Improving discrimination in data envelopment analysis: PCA-DEA or variable reduction
Within the data envelopment analysis context, problems of 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 applies Monte Carlo simulation to generalize and compare two discrimination improving methods; principal component analysis applied to data envelopment analysis (PCA-DEA) and variable reduction based on partial covariance (VR). Performance criteria are based on the percentage of observations incorrectly classified; efficient decision-making units mistakenly defined as inefficient and inefficient units defined as efficient. 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. A comparison of the methodologies demonstrates that PCA-DEA provides a more powerful tool than VR with consistently more accurate results. PCA-DEA is applied to all basic DEA models and guidelines for its application are presented in order to minimize misclassification and prove particularly useful when analyzing relatively small datasets, removing the need for additional preference information.
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