R/ROCscore.r

In frontiles: Partial Frontier Efficiency Analysis

ROCscore <- function(xobs, yobs, type = "output") {
  # verification
  n1 <- nrow(xobs)    # number of observations
  p.input <- ncol(xobs)     # number of inputs

  # verification of some conditions
  if(n1 != nrow(yobs)) 
    stop("xobs and yobs have not the same number of observations")
 
  match.arg(type,c("output","input","hyper"))

  # initialisation
  alpha <- seq(0.01, 1, by = 0.01)
  m <- c(1, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 40, 45,
        50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 
        seq(100, 2500, length.out = 76))

  # Representation of the alpha quantile efficiency frontier 
  oldpar <- par(no.readonly = TRUE) 
  on.exit(par(oldpar))
 
  # 1- Computation of the alpha-quantile score
  perf1 <- numeric(length(alpha))
  perf2 <- numeric(length(alpha))
  for (k in 1:length(alpha)) {
    res1 <- alphascore(xobs,yobs, alpha=alpha[k])[,type]  # score computed on (xtab,ytab)
    res2 <- ordermscore(xobs,yobs, m=m[k])[,type]   # score computed on (xtab,ytab)
    perf1[k] <- length(which(res1 > 1)) / n1
    perf2[k] <- length(which(res2>1)) / n1
   }
  plot(alpha, perf1, type = 'l', xlab = "alpha", 
       ylab = "Percentage of super-efficiency firms",
       ylim = c(0, 1),
       col = 'royalblue')
  par(new = TRUE)
  plot(m, perf2, type = 'l', lty = 2, ann = FALSE, yaxt = "n", xaxt="n", 
       yaxt = "n", ylim = c(0, 1), col = 'red')
  axis(3)
  mtext(side = 3, "m")
  legend("topright", legend = c("f(alpha)", "f(m)"), 
         lty = 1:2, col = c("royalblue", "red"))

  res <- data.frame(alpha, perf1, m, perf2)
  names(res) <- c("alpha", "f(alpha)", "m", "f(m)")
  return(res)
}