Advertisement

Identification of Outliers in Data Envelopment Analysis

An Approach Using Structure-detecting Statistical Procedures
  • Marcel ClermontEmail author
  • Julia Schaefer
Original Article

Abstract

Data Envelopment Analysis (DEA) is a deterministic method for the aggregation of multidimensional measures and subsequent efficiency analysis. Due to its inherent determinism, however, it reacts sensitively to outliers in datasets. Existing methods for identifying such outliers have two main disadvantages. First, from a more conceptional point of view, a uniform definition of an outlier is missing. Second, there are technical disadvantages of each method. For instance, arbitrarily limited values have to be set by the user, like the amount of efficiency value from which on a decision making unit is regarded as an outlier. This paper initially presents a definition of outliers, which explicitly takes the specifics of DEA into account. Based on this definition, an approach for identifying outliers in DEA is introduced which explicitly tackles the technical disadvantages and takes them into account in the developed algorithm. The plausibility of this approach is validated on the basis of empirical examples from performance measurement at the university level.

Keywords

Data Envelopment Analysis Outlier detection Efficiency analysis Performance measurement Cluster analysis 

JEL Classification

C67 M11 M49 P47 

Notes

Compliance with ethical guidelines

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical standards

This article does not contain any studies with human participants or animals performed by any of the authors.

Informed consent

Not applicable, since there are no individual participants included in the study.

References

  1. Agasisti, T., G. Munda, and R. Hippe. 2019. Measuring the efficiency of European education systems by combining data envelopment analysis and multiple-criteria evaluation. Journal of Productivity Analysis 51:105–124.Google Scholar
  2. Agasiti, T., and C. Pérez-Esparrells. 2010. Comparing efficiency in a cross-country perspective: the case of Italian and Spanish state universities. Higher Education 59:85–103.Google Scholar
  3. Aigner, D., C.A.K. Lovell, and P. Schmidt. 1977. Formulation and estimation of stochastic frontier production function models. Journal of Econometrics 6:21–37.Google Scholar
  4. Albers, S. 2015. What drives publication productivity in German business faculties? Publication Productivity 67:6–33.Google Scholar
  5. Andersen, P., and N.C. Petersen. 1993. A procedure for ranking efficient units in Data Envelopment Analysis. Management Science 39:1261–1264.Google Scholar
  6. Aragon, Y., A. Daouia, and C. Thomas-Agnan. 2005. Nonparametric frontier estimation: a conditional quantile-based approach. Econometric Theory 21:358–389.Google Scholar
  7. Avkiran, N.K. 2001. Investigating technical and scale efficiencies of Australian universities through data envelopment analysis. Socio-Economic Planning Sciences 35:57–80.Google Scholar
  8. Bahari, A.R., and A. Emrouznejad. 2014. Influential DMUs and outlier detection in Data Envelopment Analysis with an application to health care. Annals of Operations Research 223:95–108.Google Scholar
  9. Ball, R., B. Mittermaier, and D. Tunger. 2009. Creation of journal-based publication profiles of scientific institutions: a methodology for the interdisciplinary comparison of scientific researcher based on the J‑factor. Scientometrics 81:381–392.Google Scholar
  10. Banker, R.D., and H. Chang. 2006. The super-efficiency procedure for outlier identification, not for ranking efficient units. European Journal of Operational Research 175:1311–1320.Google Scholar
  11. Banker, R.D., A. Charnes, and W.W. Cooper. 1984. Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management Science 30:1078–1092.Google Scholar
  12. Banker, R.D., S. Das, and S.M. Datar. 1989. Analysis of cost variances for management control in hospitals. Research in Governmental and Nonprofit Accounting 5:269–291.Google Scholar
  13. Barnett, V., and T. Lewis. 1984. Outlier in statistical data, 2nd edn., Chichester: John Wiley & Sons.Google Scholar
  14. Ben-Gal, I. 2005. Outlier detection. In Data mining and knowledge discovery handbook, 2nd edn., ed. O. Maimon, L. Rokach, 117–130. New York: Springer.Google Scholar
  15. Bogetoft, P., and L. Otto. 2011. Benchmarking with DEA, SFA, and R. New York: Springer.Google Scholar
  16. Bolli, T., and M. Farsi. 2015. The dynamics of productivity in Swiss universities. Journal of Productivity Analysis 44:21–38.Google Scholar
  17. Bonesrønning, H., and J. Rattsø. 1994. Efficiency variation among the Norwegian high schools: consequences of equalization policy. Economics of Education Review 13:289–304.Google Scholar
  18. Bourne, M., A. Neely, J. Mills, and K. Platts. 2003. Implementing performance measurement systems: a literature overview. International Journal of Business Performance Management 5:1–24.Google Scholar
  19. Calinski, T., and J. Harabasz. 1974. A dendrite method for cluster analysis. Communications in Statistics: Theory and Methods 3:1–27.Google Scholar
  20. Cazals, C., J.-P. Florens, and L. Simar. 2002. Nonparametric frontier estimation: a robust approach. Journal of Econometrics 106:1–25.Google Scholar
  21. Charnes, A., W.W. Cooper, B. Golany, L. Seiford, and J. Stutz. 1985. Foundations of data envelopment analysis for Pareto-Koopmans efficient empirical production functions. Journal of Econometrics 30:91–107.Google Scholar
  22. Charnes, A., W.W. Cooper, and E. Rhodes. 1978. Measuring the efficiency of decision making units. European Journal of Operational Research 2:429–444.Google Scholar
  23. Clermont, M. 2016. Effectiveness and efficiency of research in Germany over time: an analysis of German business schools between 2001 and 2009. Scientometrics 108:1347–1381.Google Scholar
  24. Clermont, M., and A. Dirksen. 2016. The measurement, evaluation, and publication of performance in higher education: An analysis of the CHE research ranking of business schools in Germany from an accounting perspective. Public Administration Quarterly 40:341–386.Google Scholar
  25. Clermont, M., A. Dirksen, and H. Dyckhoff. 2015. Returns to scale of business administration research in Germany. Scientometrics 103:583–614.Google Scholar
  26. Daghbashyan, Z., E. Deiaco, and M. McKelvey. 2014. How and why does cost efficiency of universities differ across European countries? An explorative attempt using new microdata. In Knowledge, diversity and performance in European higher education: A changing landscape, ed. A. Bonaccorsi, 267–291. Cheltenham & Northampton: Edward Elgar.Google Scholar
  27. Dellnitz, A. 2016. RTS-mavericks in Data Envelopment Analysis. Operations Research Letters 44:622–624.Google Scholar
  28. Dilger, A., and H. Müller. 2012. Ein Forschungsleistungsranking auf der Grundlage von Google Scholar. Zeitschrift für Betriebswirtschaft 82:1089–1105.Google Scholar
  29. Doyle, J., and R. Green. 1994. Efficiency and cross-efficiency in DEA: derivations, meanings and use. Journal of the Operational Research Society 45:567–578.Google Scholar
  30. Dyckhoff, H., and H. Ahn. 2010. Verallgemeinerte DEA-Modelle zur Performanceanalyse. Zeitschrift für Betriebswirtschaft 80:1249–1276.Google Scholar
  31. Dyckhoff, H., and K. Allen. 1999. Theoretische Begründung einer Effizienzanalyse mittels Data Envelopment Analysis (DEA). Zeitschrift für betriebswirtschaftliche Forschung 51:411–436.Google Scholar
  32. Dyckhoff, H., H. Ahn, S. Rassenhövel, and K. Sandfort. 2008. Skalenerträge der Forschung wirtschaftswissenschaftlicher Fachbereiche: Empirische Ergebnisse und ihre Interpretation. Hochschulmanagement 3:62–66.Google Scholar
  33. Dyckhoff, H., S. Rassenhövel, and K. Sandfort. 2009. Empirische Produktionsfunktion betriebswirtschaftlicher Forschung: Eine Analyse der Daten des Centrums für Hochschulentwicklung. Zeitschrift für betriebswirtschaftliche Forschung 61:22–56.Google Scholar
  34. Emrouznejad, A., and G.-L. Yang. 2018. A survey and analysis of the first 40 years of scholarly literatur in DEA: 1978–2016. Socio-Economic Planning Sciences 61:4–8.Google Scholar
  35. Fandel, G. 2007. On the performance of universities in North-Rhine-Westphalia, Germany: Government’s redistribution of funds judged using DEA efficiency measures. European Journal of Operational Research 176:521–533.Google Scholar
  36. Färe, R., S. Grosskopf, B. Lindgren, and P. Roos. 1994. Productivity development in Swedish hospitals: a Malmquist output index approach. In Data envelopment analysis: theory, methodology, and applications, ed. A. Charnes, W.W. Cooper, A.Y. Lewin, and L.M. Seiford, 253–272. New York: Springer.Google Scholar
  37. Färe, R., S. Grosskopf, and W. Weber. 1989. Measuring school district performance. Public Finance Review 17:409–428.Google Scholar
  38. Flegg, A.T., and D.O. Allen. 2007. Does expansion cause congestion? The case of the older British universities, 1994–2004. Education Economics 15:75–102.Google Scholar
  39. Fouchet, R., and M. Guenoun. 2007. Performance management in intermunicipal authorities. International Journal of Public Sector Performance Management 1:62–82.Google Scholar
  40. Franco-Santos, M., L. Lucianetti, and M. Bourne. 2012. Contemporary performance measurement systems: a review of their consequences and a framework for research. Management Accounting Research 23:79–119.Google Scholar
  41. Frey, B.S. 2007. Evaluierungen, Evaluierungen… Evaluitis. Perspektiven der Wirtschaftspolitik 8:207–220.Google Scholar
  42. García-Aracil, A. 2013. Understanding productivity changes in public universities: evidence from Spain. Research Evaluation 22:351–368.Google Scholar
  43. Golany, B., and Y. Roll. 1989. An application procedure for DEA. Omega 17:237–250.Google Scholar
  44. Halkos, G.E., and N.G. Tzeremes. 2011. Measuring economic journals’ citation efficiency: a data envelopment analysis approach. Scientometrics 88:979–1001.Google Scholar
  45. Hammerschmidt, M., R. Wilken, and M. Staat. 2009. Methoden zur Lösung grundlegender Probleme der Datenqualität in DEA-basierten Effizienzanalysen. Die Betriebswirtschaft 69:289–309.Google Scholar
  46. Hawkins, D. 1980. Identification of outliers. London: Chapman and Hall.Google Scholar
  47. Horne, J., and B. Hu. 2008. Estimation of cost efficiency of Australian universities. Mathematics and Computers in Simulation 78:266–275.Google Scholar
  48. Hosseinzadeh Lotfi, F., G.R. Jahanshahloo, M. Khodabakhshi, M. Rostamy-Malkhlifeh, Z. Moghaddas, and M. Vaez-Ghasemi. 2013. A review of ranking Models in data envelopment analysis. Journal of Applied Mathematics  https://doi.org/10.1155/2013/492421.Google Scholar
  49. Jarwal, S.D., A.M. Brion, and M.L. King. 2009. Measuring research quality using the journal impact factor, citations and ‘ranked journals’: blunt instruments or inspired metrics? Journal of Higher Education Policy & Management 31:289–300.Google Scholar
  50. Johnes, J. 2006. Data envelopment analysis and its application to the measurement of efficiency in higher education. Economics of Education Review 25:273–288.Google Scholar
  51. Johnson, A.L., and L.F. McGinnis. 2009. The hyperbolic oriented efficiency measure as a remedy to infeasibility of super efficiency models. Journal of the Operational Research Society 60:1511–1517.Google Scholar
  52. Jradi, S., and J. Ruggiero. 2019. Stochastic data envelopment analysis: a quantile regression approach to estimate the production function. European Journal of Operational Research 278:385–393.Google Scholar
  53. Keeney, R.L., K.E. See, and D. von Winterfeldt. 2006. Evaluating academic programs: with applications to U.S. graduate decision science programs. Operations Research 54:813–828.Google Scholar
  54. Kerpen, P. 2016. Praxisorientierte Data Envelopment Analysis. Wiesbaden: Springer.Google Scholar
  55. Kieser, A. 2012. JOURQUAL: Der Gebrauch, nicht der Missbrauch, ist das Problem. Oder: Warum Wirtschaftsinformatik die beste deutschsprachige betriebswirtschaftliche Zeitschrift ist. Die Betriebswirtschaft 72:93–110.Google Scholar
  56. Lampe, H.W., and D. Hilgers. 2015. Trajectories of efficiency measurement: a bibliometric analysis of DEA and SFA. European Journal of Operational Research 240:1–21.Google Scholar
  57. Lisi, I.E. 2015. Translating environmental motivations into performance: the role of environmental performance measurement systems. Management Accounting Research 29:27–44.Google Scholar
  58. Liu, H.-H., Y.-Y. Song, and G.-L. Yang. 2019. Cross-efficiency evaluation in data envelopment analysis based on prospect theory. European Journal of Operational Research 273:364–375.Google Scholar
  59. Liu, J.S., L.Y. Lu, W.M. Lu, and B.J. Lin. 2013. A survey of DEA applications. Omega 40:893–902.Google Scholar
  60. Marginson, S., and M. van der Welde. 2007. To rank or to be ranked: the impact of global rankings in higher education. Journal of Studies in International Education 11:206–329.Google Scholar
  61. Maugeri, S., and J.L. Metzger. 2013. Public action: a question of performance? International Journal of Public Sector Performance Management 2:105–122.Google Scholar
  62. Maulik, U., and S. Bandyopadhyay. 2002. Performance evaluation of some clustering algorithms and validity indices. IEEE Transactions on Pattern Analysis and Machine Intelligence 24:1650–1654.Google Scholar
  63. Meeusen, W., and J. van den Broeck. 1977. Efficiency estimation from Cobb-Douglas production functions with composed error. International Economic Review 18:435–444.Google Scholar
  64. Milligan, G.W., and M.C. Cooper. 1985. An examination of procedures for determining the number of clusters in a data set. Psychometrika 50:159–179.Google Scholar
  65. Olivares, M., and A. Schenker-Wicki. 2012. The dynamics of productivity in the Swiss and German university sector: a non-parametric analysis that accounts for heterogeneous production. Zürich: University of Zurich.Google Scholar
  66. Ondrich, J., and J. Ruggiero. 2002. Outlier detection in data envelopment analysis: an analysis of jackknifing. Journal of the Operational Research Society 53:342–346.Google Scholar
  67. Peffers, K., T. Tuunanen, M.A. Rothenberger, and S. Chatterjee. 2008. A design science research methodology for information systems research. Journal of Management Information Systems 24:45–77.Google Scholar
  68. Rassenhövel, S., and H. Dyckhoff. 2006. Die Relevanz von Drittmittelindikatoren bei der Beurteilung der Forschungsleistung im Hochschulbereich. In Fortschritt in den Wirtschaftswissenschaften: Wissenschaftstheoretische Grundlagen und exemplarische Anwendungen, ed. S. Zelewski, N. Akca, 85–112. Wiesbaden: Gabler.Google Scholar
  69. Schaefer, J., and M. Clermont. 2018. Stochastic non-smooth envelopment of data for multi-dimensional output. Journal of Productivity Analysis 50:139–154.Google Scholar
  70. Schrader, U., and T. Hennig-Thurau. 2009. VHB-JOURQUAL2: Method, results, and implication of the German academic association for business research’s journal ranking. Business Research 2:180–204.Google Scholar
  71. Simar, L. 2003. Detecting outliers in frontier models: a simple approach. Journal of Productivity Analysis 20:391–424.Google Scholar
  72. Simar, L., and P.W. Wilson. 1998. Sensitivity analysis of efficiency scores: how to bootstrap in nonparametric frontier models. Management Science 44:49–61.Google Scholar
  73. Smirlis, Y.G., and D.K. Despotis. 2012. Relaxing the impact of extreme units in data envelopment analysis. International Journal of Information Technology & Decision Making 11:893–907.Google Scholar
  74. Sousa, M.D.C.S.D., and B. Stošić. 2005. Technical efficiency of the Brazilian municipalities: correcting nonparametric frontier measurements for outliers. Journal of Productivity Analysis 24:157–181.Google Scholar
  75. Speklé, R.F., and F.H.M. Verbeeten. 2014. The use of performance measurement systems in the public sector: effects on performance. Management Accounting Research 25:131–146.Google Scholar
  76. Stolz, I., D.D. Hendel, and A.S. Horn. 2010. Ranking of rankings: Benchmarking twenty-five higher education ranking systems in Europe. Higher Education 60:507–528.Google Scholar
  77. Thanassoulis, E. 1999. Setting achievement targets for school children. Education Economics 7:101–119.Google Scholar
  78. Thanassoulis, E., M. Kortelainen, G. Johnes, and J. Johnes. 2011. Costs and efficiency of higher education institutions in England: a DEA analysis. Journal of the Operational Research Society 62:1282–1297.Google Scholar
  79. Tone, K. 2001. A slacks-based measure of efficiency in data envelopment analysis. European Journal of Operational Research 130:498–509.Google Scholar
  80. Tran, N.A., G. Shively, and P. Preckel. 2008. A new method for detecting outliers in data envelopment analysis. Applied Economics Letters 17:313–316.Google Scholar
  81. Tunger, D., M. Clermont, and A. Meier. 2018. Altmetrics: state of the art and a look into the future. In Scientometrics, ed. M. Jibu, Y. Osabe, 123–134. London: IntechOpen.Google Scholar
  82. Usher, A., and M. Savino. 2006. A world of difference: a global survey of university league tables. Toronto: Educational Policy Institute.Google Scholar
  83. Wilson, P.W. 1995. Detecting influential observations in data envelopment analysis. Journal of Productivity Analysis 6:27–45.Google Scholar
  84. de Witte, K., and R.C. Marques. 2010. Influential observations in frontier models, a robust non-oriented approach to the water sector. Annals of Operations Research 181:377–392.Google Scholar
  85. Wojcik, V., H. Dyckhoff, and M. Clermont. 2018. Is Data Envelopment Analysis a suitable tool for performance measurement and benchmarking in non-production contexts? Business Research.  https://doi.org/10.1007/s40685-018-0077-z.Google Scholar
  86. Worthington, A.C., and B.L. Lee. 2008. Efficiency, technology and productivity change in Australian universities: 1998–2003. Economics of Education Review 27:285–298.Google Scholar
  87. Yang, Z., X. Wang, and D. Sun. 2010. Using the bootstrap method to dectect influential DMUs in Data Envelopment Analysis. Annals of Operations Resarch 173:89–103.Google Scholar
  88. Zhu, J. 2014. Quantitative models for performance evaluation and benchmarking, Data Envelopment Analysis with spreadsheets, 3rd edn., Berlin: Springer.Google Scholar

Copyright information

© Schmalenbach-Gesellschaft für Betriebswirtschaft e.V. 2019

Authors and Affiliations

  1. 1.Duale Hochschule Gera-EisenachEisenachGermany
  2. 2.School of Business and EconomicsRWTH Aachen UniversityAachenGermany

Personalised recommendations