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#' A function to compute partial F statistics
#'
#' This is an internal function used in FSelect. It can only be used for two
#' groups. The partial F statistic is the additional contribution to the model
#' from adding one more trait.
#'
#'
#' @param m.lda An object of class 'lda'
#' @param GROUP A factor vector indicating group membership
#' @param T_pm1 The F statistic calculated for a discriminant analysis with
#' only the most informative trait.
#' @return Returns a partial F statistic
#' @seealso \code{\link{FSelect}}
#' @references Habbema J, Hermans J (1977). Selection of Variables in
#' Discriminant Analysis by F-Statistics and Error Rate. Technometrics, 19(4),
#' 487 - 493.
#' @examples
#'
#' #Internal function used in FSelect
#'
#' data(Nuclei)
#' data(Groups)
#'
#' NPC<-floor(ncol(Nuclei)/5)
#'
#' DAT.comp<-completeData(Nuclei, n_pcs = NPC)
#' Groups.use<-c(1,2)
#' use.DAT<-which(Groups==Groups.use[1]|Groups==Groups.use[2])
#'
#' DAT.use<-Nuclei[use.DAT,]
#' GR.use<-Groups[use.DAT]
#'
#' traitA<-2
#'
#' mlda<-MASS::lda(GR.use~DAT.use[,traitA])
#'
#' F1<-partialF(mlda,GR.use,0)
#'
#' traitB<-1
#'
#' mlda2<-MASS::lda(GR.use~DAT.use[,c(traitA,traitB)])
#'
#' partialF(mlda2,GR.use,F1)
#'
#'
#' @export partialF
partialF <- function(m.lda, GROUP, T_pm1) {
GRS <- unique(GROUP)
n1 <- length(which(GROUP == GRS[1]))
n2 <- length(which(GROUP == GRS[2]))
v <- n1 + n2 - 2
p <- ncol(m.lda$means)
T_p <- sum(m.lda$svd)
T_pm1 <- T_pm1
Fp <- (v - p + 1) * ((T_p - T_pm1)/(v + T_pm1))
return(Fp)
} #end partialF
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