Improving discrimination in Data Envelopment Analysis: PCA-DEA versus Variable Reduction. Which method at what cost?

In the data envelopment analysis context, problems related to discrimination between efficient and inefficient decision-making units often arise, particularly if there are a relatively large number of variables with respect to observations. This paper presents a comparison of two discrimination-improving methods published in the literature that do not require additional preferential information; principal component analysis applied to data envelopment analysis (PCA-DEA) and variable reduction based on partial covariance (VR). A simulation based approach was used to generalize the comparison as to which methodology was preferable under which conditions. Performance criteria were based on the percentage of observations incorrectly classified; efficient decision-making units mistakenly defined as inefficient and inefficient units defined as efficient. According to the simulation results, a trade-off was observed with both methods improving discrimination by reducing the probability of the latter error at the expense of a small increase in the probability of the former error. The comparison of the two methodologies showed that PCA-DEA provides a more powerful discrimination tool than VR with consistently more accurate results when the curse of dimensionality exists. Guidelines for the PCA-DEA user are presented based on a rule-of-thumb that aims to minimize both types of error.