Stepwise Selection of Variables in Dea Using Contribution Loads

Abstract

In this paper, we propose a new methodology for variable selection in Data Envelopment Analysis (DEA). The methodology is based on an internal measure which evaluates the contribution of each variable in the calculation of the efficiency scores of DMUs. In order to apply the proposed method, an algorithm, known as "ADEA", was developed and implemented in R. Step by step, the algorithm maximizes the load of the variable (input or output) which contribute least to the calculation of the efficiency scores, redistributing the weights of the variables without altering the efficiency scores of the DMUs. Once the weights have been redistributed, if the lower contribution does not reach a previously given critical value, a variable with minimum contribution will be removed from the model and, as a result, the DEA will be solved again. The algorithm will stop when all variables reach a given contribution load to the DEA or until no more variables can be removed. In this way and contrary to what is usual, the algorithm provides a clear stop rule. In both cases, the efficiencies obtained from the DEA will be considered suitable and rightly interpreted in terms of the remaining variables, indicating the load themselves; moreover, the algorithm will provide a sequence of alternative nested models-potential solutions-that could be evaluated according to external criterion. To illustrate the procedure, we have applied the methodology proposed to obtain a research ranking of Spanish public universities. In this case, at each step of the algorithm, the critical value is obtained based on a simulation study.

Measuring the efficiency of materials management based on data envelopment analysis approach: the case of Polish regions

“…Firstly, the selection of variables is carried out on the basis of experience and recommendation of experts related to the studied field (Jitthavech, 2016). The researchers assume that their selection is correct and that the variables will not cause bias in the results (Fernandez‐Palacin et al, 2018). Secondly, known statistical procedures, like correlation analysis and Hellwig's method, can be used.…”

Modelling Efficiency of Electric Utilities Using Three Stage Virtual Frontier Data Envelopment Analysis with Variable Selection by Loads Method

“…Moreover, the variables chosen by the policy makers or regulators may not be perfect and may include extraneous variables. Therefore, it is important that the variables are selected correctly because inclusion of irrelevant variables or exclusion of significant variables may lead to inaccurate efficiency score [26]. Additionally, the selection of variables may affect methods such as DEA by altering its frontier and may produce inaccurate efficiency scores [27].…”

“…The authors of this method have created an online application at http://knuth.uca. es/DEA (accessed on 8 June 2021) [26].…”

Feature Selection in Data Envelopment Analysis: A Mathematical Optimization approach

“…whereM is another big constant. Constraints (11)- (13) are the counterparts of (7)-(9) but modelling the selection of inputs instead of outputs. (FSDEA (k) (p)) has K + O + I + 3 linear constraints and 2 I + 2 O variables, where half of them are continuous and the other half binary.…”

“…Alternatively, an ex-post analysis of the sensitivity of the efficient frontier to additional features can be run to detect whether relevant features have been left out. See [1,13,22,25,27,36,37,38], and references therein. Recently, there have been attempts to use LASSO techniques from Statistical Learning to build sparse benchmarking models, i.e., models using just a few features, [17,21,31].…”