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DEA, that means Data Envelopment Analysis, consider a set of DMUs (Decision Making Units) and computes an efficiency score for each DMU. Such score is defined as a weighted ratio between several inputs and outputs values for such DMU.
This package provides an implementation of the ADEA method for variable selection in DEA. ADEA methodology includes a new phase in the classical DEA analysis that measures the relative importance of each input and output variable. This above-mentioned measure is called load ratio or contribution. A load for the whole model is also defined. Using such measure, a procedure to select an optimised or relevant set of variables has been developed.
A variable load is a number between 0 and 1. Where 0 means that the contribution of that variable to the efficiency values is negligible. In an ideal case, each input or output variable will have a load of 1.
As it is usually done in DEA, these loads are computed as its maximum allowable value. Using alternative sets of weights, this procedure don't change efficiency scores. But because the sum of all of them is 1, when one variable increases its load, any other decrease in value. So only the lowest value of all loads has a real meaning. This lowest value can be taken as a significance measure of the entire model.
This measure, load, has two important properties that easy its interpretation:
It has a bounded range from 0 to the number of input or output, and 1 as its ideal value.
It is invariant by changes of scale.
ADEA analysis can be done measuring only input variables, in this case ADEA analysis has input
output when only output variables are considered.
load.orientation when all variables in the model are taken into account.
The package is named after its main function. adea makes a DEA analysis using alternative optimal solution of the same programs that DEA uses to compute efficiency scores. For a detailed description of the maths behind the model, see the references.
The main functions that this package provides are:
adea: It makes ADEA analysis giving, efficiency scores for each DMU, a set of weight, and a load for each input and output variable, and also model load.
cadea: Constrained ADEA analysis to force that variable loads fall in a given range. The efficiencies scores will change in order to allow this.
adea_load_average: Search for DMU's with higher impact on ADEA model.
The package is ready for translations, so contributions with translated versions of po files will be very welcomed.
Fernando Fernandez-Palacin <firstname.lastname@example.org> and Manuel Munoz-Marquez <email@example.com>
Mantainer: Manuel Munoz-Marquez <firstname.lastname@example.org>
Stepwise Selection of Variables in DEA Using Contribution Load. F. Fernandez-Palacin, M. A. Lopez-Sanchez and M. Munoz-Marquez. Pesquisa Operacional 38 (1), pg. 1-24, 2018. <DOI:10.1590/0101-7438.2018.038.01.0000>.
Methodology for calculating critical values of relevance measures in variable selection methods in data envelopment analysis. Jeyms Villanueva-Cantillo and Manuel Munoz-Marquez. European Journal of Operational Research, 290 (2), pg. 657-670, 2021. <DOI:10.1016/j.ejor.2020.08.021>.
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