#' Within-class Sum of Squares Matrix
#'
#' Calculates within-class sum of squares and cross product matrix (a.k.a.
#' within-class scatter matrix)
#'
#'
#' @param variables matrix or data frame with explanatory variables (No missing
#' values are allowed)
#' @param group vector or factor with group memberships (No missing values are
#' allowed)
#' @author Gaston Sanchez
#' @seealso \code{\link{withinCov}}, \code{\link{betweenSS}},
#' \code{\link{totalSS}}
#' @export
#' @examples
#'
#' \dontrun{
#' # load iris dataset
#' data(iris)
#'
#' # within-class scatter matrix
#' withinSS(iris[,1:4], iris[,5])
#' }
#'
withinSS <-
function(variables, group)
{
# Pooled within-class sum of squares and cross products
# variables: matrix or data frame with explanatory variables
# group: vector or factor with group memberships
# check inputs
verify_Xy = my_verify(variables, group, na.rm=FALSE)
X = verify_Xy$X
y = verify_Xy$y
# how many observations
nrx = nrow(X)
# how many variables
ncx = ncol(X)
# group levels and number of levels
glevs = levels(y)
ng = nlevels(y)
# within cov matrix
Within = matrix(0, ncx, ncx)
for (k in 1:ng)
{
# select obs of k-th group
tmp <- y == glevs[k]
# mean k-th group
mean_k = colMeans(X[tmp,])
# center k-th group matrix
Xk = scale(X[tmp,], center=mean_k, scale=FALSE)
# add k-th intra-class SS matrix
Within = Within + t(Xk) %*% Xk
}
# add names
if (is.null(colnames(variables))) {
var_names = paste("X", 1:ncol(X), sep="")
dimnames(Within) = list(var_names, var_names)
} else {
dimnames(Within) = list(colnames(variables), colnames(variables))
}
# result
Within
}
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