dea.plot {Benchmarking} R Documentation

## Plot of DEA technologies

### Description

Draw a graph of a DEA technology. Designed for two goods illustrations, either isoquant (2 inputs), transformation curve (2 outputs), or a production function (1 input and 1 output). If the number of good is larger than 2 then aggregation occur, either simple or weighted.

### Usage

```
dea.plot(x, y, RTS="vrs", ORIENTATION="in-out", txt=NULL, add=FALSE,
wx=NULL, wy=NULL, TRANSPOSE=FALSE, fex=1, GRID=FALSE,
RANGE=FALSE, param=NULL, ..., xlim, ylim, xlab, ylab)

dea.plot.frontier(x, y, RTS="vrs",...)

dea.plot.isoquant(x1, x2, RTS="vrs",...)

dea.plot.transform(y1, y2, RTS="vrs",...)

```

### Arguments

 `x` The good illustrated on the first axis. If there are more than 1 input then inputs are just summed or, if `wx` is present, a weighted sum of inputs is used. `y` The good illustrated on the second axis. If there are more than 1 output then outputs are just summed or, if `wy` is present, a weighted sum of outputs is used. `x1, y1` The good illustrated on the first axis `x2, y2` The good illustrated on the second axis `RTS` Underlying DEA model / assumptions about returns to scale: "fdh" (0), "vrs" (1), "drs" (2), "crs" (3), "irs" (4), "irs2" (5) (irs without convexity), "add" (6), and "fdh+" (7). Numbers in parenthesis can also be used as values for `RTS` `ORIENTATION` Input-output graph of 1 input and 1 output is "in-out" (0), graph of 2 inputs is "in" (1), and graph of 2 outputs is "out" (2). `txt` `txt` is an array to label the observations. If `txt=TRUE` the observations are labeled by the observation number or rownames if there are any. `add` For `add=T` the technology is drawn on top of an existing graph. With the default `add=F`, a new graph is made. `wx` Weight to aggregate the first axis if there are more than 1 good behind the first axis. `wy` Weights to aggregate for the second axis if there are more than 1 good behind the second the second axis. `TRANSPOSE` Only relevant for more than 1 good for each axis, see `dea` for a description of this option. `GRID` If `GRIF=TRUE` a gray grid is put on the plot. `...` Usual options for the methods `plot`, `lines`, and `abline` etc. `fex` Relative size of the text/labels on observations; corresponds to `cex`, but only changes the size of the text. `RANGE` A logical variable, if `RANGE=TRUE` the limits for the graph is the range of the variables; zero is always included. Default is `RANGE=FALSE` when the range is from zero to the max values. Relevant if some values are negative. `param` Possible parameters. At the moment only used for RTS="fdh+"; see the section details and examples for its use. Future versions might also use `param` for other purposes. `xlim` Possible limits `c(x1,x2)` for the first axis `ylim` Possible limits `c(y1,y2)` for the second axis `xlab` Possible label for the x-axis `ylab` Possible label for the y-axis

### Details

The method `dea.plot` is the general plotting method. The the 3 others are specialized versions for frontiers (1 input and 1 output), isoquant curves (2 inputs for given outputs), and transformation curves (2 outputs for given inputs) obtained by using the argument `ORIENTATION`.

The crs factor in RTS="fdh+" that sets the lower and upper bound can be changed by the argument `param` that will set the lower and upper bound to 1-param and 1+param; the default value is param=.15. The value must be greater than or equal to 0 and strictly less than 1. A value of 0 corresponds to RTS="fdh". The FDH+ technology set is described in Bogetoft and Otto (2011) pages 72–73.

### Value

No return, uses the original graphing system.

### Note

If there are more than 1 good for the arguments `x` and `y` then the goods are just summed or, if `wx` or `wy` are present, weighted sum of goods are used. In this case the use of the command `identify` must be calles as `dea.plot(rowSums(x),rowSums(y))`.

Warning If you use this facility to plot multi input and multi output then the plot may deceive you as fully multi efficient firms are not necessarely placed on the two dimensional frontier.

Note that `RTS="add"` and `RTS="fdh+"` only works for `ORIENTATION="in-out"` (0).

### Author(s)

Peter Bogetoft and Lars Otto larsot23@gmail.com

### References

Peter Bogetoft and Lars Otto; Benchmarking with DEA, SFA, and R; Springer 2011

Paul Murrell; R Graphics; Chapman & Hall 2006

The documentation for the function `plot` and Murrell (2006) for further options and on customizing plots.

### Examples

```
x <- matrix(c(100,200,300,500,600,100),ncol=1)
y <- matrix(c(75,100,300,400,400,50),ncol=1)

dea.plot(x,y,RTS="vrs",ORIENTATION="in-out",txt=LETTERS[1:length(x)])

dea.plot.frontier(x,y,txt=1:dim(x))

n <- 10
x <- matrix(1:n,,1)
y <- matrix(x^(1.6) + abs(rnorm(n)),,1)
dea.plot.frontier(x,y,RTS="irs",txt=1:n)

# Two different forms of irs: irs and irs2, and two different ways to
# make a frontier
id <- sample(1:n,30,replace=TRUE)
dea.plot(x[id],y[id],RTS="irs",ORIENTATION="in-out")
dea.plot.frontier(x[id],y[id],RTS="irs2")

# Difference between the FDH technology and the additive
# FRH technology
x <- matrix(c(100,220,300,520,600,100),ncol=1)
y <- matrix(c(75,100,300,400,400,50),ncol=1)
dea.plot(x,y,RTS="fdh",ORIENTATION="in-out",txt=LETTERS[1:length(x)])