Constrained ADEA model

In adea: Alternate DEA Package

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  fig.width = 6,
  fig.height = 4
)
library('adea')

Introduction

Variable selection in DEA is a question that requires full attention before the results of an analysis can be used in a real case, because its results can be significantly modified depending on the variables included in the model. So, variable selection is a keystone step in each DEA application.

The selection procedure can lead to remove a variable that decision maker could want to keep a variable in the model for political, tactical or any other reason. But the contribution of that variable will be negligible if nothing is done. cadea function provides a way force the contribution of a variable to a model be at least a given value.

For more information about loads help of the package about adea or see [@Fernandez2018] and [@Villanueva2021].

Let's load and have a look at the tokyo_libraries dataset with

data(tokyo_libraries)
head(tokyo_libraries)

Constrained ADEA

First of all let's do an adea with the following call

input <- tokyo_libraries[, 1:4]
output <- tokyo_libraries[, 5:6]
m <- adea(input, output)
summary(m)

It shows that Area.I1 has a load under 0.6, which means its contribution to DEA model is negligible.

With the following call to cadea the contribution of Area.I1 is force to be higher than 0.6:

mc <- cadea(input, output, load.min = 0.6, load.max = 4)
summary(mc)

Note that the maximum value of a variable load is the maximum number of variables of its types, so load.max = 4 has no effect on results.

Now load level raises to the given value of 0.6, efficiency average decreases a little.

To compare both efficiency set, observe that Spearman correlation coefficient between them is r round(cor(m$eff, mc$eff, method = 'spearman'), 4). This can also be seen in the next plot:

plot(m$eff, mc$eff, main ='Initial efficiencies vs constrained model efficiencies')

All these mean that in this case the change are small. Bigger change can be expected if load.min grows.

References

adea documentation built on Nov. 23, 2023, 3:02 p.m.