robust_DEA {rcDEA}

Robust Data Envelopment Analysis (DEA)

Description

This function allows to compute Robust DEA scores.

Usage

robust_DEA(
  input,
  output,
  m,
  B,
  RTS = "crs",
  ORIENTATION = "in",
  alpha = FALSE,
  inclusion = FALSE,
  print = FALSE
)

Arguments

input

matrix (or vector) of inputs along which the units are evaluated.

output

matrix (or vector) of outputs along which the units are evaluated.

m

number of unit to be included in the reference set

B

number of bootstrap replicates

RTS

For more details see the dea function in the package Benchmarking. Text string or a number defining the underlying DEA technology / returns to scale assumption. 0 fdh Free disposability hull, no convexity assumption 1 vrs Variable returns to scale, convexity and free disposability 2 drs Decreasing returns to scale, convexity, down-scaling and free disposability 3 crs Constant returns to scale, convexity and free disposability 4 irs Increasing returns to scale, (up-scaling, but not down-scaling), convexity and free disposability 5 irs2 Increasing returns to scale (up-scaling, but not down-scaling), additivity, and free disposability 6 add Additivity (scaling up and down, but only with integers), and free disposability; also known af replicability and free disposability, the free disposability and replicability hull (frh) – no convexity assumption 7 fdh+ A combination of free disposability and restricted or local constant return to scale 10 vrs+ As vrs, but with restrictions on the individual lambdas via param

ORIENTATION

For more details see the dea function in the package Benchmarking. Input efficiency "in" (1), output efficiency "out" (2), and graph efficiency "graph" (3). For use with DIRECT, an additional option is "in-out" (0).

alpha

This allow to choose the size of the Confidence Intervals computed. By defaulta alpha = FALSE. In this case no confidence interval are computed

inclusion

If inclusion = TRUE the unit under analysis is included in the reference set. So, no super efficient scores are allowed. By default inclusion = FALSE.

print

If print = TRUE the number of the unit under evaluation is printed. In case of large sample the function could require some time, so it could be useful to control how many units have already been evaluated and which one still have to be evaluated. By default print = FALSE.

Value

If the parameter alpha is specified, the function returns a data frame with three numeric columns. The first column is the vector representing the robust DEA scores (eff); the second column is the vector representing the lower bound of the condifence interval (ci_low); the third column is the vector representing the upper bound of the confidence interval (Ci_up). If alpha is not specified, the functions returns only the first column of the data frame (eff).

Examples

#Example with a very small sample to decrease computational time.
          x1 <-runif(50, 50, 75)
          x2 <-runif(50, 30, 75)
          x <- cbind(x1, x2)
          e <- rnorm(50, 0, 36)
          a1 <- 0.4
          a2 <- 0.6
          y <- a1*x1 + a2*x2 + e

          #Robust DEA
          r_DEA <- robust_DEA(input = x, output = y, m = 20, B = 50,
          RTS = "crs", ORIENTATION = "in", print = TRUE)
          summary(r_DEA$eff)

 #Example with random data x and y
          x1 <-runif(100, 50, 75)
          x2 <-runif(100, 30, 75)
          x <- cbind(x1, x2)
          y <- cbind(x+runif(100, -10, 0), rnorm(100, 15, 4))

          #Robust DEA
          r_DEA <- robust_DEA(input = x, output = y, m = 30, B = 40,
          RTS = "crs", ORIENTATION = "in", print = TRUE)
          summary(r_DEA$eff)