Constrained ADEA model

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



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adea documentation built on Sept. 7, 2021, 5:09 p.m.