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Clustering in a Data Envelopment Analysis Using Bootstrapped Efficiency Scores

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  • Joseph G. Hirschberg
  • Jenny N. Lye

Abstract

This paper explores the insight from the application of cluster analysis to the results of a Data Envelopment Analysis of productive behaviour. Cluster analysis involves the identification of groups among a set of different objects (individuals or characteristics). This is done via the definitions of a distance matrix that defines the relationship between the different objects, which then allows the determination of which objects are most similar into clusters. In the case of DEA, cluster analysis methods can be used to determine the degree of sensitivity of the efficiency score for a particular DMU to the presence of the other DMUs in the sample that make up the reference technology to that DMU. Using the bootstrapped values of the efficiency measures we construct two types of distance matrices. One is defined as a function of the variance covariance matrix of the scores with respect to each other. This implies that the covariance of the score of one DMU is used as a measure of the degree to which the efficiency measure for a single DMU is influenced by the efficiency level of another. An alternative distance measure is defined as a function of the ranks of the bootstrapped efficiency. An example is provided using both measures as the clustering distance for both a one input one output case and a two input two output case.

Suggested Citation

  • Joseph G. Hirschberg & Jenny N. Lye, 2001. "Clustering in a Data Envelopment Analysis Using Bootstrapped Efficiency Scores," Department of Economics - Working Papers Series 800, The University of Melbourne.
    • Handle: RePEc:mlb:wpaper:800
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    References listed on IDEAS

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    Cited by:

    1. Li, Yang, 2020. "Analyzing efficiencies of city commercial banks in China: An application of the bootstrapped DEA approach," Pacific-Basin Finance Journal, Elsevier, vol. 62(C).
    2. Sethi, Amarjit Singh, 2016. "Sources of Growth in India: Evidence from Punjab and Haryana," Journal of Regional Development and Planning, Rajarshi Majumder, vol. 5(1), pages 15-34.
    3. Yang Li & An-Chi Liu & Yi-Ying Yu & Yueru Zhang & Yiting Zhan & Wen-Cheng Lin, 2022. "Bootstrapped DEA and Clustering Analysis of Eco-Efficiency in China’s Hotel Industry," Sustainability, MDPI, vol. 14(5), pages 1-16, March.
    4. Kelly P. Murillo & Eugenio M. Rocha, 2020. "Factors Influencing the Economic Behavior of the Food, Beverages and Tobacco Industry: A Case Study for Portuguese Enterprises," World Journal of Applied Economics, WERI-World Economic Research Institute, vol. 6(2), pages 99-121, December.
    5. Fuad Aleskerov & Vsevolod Petrushchenko, 2016. "DEA by sequential exclusion of alternatives in heterogeneous samples," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 15(01), pages 5-22, January.
    6. Dickens S Omondi Aduda & Collins Ouma & Rosebella Onyango & Mathews Onyango & Jane Bertrand, 2015. "Voluntary Medical Male Circumcision Scale-Up in Nyanza, Kenya: Evaluating Technical Efficiency and Productivity of Service Delivery," PLOS ONE, Public Library of Science, vol. 10(2), pages 1-17, February.
    7. Samoilenko, Sergey & Osei-Bryson, Kweku-Muata, 2010. "Determining sources of relative inefficiency in heterogeneous samples: Methodology using Cluster Analysis, DEA and Neural Networks," European Journal of Operational Research, Elsevier, vol. 206(2), pages 479-487, October.
    8. Yang Li & An-Chi Liu & Shu-Mei Wang & Yiting Zhan & Jingran Chen & Hsiao-Fen Hsiao, 2022. "A Study of Total-Factor Energy Efficiency for Regional Sustainable Development in China: An Application of Bootstrapped DEA and Clustering Approach," Energies, MDPI, vol. 15(9), pages 1-13, April.
    9. Hassan Najadat & Ahmad Alaiad & Sanaa Abu Alasal & Ghadeer Anwar Mrayyan & Izzat Alsmadi, 2020. "Integration of Data Envelopment Analysis and Clustering Methods," Journal of Information & Knowledge Management (JIKM), World Scientific Publishing Co. Pte. Ltd., vol. 19(01), pages 1-19, March.
    10. Tsionas, Mike G., 2023. "Clustering and meta-envelopment in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 304(2), pages 763-778.

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