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.