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 Data Envelopment Analysis (DEA) is a critical aspect that demands careful consideration before the results of an analysis are applied in a real-world scenario. This is because the outcomes can undergo significant changes based on the variables included in the model. As a result, variable selection stands as a pivotal step in every DEA application.

The variable selection process may lead to the removal of a variable that a decision-maker might want to retain for political, tactical, or other reasons. However, if no action is taken, the contribution of that variable will be negligible. The cadea function provides a means to ensure that the contribution of a variable to the model is at least a specified value.

For more information about loads see the help of the package \code{\link{adea}} or see [@Fernandez2018] and [@Villanueva2021].

Let's load and examine the tokyo_libraries dataset using the following code:

data(tokyo_libraries)
head(tokyo_libraries)

Constrained ADEA

First, let's perform an ADEA analysis with the following code:

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

This analysis reveals that Area.I1 has a load value below 0.6, indicating that its contribution to the DEA model is negligible.

With the subsequent cadea call, the contribution of Area.I1 is enforced to be greater than 0.6:

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

It is worth noting that the maximum value of a variable's load is the maximum number of variables of its type, so setting load.max = 4 has no effect on the results. As a result, the load level increases to the specified value of 0.6, causing a slight decrease in the average efficiency.

To compare the two efficiency sets, it is essential to observe that the Spearman correlation coefficient between them is r round(cor(m$eff, mc$eff, method = 'spearman'), 4). This can also be visualized in the following plot:

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

All of these findings indicate that, in this particular case, the changes are minimal. More substantial changes can be expected if load.min is increased.