# At a crossroad of data envelopment and principal component analyses

*Ramalingam Shanmugam* and
*Charles Johnson*

*Omega*, 2007, vol. 35, issue 4, 351-364

**Abstract:**
Data envelopment analysis (DEA), a popular linear programming technique is useful to rate comparatively operational efficiency of decision making units (DMU) based on their deterministic (not necessarily stochastic) input-output data. Only when the input-output data are stochastic (preferably distributed as a multivariate Gaussian), a statistical technique called principal component analysis (PCA) could alternatively be used for the same purpose of rating DMU. Because of these choices, research interest has been growing among statisticians and mathematical programmers to explore benefits versus disadvantages of using one technique over the other. Yet, the duality between DEA and PCA has not been fully understood. This article is devoted to investigate their complementarities. With an expectation that an integration of both techniques would offer the best of DEA and PCA, several integration methods have been suggested in the literature. In these methods, ratio of two Gaussian random variables is involved and this creates a flaw. The ratio is Cauchy distributed and not Gaussian distributed. Neither mean nor dispersion exists in Cauchy distribution. To overcome this flaw of trapping into a Cauchy distribution, a novel method of integrating DEA and PCA, as it is proposed and demonstrated in this article, would enrich the validity of the integration. A medical example is considered for illustration. In the medical example, 45 countries are rated with respect to their survival rate from melanoma cancer among men and among women as output data variable and data on location latitude, ozone thickness, ultraviolet rays of type A and type B as input data variables. Firstly, DEA, secondly PCA are separately applied and then thirdly integrated approach of this article is tried on data. The results are compared and commented with a few concluding thoughts.

**Keywords:** Profiling; Efficiency; rating; Decision; making; Ratio; of; Gaussian; random; variables; Melanoma; cancer (search for similar items in EconPapers)

**Date:** 2007

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