Abstract
In this study, a new definition of a relevant variable in a DEA model is proposed for variable selection. The selection procedure is the conventional iterative backward elimination procedure with multiple statistical comparisons. The multiple tests of null hypothesis are reduced to a simple hypothesis test using either the binomial probability or the McNemar test with Bonferroni correction of significant level. From the results based on two simulation populations of moderately and lowly correlated input variables, the proposed procedure using either one of the suggested statistical tests can identify the relevant variables with high accuracy and eliminate the irrelevant variables effectively. In the dataset from a large scale experiment in the US public school education, the reduced model selected by the proposed procedure is shown to be the better approximation of the full model than the ones selected by the Pastor et al. method.
Highlights
Data envelopment analysis (DEA) is a non-parametric method for measuring a decision making unit’s (DMU) relative efficiency in both multiple input and multiple output production settings
After analysing the simulation results from 100 datasets in each case of correlation, we found that the proposed procedure for variable elimination using the statistical tests as described in Section 2.2 with Bonferroni adjusted levels of significance can effectively withhold the relevant variables and eliminate the irrelevant variables
An iterative backward procedure for variable elimination is proposed using a new definition of a relevant variable based on the number of efficient DMUs and not based on the efficiency scores of the DMUs
Summary
Data envelopment analysis (DEA) is a non-parametric method for measuring a decision making unit’s (DMU) relative efficiency in both multiple input and multiple output production settings. In the earlier studies of the statistical approach, the correlation analysis between variables and efficiency scores has been used as a criterion for selecting the variables included in a DEA model (Lewin et al, 1982; Roll et al, 1989; Chilingerian, 1995). A statistical test of nested radial DEA models is proposed based on the efficiency contribution measure (Pastor et al 2002) in which a candidate variable is considered to be relevant if more than p0% of DMUs have an associated efficiency score change greater than a threshold ρ. The objectives of the paper are three folds: to propose a new definition of a relevant variable in a DEA model, to introduce two hypothesis tests for using in the proposed iterative procedure of backward variable elimination in nested DEA models and to sequentially select an appropriate DEA model for a particular application.
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