alphafrontier.3d: 3d representation of alpha-quantile frontier in the case of 2... In frontiles: Partial Frontier Efficiency Analysis

Description

3d representation of alpha-quantile frontier for a set of reference points (xobs,yobs) in the case of two input and one output. No representation yet for hyperbolic direction.

Usage

 1 2 alphafrontier.3d(xobs, yobs, type="output",alpha=0.95, digits=4, box.leg=TRUE, palette=heat_hcl, rgl=FALSE, n.class=NULL, ...) 

Arguments

 xobs a matrix of size n1 x 2, input of reference points yobs a matrix of size n1 x 1, output of reference points type a character, "output" or "input" direction alpha a scalar digits a precision parameter to compute the alpha-frontier box.leg representation of a legend-box on the plot with the values of frontier palette function to use for colors in case where option col has not been called. See package colorspace for more informations. rgl a boolean, for output direction, representation of the graphic in 3d if TRUE n.class a numeric, for output direction, the number of class ... usual parameters of function plot. Use the parameter asp to modify the scale of window...

Details

In "input" direction: You choose a value of output in the legend box, the efficiency-frontier of the input is represented with the corresponding color on the 2d graphic. In "output" direction : For calculate the alpha-quantile efficiency output frontier everywhere, we have constructed a grid of size n x n by drawing vertical and horizontal lines which intersect each reference observations. Then, we have calculated for each cell C_k k=1,...,n^2 the prediction of the alpha-quantile output efficiency frontier which correspond to the α^{th} elements of the suite {y_j}_{j=1,...,n_k} where reference observations j, j=1,...,n_k verify

\ x^1_j≤q\inf_{(x^1,x^2) \in C_k}x^1

and x^2≤q\inf_{(x_1,x_2) \in C_k}x^2.
We propose to use an algorithm which filled up cells with colors depending on the values taken by the alpha-quantile output efficiency frontier. The algorithm attach the row and vary the column as the folling figure can show it.

no values

Note

The algorithm used is certainly not optimized. For a data set of 61 observations, the function necessits 15.17s on an Optiplex GX745 2 duo 2.13GHz under Windows Vista and probably bugs beyond a certain number of observation

Author(s)

Abdelaati Daouia and Thibault Laurent

alphascore

Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 data(spain) xyn<-cbind(spain[,3:4],spain[,1]) xtab<-as.matrix(xyn[,c(1,2)]) ytab<-matrix(xyn[,3]) # representation in 2-d op <- par(no.readonly = TRUE) # the whole list of settable par's. alphafrontier.3d(xtab,ytab, type="output", alpha=0.6, xlab="input 1", ylab="input 2",main="blabla") points(xtab,pch=16) par(op) # alphafrontier.3d(xtab,ytab,type="output", alpha=0.6, xlab="input 1", # ylab="input 2",main="blabla", rgl=TRUE) # aspect3d(1,1,1) #### second exemple #data(charnes1981) #x <- with(charnes1981, cbind(x1,x2)) #y <- with(charnes1981, y1) #front_out_plot_3d(x,y,alpha=0.8, xlab="input 1",ylab="input 2",main="blabla") #front_out_plot_3d(x,y,alpha=0.8, xlab="input 1",ylab="input 2",main="blabla", # rgl=TRUE) #points(x,pch=16) #abline(h=x[,2],v=x[,1],lty=2) # representation in 3-d #res<-front_out_plot_3d(xtab,ytab,type='3d',xlab="input 1",ylab="input 2", #zlab="output",main=bquote(paste(alpha,"-quantile output frontier with ", #alpha,"=.95"))) #res\$points3d(xtab[,1],xtab[,2],ytab,type='h') 

Example output

Loading required package: classInt
Warning messages:
1: In rgl.init(initValue, onlyNULL) : RGL: unable to open X11 display
2: 'rgl_init' failed, running with rgl.useNULL = TRUE
3: .onUnload failed in unloadNamespace() for 'rgl', details:
call: fun(...)