Influential or leverage units in ADEA
In adea: Alternate DEA Package

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

Introduction

An influential or leverage units is a one that produce a big changes in results. In this case is a unit that produce a big change in model load.

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)

Searching for influential units

adea_load_leverage function looks for units that produce higher change in loads. The following call

input <- tokyo_libraries[, 1:4]
output <- tokyo_libraries[, 5:6]
adea_load_leverage(input, output)

shows that units 23 and 6 produce changes greater than the default value for load.diff which is 0.05.

The output is sorted in decreasing order of load.diff which is the change in load model.

Those call only considers changes taking units one by one, but using ndel parameter remove of more than one unit at the same time can be tested. The following call tests all groups of two units

adea_load_leverage(input, output, load.diff = 0.1, ndel = 2)

This results in a very long list, so the number or groups in output can be limited, for example, to 10, as in the following call

adea_load_leverage(input, output, load.diff = 0.1, ndel = 2, nmax = 10)

This shows that the best option to remove two units is not the same as remove the two firsts in the one by one analysis. This is because that there are interactions between the units effects.

From this point, decision maker or researcher have to handle this units properly, to avoid biases in DEA results.

Each call to adea_load_leverage requires to solve a big set of a large linear program, so is a very demanding of computation resource, and can require a very large time, so be patient.