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#' @title Between-class Covariance Matrix
#'
#' @description Calculates between-class covariance matrix
#'
#' @details When \code{div_by_n=TRUE} the covariance matrices are divided by n
#' (number of observations), otherwise they are divided by n-1
#'
#' @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)
#' @param div_by_n logical indicating division by number of observations
#' @author Gaston Sanchez
#' @seealso \code{\link{getWithin}}, \code{\link{betweenSS}},
#' \code{\link{withinCov}}, \code{\link{totalCov}}
#' @export
#' @examples
#' \dontrun{
#' # load iris dataset
#' data(iris)
#'
#' # between-class covariance matrix (dividing by n-1)
#' betweenCov(iris[,1:4], iris[,5])
#'
#' # between-class covariance matrix (dividing by n)
#' betweenCov(iris[,1:4], iris[,5], div_by_n=TRUE)
#' }
#'
betweenCov <-
function(variables, group, div_by_n=FALSE)
{
# check inputs
verify_Xy = my_verify(variables, group, na.rm=FALSE)
X = verify_Xy$X
y = verify_Xy$y
# how many obs and variables
n = nrow(X)
p = ncol(X)
# group levels and number of levels
glevs = levels(y)
ng = nlevels(y)
# global mean
mean_global = colMeans(X)
# matrix to store results
Between = matrix(0, p, p)
# pooled between-class covariance matrix
for (k in 1:ng)
{
# select obs of k-th group
tmp <- y == glevs[k]
# how many obs in group k
nk = sum(tmp)
# mean k-th group
mean_k = colMeans(X[tmp,])
# mean k-th group - global mean
dif_k = mean_k - mean_global
# k-th group between cov matrix
if (div_by_n) {
between_k = (nk/n) * tcrossprod(dif_k)
} else {
between_k = (nk/(n-1)) * tcrossprod(dif_k)
}
Between = Between + between_k
}
# add names
if (is.null(colnames(variables))) {
var_names = paste("X", 1:ncol(X), sep="")
dimnames(Between) = list(var_names, var_names)
} else {
dimnames(Between) = list(colnames(variables), colnames(variables))
}
# result
Between
}
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