#Part of the DiDiSTATIS function within DiDiSTATIS
#
#'Integrate tables hierarchically, to give barycentric group and grand compormises
#'Differs from GetBaryGrandComp.R by computing alpha2_supp,
#'because bootstrapped group compormises are projected as supplementary
#'and so need to be weighted as supplementary to the original Rv_D space.
#'
#'@param CP_array An array of CP matrices
#'@param DESIGN_rows List of DESIGN info for rows
#'@param DESIGN_tables List of DESIGN info for tables
#'@param Hierarchy_of_tables Results related to computing Group and Grand Compromises
#'@param MFA1_Flag #TRUE gives MFA-norm; FALSE gives no norm
#'@param RV1_Flag # TRUE gives RV; FALSE gives C; "skip" sets alpha-weights to 1/CD (1/N)
#'@param MFA2_Flag #TRUE gives MFA-norm; FALSE gives no norm
#'@param RV2_Flag # TRUE gives RV; FALSE gives C; "skip" sets alpha-weights to 1/D
#'@return A list of compromises and other computed objects
#'@export
GetBaryGrandComp_BootTables <- function(CP_array, DESIGN_rows, DESIGN_tables, Hierarchy_of_tables, MFA1_Flag=TRUE, RV1_Flag=TRUE, MFA2_Flag=TRUE, RV2_Flag=TRUE){
RETURN <- list()
RETURN$data$CP_array <- CP_array
###########################
## 1. Get Group Compromises
# 1a. dilate1, a vector of length "D", that gives the number of people in each group, "C(d)"
dilate1 <- colSums(DESIGN_tables$mat)
RETURN$coef$dilate1 <- dilate1
# 1b. MFA1, a vector of length "CD", that gives the MFA coefficient of each of the CD tables (this is 1 for each participant)
if(MFA1_Flag){
MFA1 <- MFAnormCPFinder(CP_array)
RETURN$coef$MFA1 <- MFA1
NormedCP_array <- CP2MFAnormedCP(CP_array) #This is CP_array with each table scaled by its MFA1 coefficient
}
if(!MFA1_Flag){
# RETURN$coef$MFA1 <- MFA1 <- c(rep(1/DESIGN_tables$CD, DESIGN_tables$CD))
RETURN$coef$MFA1 <- MFA1 <- rep(mean(MFAnormCPFinder(CP_array)), DESIGN_tables$CD)
NormedCP_array <- CP_array * mean(MFAnormCPFinder(CP_array))
}
RETURN$data$NormedCP_array <- NormedCP_array
# 1c. alpha1 (on the way, compute RV_C_in_d<d>, alpha_C_in_d<d>,
# and while looping, may as well compute GroupCompromise_array[,,<d>])
alpha1 <- rep(NA, nrow(DESIGN_tables$mat))
RETURN$data$GroupCompromise_array <- array(NA, dim=c(nrow(CP_array),nrow(CP_array),DESIGN_tables$D))
RETURN$data$Pb_GroupCompromise_Pb_array <- array(NA, dim=c(nrow(CP_array),nrow(CP_array),DESIGN_tables$D))
#For each of the D groups...
for(d in 1:DESIGN_tables$D){
#designate the relevant tables
these_tables <- c(which(DESIGN_tables$mat[,d]==1))
if(is.logical(RV1_Flag)){
##Compute the inner product (the RV matrix, or C matrix) within each group: RV_C_in_d<d>
#depends (GetCmat.R)
RV = TRUE #TRUE gives RV; FALSE gives C.
GetRVwithin <- paste0("RETURN$InnerProduct$RV_C_in_d",d," <- GetCmat(NormedCP_array[,,these_tables], RV=",RV,")")
eval(parse(text = GetRVwithin))
##From eig(RV_within_d<d>), get AlphaWithin; alpha_C_in_d<d>
#depends (GetAlpha.R)
GetAlphaWithin <- paste0("RETURN$InnerProduct$alpha_C_in_d" ,d, " <- GetAlpha(RETURN$InnerProduct$RV_C_in_d" ,d, ")")
eval(parse(text = GetAlphaWithin))
#Get all alpha-weights back into 1 vector in the same order as rows of DESIGN_tables$mat
GoGetAlpha1 <- paste0("alpha1[these_tables] <- RETURN$InnerProduct$alpha_C_in_d" ,d, "$alpha")
eval(parse(text = GoGetAlpha1))
}
if(RV1_Flag=="skip"){
alpha1[these_tables] <- rep(1/colSums(DESIGN_tables$mat)[d], colSums(DESIGN_tables$mat)[d])
}
##Compute each GroupCompromise (depends on ComputeSplus.R)
#use alpha_C_in_D<d> to compute Compromise_Plus_in_d<d>
GetGroupCompromise <- paste0("RETURN$data$GroupCompromise_array[,,",d,"] <- ComputeSplus(NormedCP_array[,,these_tables], RETURN$InnerProduct$alpha_C_in_d",d,"$alpha)")
eval(parse(text = GetGroupCompromise))
###########################
## 2. Apply row design
RETURN$data$Pb_GroupCompromise_Pb_array[,,d] <- DESIGN_rows$Pb_Full %*% RETURN$data$GroupCompromise_array[,,d] %*% DESIGN_rows$Pb_Full
###########################
}
RETURN$coef$alpha1 <- alpha1
#And reassign the names to the Group Compromises
dimnames(RETURN$data$GroupCompromise_array) <- list(rownames(CP_array), rownames(CP_array), colnames(DESIGN_tables$mat))
dimnames(RETURN$data$Pb_GroupCompromise_Pb_array) <- dimnames(RETURN$data$GroupCompromise_array)
###########################
## 3. Get Grand Compromise
# 3a. dilate2, a scalar, the number of groups, "D".
dilate2 <- DESIGN_tables$D
RETURN$coef$dilate2 <- dilate2
# 3b. MFA2, a vector of length "D", that gives the MFA coefficient of each of the D GroupCompromises
if(MFA2_Flag){
MFA2 <- MFAnormCPFinder(RETURN$data$Pb_GroupCompromise_Pb_array)
RETURN$coef$MFA2 <- MFA2
Normed_Pb_GroupCompromise_Pb_array <- CP2MFAnormedCP(RETURN$data$Pb_GroupCompromise_Pb_array)
}
if(!MFA2_Flag){
# RETURN$coef$MFA2 <- MFA2 <- c(rep(1/DESIGN_tables$D, DESIGN_tables$D))
RETURN$coef$MFA2 <- MFA2 <- rep(mean(MFAnormCPFinder(RETURN$data$Pb_GroupCompromise_Pb_array)), DESIGN_tables$D)
Normed_Pb_GroupCompromise_Pb_array <- RETURN$data$Pb_GroupCompromise_Pb_array * mean(MFAnormCPFinder(RETURN$data$Pb_GroupCompromise_Pb_array))
}
# and apply MFA2 to the Barycentric Group Compromises to give the Normed_Pb_GroupCompromise_Pb_array
RETURN$data$Normed_Pb_GroupCompromise_Pb_array <- Normed_Pb_GroupCompromise_Pb_array
# 3c. alpha2, a vector of length "D", that gives the alpha-weight for each MFA-Normalized Group
if(is.logical(RV2_Flag)){
#on the way, compute RV_D
array_for_RV_supp <- array(c(Hierarchy_of_tables$data$Normed_Pb_GroupCompromise_Pb_array, RETURN$data$Normed_Pb_GroupCompromise_Pb_array),
dim=c(nrow(Hierarchy_of_tables$data$Normed_Pb_GroupCompromise_Pb_array),
ncol(Hierarchy_of_tables$data$Normed_Pb_GroupCompromise_Pb_array),
dim(Hierarchy_of_tables$data$Normed_Pb_GroupCompromise_Pb_array)[3]*2))
#Get Rv_rows... the Rvs between the original normed group compromises and the booted normed group compromises
RV_B_D_supp <- GetCmat(array_for_RV_supp, RV=RV2_Flag)[1:DESIGN_tables$D, -c(1:DESIGN_tables$D)]
rownames(RV_B_D_supp) <- paste0("boot", dimnames(Hierarchy_of_tables$data$Normed_Pb_GroupCompromise_Pb_array)[[3]])
colnames(RV_B_D_supp) <- dimnames(Hierarchy_of_tables$data$Normed_Pb_GroupCompromise_Pb_array)[[3]]
RETURN$InnerProduct$RV_B_D_supp <- RV_B_D_supp
#compute alpha2_supp
# Project supplementary RV_rows into the original Rv space,
#reconstitute supplementary factor scores for the booted tables
#and work backward to get to supplementary alpha weights, called alpha2_supp
RV_B_D_F_supp <- RV_B_D_supp %*% Hierarchy_of_tables$InnerProduct$res_RV_B_D$eig$ProjMat
RV_B_D_U_supp <- abs(RV_B_D_F_supp[,1] * Hierarchy_of_tables$InnerProduct$res_RV_B_D$eig$Lambda_vec[1]^(-1/2))
alpha2_supp <- as.matrix(RV_B_D_U_supp) %*% sum(Hierarchy_of_tables$InnerProduct$res_RV_B_D$eig$U[,1])^-1
RETURN$coef$alpha2_supp <- alpha2_supp
}
if(RV2_Flag=="skip"){
RETURN$coef$alpha2_supp <- alpha2_supp <- rep(1/DESIGN_tables$D, DESIGN_tables$D)
}
# Compute the Bary_Grand Compromise
Bary_GrandCompromise <- ComputeSplus(Normed_Pb_GroupCompromise_Pb_array, alpha2_supp)
RETURN$data$Bary_GrandCompromise <- Bary_GrandCompromise
# Compute SS of Bary_Grand Compromise
RETURN$data$SSb.._fromTrace <- sum(diag(Bary_GrandCompromise))
###########################
## 4. Apply coefficients to compute the OverWeighted individual and group data.
######
# 4a. OverWeighted_CP_array
OverWeighted_CP_array <- array(NA, dim=c(nrow(CP_array), nrow(CP_array), DESIGN_tables$CD))
for(d in 1:DESIGN_tables$D){
for(c in 1:colSums(DESIGN_tables$mat)[d]){
this_table <- which(DESIGN_tables$mat[,d]==1)[c]
OverWeighted_CP_array[,,this_table] <- (CP_array[,,this_table] *
dilate1[d] *
MFA1[this_table] *
alpha1[this_table] *
dilate2 *
MFA2[d] *
alpha2_supp[d])
}
}
RETURN$data$OverWeighted_CP_array <- OverWeighted_CP_array
#Compute SS of Individual data tables
RETURN$data$Overweighted_SScd <- matrix(NA, DESIGN_tables$CD, 1)
for(cd in 1:DESIGN_tables$CD){
RETURN$data$Overweighted_SScd[cd] <- sum(diag(RETURN$data$OverWeighted_CP_array[,,cd]))
}
#####
# 4b. OverWeighted_GroupCompromise_array
OverWeighted_GroupCompromise_array <- array(NA, dim=c(nrow(CP_array), nrow(CP_array), DESIGN_tables$D))
for(d in 1:DESIGN_tables$D){
OverWeighted_GroupCompromise_array[,,d] <- (RETURN$data$GroupCompromise_array[,,d] *
dilate2 *
MFA2[d] *
alpha2_supp[d])
}
RETURN$data$OverWeighted_GroupCompromise_array <- OverWeighted_GroupCompromise_array
#Compute SS of Group Compromises
RETURN$data$Overweighted_SS.d <- matrix(NA, DESIGN_tables$D, 1)
for(d in 1:DESIGN_tables$D){
RETURN$data$Overweighted_SS.d[d] <- sum(diag(RETURN$data$OverWeighted_GroupCompromise_array[,,d]))
}
RETURN$data$OverWeighted_GrandCompromise <- apply(OverWeighted_GroupCompromise_array, c(1,2), mean)
#####
# 3c. OverWeighted_Pb_GroupCompromise_Pb_array
OverWeighted_Pb_GroupCompromise_Pb_array <- array(NA, dim=c(nrow(CP_array), nrow(CP_array), DESIGN_tables$D))
for(d in 1:DESIGN_tables$D){
OverWeighted_Pb_GroupCompromise_Pb_array[,,d] <- (RETURN$data$Pb_GroupCompromise_Pb_array[,,d] *
dilate2 *
MFA2[d] *
alpha2_supp[d])
}
RETURN$data$OverWeighted_Pb_GroupCompromise_Pb_array <- OverWeighted_Pb_GroupCompromise_Pb_array
#Compute SS of Group Compromises
RETURN$data$Overweighted_SSb.d <- matrix(NA, DESIGN_tables$D, 1)
for(d in 1:DESIGN_tables$D){
RETURN$data$Overweighted_SSb.d[d] <- sum(diag(RETURN$data$OverWeighted_Pb_GroupCompromise_Pb_array[,,d]))
}
######
# 3d. OverWeighted_Pb_CP_Pb_array
OverWeighted_Pb_CP_Pb_array <- array(NA, dim=c(nrow(CP_array), nrow(CP_array), nrow(DESIGN_tables$mat)))
for(d in 1:DESIGN_tables$D){
for(c in 1:colSums(DESIGN_tables$mat)[d]){
this_table <- which(DESIGN_tables$mat[,d]==1)[c]
OverWeighted_Pb_CP_Pb_array[,,this_table] <- (DESIGN_rows$Pb_Full %*% CP_array[,,this_table] %*% DESIGN_rows$Pb_Full *
dilate1[d] *
MFA1[this_table] *
alpha1[this_table] *
dilate2 *
MFA2[d] *
alpha2_supp[d])
}
}
RETURN$data$OverWeighted_Pb_CP_Pb_array <- OverWeighted_Pb_CP_Pb_array
#Compute SS of Individual data tables
RETURN$data$Overweighted_SSbcd <- matrix(NA, nrow(DESIGN_tables$mat), 1)
for(cd in 1:nrow(DESIGN_tables$mat)){
RETURN$data$Overweighted_SSbcd[cd] <- sum(diag(RETURN$data$OverWeighted_Pb_CP_Pb_array[,,cd]))
}
### RETURNS ###
#Part I
# RETURN$data$CP_array
# RETURN$coef$dilate1
# RETURN$coef$MFA1
# RETURN$data$NormedCP_array
# RETURN$coef$alpha1
# RETURN$data$GroupCompromise_array
#Part II
# RETURN$coef$dilate2
# RETURN$coef$MFA2
# RETURN$coef$alpha2
# RETURN$data$GrandCompromise
#OverWeight
# RETURN$data$OverWeighted_CP_array
# RETURN$data$OverWeighted_GroupCompromise_array
return(RETURN)
}
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