Nothing
Collapsing <- function(fit){
## Make the difference in three-way interactions
D3function <- function(alevel,blevel,clevel,type="A",ordABC=c(FALSE,FALSE,FALSE)){
if(type=="A"){
D3 <- D3Afunction(alevel=alevel,blevel=blevel,clevel=clevel,ord=ordABC[1])
}else if(type=="B"){
D3 <- D3Bfunction(alevel=alevel,blevel=blevel,clevel=clevel,ord=ordABC[2])
}else if(type=="C"){
D3 <- D3Cfunction(alevel=alevel,blevel=blevel,clevel=clevel,ord=ordABC[3])
}
return(D3)
}
D3Afunction <- function(alevel,blevel,clevel,ord=FALSE){
D3a <- matrix(0,nrow=0,ncol=(alevel*blevel*clevel))
if(ord==FALSE){
for(i in 1:(alevel-1)){
for(j in (i+1):alevel){
base.v <- rep(0,alevel)
base.v[i] <- -1
base.v[j] <- 1
base.mat <- diag((blevel*clevel)) %x% t(base.v)
D3a <- rbind(D3a,base.mat)
}
}
}else if(ord==TRUE){
for(i in 1:(alevel-1)){
base.v <- rep(0,alevel)
base.v[i] <- -1
base.v[(i+1)] <- 1
base.mat <- diag((blevel*clevel)) %x% t(base.v)
D3a <- rbind(D3a,base.mat)
}
}
return(D3a)
}
## (B): Make the difference in two-way interactions
D3Bfunction <- function(alevel,blevel,clevel,ord=FALSE){
if(ord==FALSE){
D3b <- matrix(0,nrow=0,ncol=(alevel*blevel*clevel))
for(i in 1:(blevel-1)){
left.temp <- matrix(0,ncol=((i-1)*(alevel)),nrow=(alevel))
left.main <- -diag((alevel))
left.final <- cbind(left.temp,left.main)
for(j in (i+1):blevel){
middle.temp <- matrix(0,ncol=((j-i-1)*(alevel)),nrow=(alevel))
right.main <- diag((alevel))
right.temp <- matrix(0,ncol=((blevel-j)*(alevel)),nrow=(alevel))
right.final <- cbind(middle.temp,right.main,right.temp)
D2b <- cbind(left.final,right.final) ## The base
D3base <- diag(clevel) %x% D2b
D3b <- rbind(D3b, D3base)
}
}
}else if (ord==TRUE){
D3b <- matrix(0,nrow=0,ncol=(alevel*blevel*clevel))
for(i in 1:(blevel-1)){
left <- matrix(0,ncol=((i-1)*(alevel)),nrow=(alevel))
Main <- cbind(-diag((alevel)),diag((alevel)))
right <- matrix(0,ncol=((blevel-(i+1))*(alevel)),nrow=(alevel))
D2b <- cbind(left,Main,right)
D3base <- diag(clevel) %x% D2b
D3b <- rbind(D3b, D3base)
}
}
return(D3b)
## psy_B(2,3), psy_B(2,4), psy_B(2,5)
}
D3Cfunction <- function(alevel,blevel,clevel,ord=FALSE){
if(ord==FALSE){
D3c <- matrix(0,nrow=0,ncol=(alevel*blevel*clevel))
for(i in 1:(clevel-1)){
left.temp <- matrix(0,ncol=((i-1)*(alevel*blevel)),nrow=(alevel*blevel))
left.main <- -diag((alevel*blevel))
left.final <- cbind(left.temp,left.main)
for(j in (i+1):clevel){
middle.temp <- matrix(0,ncol=((j-i-1)*(alevel*blevel)),nrow=(alevel*blevel))
right.main <- diag((alevel*blevel))
right.temp <- matrix(0,ncol=((clevel-j)*(alevel*blevel)),
nrow=(alevel*blevel))
right.final <- cbind(middle.temp,right.main,right.temp)
D3c <- rbind(D3c,cbind(left.final,right.final))
}
}
}else if (ord==TRUE){
Left <- cbind(-diag((alevel*blevel)*(clevel-1)),
matrix(0,ncol=(alevel*blevel),nrow=(alevel*blevel)*(clevel-1)))
Right <- cbind(matrix(0,ncol=(alevel*blevel),nrow=(alevel*blevel)*(clevel-1)),
diag((alevel*blevel)*(clevel-1)))
D3c <- Left + Right
}
return(D3c)
}
## From this version, I use D2 rather than D3
## Make the difference in two-way interactions
D2function <- function(alevel,blevel,type,ordAB){
if(type=="A"){
D2 <- D2Afunction(alevel=alevel,blevel=blevel,ord=ordAB[1])
}else if(type=="B"){
D2 <- D2Bfunction(alevel=alevel,blevel=blevel,ord=ordAB[2])
}
return(D2)
## D2 matrix
## nrow = differences between two-way interactions fixing the sublevel
## ncol = alevel*blevel (coefficients for two-ways)
}
## (A): Make the difference in two-way interactions
D2Afunction <- function(alevel,blevel,ord=FALSE){
D2a <- matrix(0,nrow=0,ncol=(alevel*blevel))
if(ord==FALSE){
for(i in 1:(alevel-1)){
for(j in (i+1):alevel){
base.v <- rep(0,alevel)
base.v[i] <- -1
base.v[j] <- 1
base.mat <- diag(blevel) %x% t(base.v)
D2a <- rbind(D2a,base.mat)
}
}
}else if(ord==TRUE){
for(i in 1:(alevel-1)){
base.v <- rep(0,alevel)
base.v[i] <- -1
base.v[(i+1)] <- 1
base.mat <- diag(blevel) %x% t(base.v)
D2a <- rbind(D2a,base.mat)
}
}
return(D2a)
}
## (B): Make the difference in two-way interactions
D2Bfunction <- function(alevel,blevel,ord=FALSE){
if(ord==FALSE){
D2b <- matrix(0,nrow=0,ncol=(alevel*blevel))
for(i in 1:(blevel-1)){
left.temp <- matrix(0,ncol=((i-1)*(alevel)),nrow=(alevel))
left.main <- -diag((alevel))
left.final <- cbind(left.temp,left.main)
for(j in (i+1):blevel){
middle.temp <- matrix(0,ncol=((j-i-1)*(alevel)),nrow=(alevel))
right.main <- diag((alevel))
right.temp <- matrix(0,ncol=((blevel-j)*(alevel)),nrow=(alevel))
right.final <- cbind(middle.temp,right.main,right.temp)
D2b <- rbind(D2b,cbind(left.final,right.final))
}
}
}else if (ord==TRUE){
Left <- cbind(-diag((alevel)*(blevel-1)),matrix(0,ncol=alevel,nrow=(alevel)*(blevel-1)))
Right <- cbind(matrix(0,ncol=alevel,nrow=(alevel)*(blevel-1)), diag((alevel)*(blevel-1)))
D2b <- Left + Right
}
return(D2b)
## psy_B(2,3), psy_B(2,4), psy_B(2,5)
}
## (Main): Making the difference between all levels
D1function <- function(nlevel,ord=FALSE){
if(ord==FALSE){
qp = (nlevel)*(nlevel-1)/2
D1.mat <- matrix(0,ncol=(nlevel),nrow=0)
if (qp==1) D1.mat <- matrix(c(-1,1),ncol=2,nrow=1)
if (qp>1){
for(i in 1 : (nlevel-1)){
w.diag <- diag((nlevel-i))
left.v <- c(rep(0,(i-1)),-1)
left.mat <- matrix(rep(left.v,(nlevel-i)),nrow=(nlevel-i),byrow=TRUE)
w.mat <- cbind(left.mat,w.diag)
D1.mat <- rbind(D1.mat,w.mat)
}
}
}else if(ord==TRUE){
if(nlevel==2){
D1.mat <- matrix(c(-1,1),ncol=2,nrow=1)
}else{
D1.mat <- cbind(0,diag(nlevel-1)) + cbind(-diag(nlevel-1),0)
}
}
return(D1.mat)
## nrow = differences between main effects
## ncol = mainlevel (coefficients for the main factor)
}
fac.level <- fit$fac.level
ord.fac <- fit$ord.fac
AME <- fit$AME
AMIE2 <- fit$AMIE2
AMIE3 <- fit$AMIE3
eps <- fit$eps
fac.name <- all.vars(fit$formula)[-1]
n.fac <- length(fac.level)
indTwo <- fit$indTwo
indThree <- fit$indThree
Gorder <- fit$Gorder
levelIndex <- CreatelevelIndex(fac.level=fac.level,ord.fac=ord.fac,Gorder=Gorder,
indTwo=indTwo, indThree=indThree)
use.ind <- (levelIndex$plus==1)*(levelIndex$dif==0)
Index.use <- levelIndex[use.ind==1,]
Fac.index <- levelIndex[,regexpr("Fac",colnames(levelIndex))>0]
Fac.Ind.use <- Fac.index[use.ind==1,]
order.f <- attr(terms(fit$formula, data=fit$data), "order")
Fac.Ind.use1 <- Fac.Ind.use[order.f==1,]
if(any(order.f==2)) Fac.Ind.use2 <- Fac.Ind.use[order.f==2,]
if(any(order.f==3)) Fac.Ind.use3 <- Fac.Ind.use[order.f==3,]
## Do Collapsing for each factor
Collapse <- list()
for(z in 1:n.fac){
## First Order
## type.ind <- z
MainD1 <- D1function(nlevel=fac.level[z],ord=ord.fac[z])
MainDif <- t(MainD1 %*% AME[[z]])
## Two-ways
onlyOne <- sum(Fac.Ind.use[,z])==1
if(any(order.f==2)==TRUE) yesTwo <- sum(Fac.Ind.use2[,z]==1)>0 else yesTwo <- FALSE
if(any(order.f==3)==TRUE) yesThree <- sum(Fac.Ind.use3[,z]==1)>0 else yesThree <- FALSE
if(onlyOne==TRUE){
## No Interaction
Dif <- abs(MainDif)
Collapse[[z]] <- apply(Dif <= eps, 2, all)
## print(Dif)
}else if(yesTwo==TRUE){
int2.index <- which(Fac.Ind.use2[,z]==1)
D2.mat <- matrix(NA, ncol=ncol(MainDif), nrow=0)
for(w in int2.index){
## Setup the coefficients
AMIE2.u <- AMIE2[[w]]
## Construct D matrix
Fac1 <- min(which(Fac.Ind.use2[w,]==1))
Fac2 <- max(which(Fac.Ind.use2[w,]==1))
if(z == Fac1) type.d2 <- "A"
if(z == Fac2) type.d2 <- "B"
D2 <- D2function(alevel=fac.level[Fac1],blevel=fac.level[Fac2],
type=type.d2, ordAB=ord.fac[c(Fac1,Fac2)])
D2.mat0 <- D2 %*% AMIE2.u
D2.mat01 <- matrix(D2.mat0, ncol=ncol(MainDif))
D2.mat <- rbind(D2.mat, D2.mat01)
}
D2.mat <- abs(D2.mat)
if(yesThree==FALSE){
Dif <- abs(rbind(MainDif, D2.mat))
Collapse[[z]] <- apply(Dif <= eps, 2, all)
}else if(yesThree==TRUE){
int3.index <- which(Fac.Ind.use3[,z]==1)
D3.mat <- matrix(NA, ncol=ncol(MainDif), nrow=0)
for(w in int3.index){
## Setup the coefficients
AMIE3.u <- AMIE3[[w]]
## Construct D matrix
Fac1 <- which(Fac.Ind.use3[w,]==1)[1]
Fac2 <- which(Fac.Ind.use3[w,]==1)[2]
Fac3 <- which(Fac.Ind.use3[w,]==1)[3]
if(z == Fac1) type.d3 <- "A"
if(z == Fac2) type.d3 <- "B"
if(z == Fac3) type.d3 <- "C"
D3 <- D3function(alevel=fac.level[Fac1], blevel=fac.level[Fac2], clevel=fac.level[Fac3],
type=type.d3, ordAB=ord.fac[c(Fac1,Fac2, Fac3)])
D3.mat0 <- D3 %*% c(AMIE3.u)
D3.mat01 <- matrix(D3.mat0, ncol=ncol(MainDif))
D3.mat <- rbind(D3.mat, D3.mat01)
}
D3.mat <- abs(D3.mat)
Dif <- abs(rbind(MainDif, D2.mat, D3.mat))
Collapse[[z]] <- apply(Dif <= eps, 2, all)
}
}
}
## I got Collapsing Index, then decide which levels will be collapsed.
collapse.level <- list()
for(z in 1:n.fac){
adj <- matrix(0, ncol=fac.level[z], nrow=fac.level[z])
if(ord.fac[z]==TRUE){
for(i in 1:length(Collapse[[z]])){
adj[i, (i+1)] <- as.numeric(Collapse[[z]][i])
}
adj <- adj + t(adj)
}else if(ord.fac[z]==FALSE){
ref <- combn(seq(1:fac.level[z]),2)
for(i in 1:length(Collapse[[z]])){
adj[ref[1,i], ref[2,i]] <- as.numeric(Collapse[[z]][i])
}
adj <- adj + t(adj)
}
g <- graph_from_adjacency_matrix(adj, mode="undirected")
collapse.level[[z]] <- components(g)$membership
}
names(collapse.level) <- fac.name
## Combine two weights.
output <- list("Collapse.Index"=Collapse, "collapse.level"=collapse.level)
return(output)
}
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