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#' @title Between Group Comparison
#'
#' @description
#' Between Group Comparison (BGC)
#'
#' @param Data a numeric matrix or data frame
#' @param Group a vector of factors associated with group structure
#' @param numc number of components assocaited with PCA on each group
#' @param ncomp number of components, if NULL number of components is equal to 2
#' @param Scale scaling variables, by defalt is FALSE. By default data are centered within groups
#' @param graph should loading and component be plotted
#' @return list with the following results:
#' @return \item{Data }{Original data}
#' @return \item{Con.Data }{Concatenated centered data}
#' @return \item{split.Data }{Group centered data}
#' @return \item{Group }{Group as a factor vector}
#' @return \item{loadings.common }{Matrix of common loadings}
#' @return \item{lambda }{The specific variances of groups}
#' @return \item{exp.var }{Percentages of total variance recovered associated with each dimension }
#' @seealso \code{\link{mgPCA}}, \code{\link{FCPCA}}, \code{\link{DCCSWA}},
#' \code{\link{DSTATIS}}, \code{\link{DGPA}}, \code{\link{summarize}},
#' \code{\link{TBWvariance}}, \code{\link{loadingsplot}},
#' \code{\link{scoreplot}}, \code{\link{iris}}
#' @export
#'
#'
#' @references W. J. Krzanowski (1979). Between-groups comparison of principal components,
#' \emph{Journal of the American Statistical Association}, 74, 703-707.
#'
#' @references A. Eslami, E. M. Qannari, A. Kohler and S. Bougeard (2013). General overview
#' of methods of analysis of multi-group datasets,
#' \emph{Revue des Nouvelles Technologies de l'Information}, 25, 108-123.
#'
#'
#' @references A. Eslami, E. M. Qannari, A. Kohler and S. Bougeard (2013). Analyses
#' factorielles de donnees structurees en groupes d'individus,
#' \emph{Journal de la Societe Francaise de Statistique}, 154(3), 44-57.
#'
#'
#'
#'
#'
#' @examples
#' Data = iris[,-5]
#' Group = iris[,5]
#' res.BGC = BGC(Data, Group, graph=TRUE)
#' loadingsplot(res.BGC, axes=c(1,2))
#' scoreplot(res.BGC, axes=c(1,2))
BGC <- function(Data, Group, numc=NULL, ncomp=NULL, Scale=FALSE, graph=FALSE){
#=========================================================================
# 1. Checking the inputs
#=========================================================================
check(Data, Group)
#=========================================================================
# 2. preparing Data
#=========================================================================
if (is.data.frame(Data) == TRUE) {
Data=as.matrix(Data)
}
if(is.null(ncomp)) {ncomp=2}
if(is.null(colnames(Data))) {
colnames(Data) = paste('V', 1:ncol(Data), sep='')
}
if(is.null(ncomp)) {ncomp=2}
Group = as.factor(Group)
rownames(Data) = Group #---- rownames of data=groups
M = length(levels(Group)) #----number of groups: M
P = dim(Data)[2] #----number of variables: P
n = as.vector(table(Group)) #----number of individuals in each group
N = sum(n) #----number of individuals
split.Data = split(Data,Group) #----split Data to M parts
if(is.null(numc)) {numc=min(M-1, P)}
# centering and scaling if TRUE
for(m in 1:M){
split.Data[[m]] = matrix(split.Data[[m]], nrow=n[m])
split.Data[[m]] = scale(split.Data[[m]], center=TRUE, scale=Scale)
}
# concatinated dataset by row as groups
Con.Data = split.Data[[1]]
for(m in 2:M) {
Con.Data = rbind(Con.Data, split.Data[[m]])
}
rownames(Con.Data) = Group
colnames(Con.Data) = colnames(Data)
# Variance-covariance matrix for each group
cov.Group = vector("list", M)
for(m in 1:M){
cov.Group[[m]] = t(split.Data[[m]]) %*% split.Data[[m]] / n[m]
}
#==========================================================================
# Outputs
#==========================================================================
res <- list(
Data = Data,
Con.Data = Con.Data,
split.Data = split.Data,
Group=Group)
#==========================================================================
# Method
#==========================================================================
#----------------- Singular Value Decomposition of a Matrix: X = U D L',
# selected number of components rk
L=vector("list",M)
for(m in 1:M){
SVD = svd(split.Data[[m]])
L[[m]] = SVD$v[,1:numc]
}
#----------------- H matrix: H=sum (L'*L)
H = matrix(0,P,P)
for(m in 1:M){
H = H + L[[m]] %*% t(L[[m]])
}
#------------- common loadings
W = eigen(H)$vectors[,1:ncomp]
res$loadings.common= W
rownames(res$loadings.common) = colnames(Data)
colnames(res$loadings.common) = paste("Dim", 1:ncomp, sep="")
#---------------- variance of each loading: lambda = t(common loading)*(t(Xm)* Xm) * common loading
# variance of each loading # lambda = t(common loading)*(t(Xm)* Xm) * common loading
lambda = matrix(0, nrow=M, ncol=ncomp)
for(m in 1:M){
lambda[m,] = round(diag(t(W) %*% cov.Group[[m]] %*% W),3)
}
res$lambda = lambda
rownames(res$lambda) = levels(Group)
colnames(res$lambda) = paste("Dim", 1:ncomp, sep="")
#
exp.var = matrix(0,M,ncomp)
for(m in 1:M){
exp.var[m,] = 100 * lambda[m,]/ sum(diag(cov.Group[[m]]))
}
res$exp.var = exp.var
rownames(res$exp.var) = levels(Group)
colnames(res$exp.var) = paste("Dim", 1:ncomp, sep="")
#============================================================================
if(graph) {plot.mg(res)}
# add class
class(res) = c("BGC", "mg")
return(res)
}
#' @S3method print BGC
print.BGC <- function(x, ...)
{
cat("\nBetween Group Comparison\n")
cat(rep("-",43), sep="")
cat("\n$loadings.common ", "common loadings")
cat("\n$Data ", "Data set")
cat("\n")
invisible(x)
}
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