects]),3),
      round(colMeans(simdata[(simdata$I==8),effects]),3))

m4=simdata[(simdata$I==0),]
m5=simdata[(simdata$I==4),]
m6=simdata[(simdata$I==8),]

# Table 6 (code01=F) and Table 8 (code01=T)
# interaction = 0 SS II
higher1=m4$effAu2 > m4$effAb1
sum(higher1); round(sum(higher1)/nrow(m4)*100,1)
higher2=m4$effBu2 > m4$effBb1
sum(higher2); round(sum(higher2)/nrow(m4)*100,1)
higher3=m4$effABu2 > m4$effABb1
sum(higher3); round(sum(higher3)/nrow(m4)*100,1)

lower1=m4$effAu2 < m4$effAb1
sum(lower1); round(sum(lower1)/nrow(m4)*100,1)
lower2=m4$effBu2 < m4$effBb1
sum(lower2); round(sum(lower2)/nrow(m4)*100,1)
lower3=m4$effABu2 < m4$effABb1
sum(lower3); round(sum(lower3)/nrow(m4)*100,1)

# interaction = 0 SS III
higher4=m4$effAu3 > m4$effAb1
sum(higher4);  round(sum(higher4)/nrow(m4)*100,1)
higher5=m4$effBu3 > m4$effBb1
sum(higher5);  round(sum(higher5)/nrow(m4)*100,1)
higher6=m4$effABu3 > m4$effABb1
sum(higher6);  round(sum(higher6)/nrow(m4)*100,1)

lower4=m4$effAu3 < m4$effAb1
sum(lower4);  round(sum(lower4)/nrow(m4)*100,1)
lower5=m4$effBu3 < m4$effBb1
sum(lower5);  round(sum(lower5)/nrow(m4)*100,1)
lower6=m4$effABu3 < m4$effABb1
sum(lower6);  round(sum(lower6)/nrow(m4)*100,1)

#interaction = 4 SS II
higher7=m5$effAu2 >m5$effAb1
sum(higher7); round(sum(higher7)/nrow(m4)*100,1)
higher8=m5$effBu2 >m5$effBb1
sum(higher8); round(sum(higher8)/nrow(m4)*100,1)
higher9=m5$effABu2 >m5$effABb1
sum(higher9); round(sum(higher9)/nrow(m4)*100,1)

lower7=m5$effAu2 < m5$effAb1
sum(lower7); round(sum(lower7)/nrow(m4)*100,1)
lower8=m5$effBu2 < m5$effBb1
sum(lower8); round(sum(lower8)/nrow(m4)*100,1)
lower9=m5$effABu2 < m5$effABb1
sum(lower9); round(sum(lower9)/nrow(m4)*100,1)

#interaction = 4 SS III
higher10=m5$effAu3 >m5$effAb1
sum(higher10); round(sum(higher10)/nrow(m4)*100,1)
higher11=m5$effBu3 >m5$effBb1
sum(higher11); round(sum(higher11)/nrow(m4)*100,1)
higher12=m5$effABu3 >m5$effABb1
sum(higher12); round(sum(higher12)/nrow(m4)*100,1)

lower10=m5$effAu3 < m5$effAb1
sum(lower10); round(sum(lower10)/nrow(m4)*100,1)
lower11=m5$effBu3 < m5$effBb1
sum(lower11); round(sum(lower11)/nrow(m4)*100,1)
lower12=m5$effABu3 < m5$effABb1
sum(lower12); round(sum(lower12)/nrow(m4)*100,1)

#interaction = 8 SS II
higher13=m6$effAu2 >m6$effAb1
sum(higher13); round(sum(higher13)/nrow(m6)*100,1)
higher14=m6$effBu2 >m6$effBb1
sum(higher14); round(sum(higher14)/nrow(m6)*100,1)
higher15=m6$effABu2 >m6$effABb1
sum(higher15); round(sum(higher15)/nrow(m6)*100,1)

lower13=m6$effAu2 < m6$effAb1
sum(lower13); round(sum(lower13)/nrow(m6)*100,1)
lower14=m6$effBu2 < m6$effBb1
sum(lower14); round(sum(lower14)/nrow(m6)*100,1)
lower15=m6$effABu2 < m6$effABb1
sum(lower15); round(sum(lower15)/nrow(m6)*100,1)

#interaction = 8 SS III
higher16=m6$effAu3 >m6$effAb1
sum(higher16); round(sum(higher16)/nrow(m6)*100,1)
higher17=m6$effBu3 >m6$effBb1
sum(higher17); round(sum(higher17)/nrow(m6)*100,1)
higher18=m6$effABu3 >m6$effABb1
sum(higher18); round(sum(higher18)/nrow(m6)*100,1)

lower16=m6$effAu3 < m6$effAb1
sum(lower16); round(sum(lower16)/nrow(m6)*100,1)
lower17=m6$effBu3 < m6$effBb1
sum(lower17); round(sum(lower17)/nrow(m6)*100,1)
lower18=m6$effABu3 < m6$effABb1
sum(lower18); round(sum(lower18)/nrow(m6)*100,1)

# delta's
# interaction 0 SSII
round(mean(m4[higher1,"effAu2"]-m4[higher1,"effAb1"]), 3)
round(mean(m4[higher2,"effBu2"]-m4[higher2,"effBb1"]), 3)
round(mean(m4[higher3,"effABu2"]-m4[higher3,"effABb1"]), 3)

round(mean(m4[lower1,"effAu2"]-m4[lower1,"effAb1"]), 3)
round(mean(m4[lower2,"effBu2"]-m4[lower2,"effBb1"]), 3)
round(mean(m4[lower3,"effABu2"]-m4[lower3,"effABb1"]), 3)

# interaction 0 SSIII
round(mean(m4[higher4,"effAu3"]-m4[higher4,"effAb1"]), 3)
round(mean(m4[higher5,"effBu3"]-m4[higher5,"effBb1"]), 3)
round(mean(m4[higher6,"effABu3"]-m4[higher6,"effABb1"]), 3)

round(mean(m4[lower4,"effAu3"]-m4[lower4,"effAb1"]), 3)
round(mean(m4[lower5,"effBu3"]-m4[lower5,"effBb1"]), 3)
round(mean(m4[lower6,"effABu3"]-m4[lower6,"effABb1"]), 3)

# interaction 4 SSII
round(mean(m5[higher7,"effAu2"]-m5[higher7,"effAb1"]), 3)
round(mean(m5[higher8,"effBu2"]-m5[higher8,"effBb1"]), 3)
round(mean(m5[higher9,"effABu2"]-m5[higher9,"effABb1"]), 3)

round(mean(m5[lower7,"effAu2"]-m5[lower7,"effAb1"]), 3)
round(mean(m5[lower8,"effBu2"]-m5[lower8,"effBb1"]), 3)
round(mean(m5[lower9,"effABu2"]-m5[lower9,"effABb1"]), 3)

# interaction 4 SSIII
round(mean(m5[higher10,"effAu3"]-m5[higher10,"effAb1"]), 3)
round(mean(m5[higher11,"effBu3"]-m5[higher11,"effBb1"]), 3)
round(mean(m5[higher12,"effABu3"]-m5[higher12,"effABb1"]), 3)

round(mean(m5[lower10,"effAu3"]-m5[lower10,"effAb1"]), 3)
round(mean(m5[lower11,"effBu3"]-m5[lower11,"effBb1"]), 3)
round(mean(m5[lower12,"effABu3"]-m5[lower12,"effABb1"]), 3)

# interaction 8 SSII
round(mean(m6[higher13,"effAu2"]-m6[higher13,"effAb1"]), 3)
round(mean(m6[higher14,"effBu2"]-m6[higher14,"effBb1"]), 3)
round(mean(m6[higher15,"effABu2"]-m6[higher15,"effABb1"]), 3)

round(mean(m6[lower13,"effAu2"]-m6[lower13,"effAb1"]), 3)
round(mean(m6[lower14,"effBu2"]-m6[lower14,"effBb1"]), 3)
round(mean(m6[lower15,"effABu2"]-m6[lower15,"effABb1"]), 3)

# interaction 8 SSIII
round(mean(m6[higher16,"effAu3"]-m6[higher16,"effAb1"]), 3)
round(mean(m6[higher17,"effBu3"]-m6[higher17,"effBb1"]), 3)
round(mean(m6[higher18,"effABu3"]-m6[higher18,"effABb1"]), 3)

round(mean(m6[lower16,"effAu3"]-m6[lower16,"effAb1"]), 3)
round(mean(m6[lower17,"effBu3"]-m6[lower17,"effBb1"]), 3)
round(mean(m6[lower18,"effABu3"]-m6[lower18,"effABb1"]), 3)

# tools for further interpretation
higherBi= which(m5$Bi > 0) ; length(higherBi)
higherAi = which(m5$Ai > 0); length(higherAi)
m5[higher7,]
m5[higherBi,]

m5[higher8,]
m5[higherAi,]

m6[higher13,]
m6[higherBi,]

m6[higher14,]
m6[higherAi,]


round(cor(simdata[,c("effAu2", "Ai","Bi","ABi2","I","rAB")]), 2)
summary(lm(effAu2~Ai+Bi+ABi2+effABu2, data=simdata))
summary(lm(effBu2~Ai+Bi+ABi2+effABu3, data=simdata))
summary(lm(effAu3~Ai+Bi+ABi2+effABu2, data=simdata))
summary(lm(effBu3~Ai+Bi+ABi2+effABu3, data=simdata))
summary(simdata[,c("Ai","Bi","ABi2","effABu2","rAB")])

#round(cor(simdata),2)
summary(lm(effAu2~Ai+Bi+I, data=simdata))
summary(lm(effBu2~Ai+Bi+I, data=simdata))
summary(lm(effAu3~Ai+Bi+I, data=simdata))
summary(lm(effBu3~Ai+Bi+I, data=simdata))


summary(lm(effAu2~Ai+Bi+effABu2, data=simdata))
summary(lm(effBu2~Ai+Bi+effABu2, data=simdata))
summary(lm(effAu3~Ai+Bi+effABu3, data=simdata))
summary(lm(effBu3~Ai+Bi+effABu3, data=simdata))


# additional analysis
round(etaSquared(lm(effAu2~Ai+Bi+ABi2+effABu2, data=simdata), anova=T),2)
round(etaSquared(lm(effBu2~Ai+Bi+ABi2+effABu2, data=simdata), anova=T),2)
round(etaSquared(lm(effAu3~Ai+Bi+ABi2+effABu2, data=simdata), anova=T),2)
round(etaSquared(lm(effBu3~Ai+Bi+ABi2+effABu2, data=simdata), anova=T),2)


#additional analysis
dAub=simdata$effAu2-simdata$effAb1
p=as.numeric(dAub>0)
sum(p)/length(p)
simdata2=cbind(simdata,dAub)
round(etaSquared(lm(dAub~Ai+Bi+ABi2+X11+ABi+effABu2, data=simdata2), anova=T),2)

dBub=simdata$effBu2-simdata$effBb1
p=as.numeric(dBub>0)
sum(p)/length(p)
simdata2=cbind(simdata,dBub)
round(etaSquared(lm(dBub~Ai+Bi+ABi2+X11+effABu2, data=simdata2), anova=T),2)

dAub3=simdata$effAu3-simdata$effAb1
p=as.numeric(dAub3>0)
sum(p)/length(p)
simdata2=cbind(simdata,dAub3)
summary(lm(dAub3~Ai+Bi+X11+ABi2+effABu3, data=simdata2))
round(etaSquared(lm(dAub3~Ai+Bi+X11+ABi2+effABu3, data=simdata2), anova=T),2)

dBub3=simdata$effBu3-simdata$effBb1
summary(dBub3)
p=as.numeric(dBub3>0)
sum(p)/length(p)
simdata2=cbind(simdata,dBub3)
round(etaSquared(lm(dBub3~Ai+Bi+X11+ABi2+effABu3, data=simdata2), anova=T),2)