R/afc.mm.R

In afc: Generalized Discrimination Score

#' 2AFC For Ordinal Polychotomous Observations And Ordinal Polychotomous
#' Forecasts
#'
#' Routine to calculate the Generalized Discrimination Score (aka
#' Two-Alternatives Forced Choice Score 2AFC) for the situation of
#' polychotomous observations (ordinal) and polychotomous forecasts (ordinal)
#'
#' This routine applies Eq.14 of Mason and Weigel (2009) to calculate the 2AFC.
#'
#' @param obsv vector with polychotomous observations (values in \{1,..,mv\})
#' @param fcst vector of same length as \emph{obsv} with polychotomous
#' forecasts (values in \{1,..,mf\})
#' @param mv number of observation categories (default = 3)
#' @param mf number of forecast categories (default = 3)
#' @param na.rm logical; if \code{TRUE} pairs where \code{obsv} or
#'   \code{fcst} is \code{NA} are removed before scoring. Default
#'   \code{FALSE} returns \code{NA} if any input contains \code{NA}.
#' @return \item{ p.afc }{ Value of Generalized Discrimination (2AFC) Score }
#' @author Andreas Weigel, Federal Office of Meteorology and Climatology,
#' MeteoSwiss, Zurich, Switzerland
#' @seealso \code{\link{afc}}
#' @references S.J. Mason and A.P. Weigel, 2009. A generic verification
#' framework for administrative purposes. Mon. Wea. Rev., 137, 331-349
#' @keywords file
#' @examples
#'   data(cnrm.nino34.mm)
#'   obsv = cnrm.nino34.mm$obsv
#'   fcst = cnrm.nino34.mm$fcst
#'   afc.mm(obsv,fcst,4,4)
#' @export afc.mm
afc.mm = function(obsv, fcst, mv=3, mf=3, na.rm = FALSE) {
  if (na.rm) {
    d <- .complete_cases(obsv, fcst); obsv <- d$obsv; fcst <- d$fcst
  } else if (anyNA(obsv) || anyNA(fcst)) {
    return(NA_real_)
  }
  if (mf == 0) mf=mv
  n.matrix = array(0,dim=c(mv,mf))
  for (nn in 1:mv) for (mm in 1:mf){
    n.matrix[nn,mm] = sum((obsv == nn) & (fcst == mm))
  }
  numer = 0
  denom = 0
  for (k in 1:(mv-1)) for (l in (k+1):mv){
    term1 = 0
    term2 = 0
    for (i in 1:(mf-1)) for (j in (i+1):mf){
      term1 = term1 + n.matrix[k,i]*n.matrix[l,j]
    }
    for (i in 1:mf){
      term2 = term2 + n.matrix[k,i]*n.matrix[l,i]
    }
    numer = numer + term1 + 0.5*term2
    denom = denom + sum(n.matrix[k,])*sum(n.matrix[l,])
  }
  p.afc = numer/denom
  type.flag = 1
  return(p.afc)
}