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Robust Coplot: Veri zarflama analizi sonuçlarının grafiksel gösterimi için bir yaklaşım

Year 2016, Volume: 9 Issue: 2, 66 - 78, 25.12.2016

Abstract

Bu çalışmanın amacı, çok kriterli karar verme ve veri analizi alanlarında mevcut olan iki yöntemin nasıl birleştirildiğini anlatmak, bu iki yöntemin bir arada nasıl etkili bir biçimde kullanıldığını göstermektir. Literatürde veri zarflama analizi sonuçlarının coplot grafiği yardımı ile görsellenmesine ilişkin çalışmalar vardır. Ancak veri kümesi aykırı değer içerdiğinde kullanılan yöntem güvenilirliğini yitirmektedir. Bu sorunun bir çözümü olarak önerilen robust coplot yöntemi ile ilgili ise, böyle bir çalışma bilindiği kadarıyla literatürde yer almamaktadır. Burada, robust coplot ile veri zarflama analizi sonuçlarının nasıl incelendiği, yorumlandığı açıklanacak ve neden robust yöntemlerin tercih edilmesi gerektiği vurgulanacaktır. Elde edilen grafik, veri kümesindeki şüpheli gözlemleri veya ihmal edilebilecek değişkenleri de tespit etme imkânı sunmaktadır. Grafiğin elde edilmesine ilişkin her bir aşama, yine literatürde veri zarflama analizi çalışmalarında sıklıkla kullanılan bir veri kümesi üzerinden açıklanmıştır. Ayrıca, çalışmada robust coplot grafiklerinin elde edilmesi amacıyla geliştirilmiş olan RobCop paket programı da kısaca tanıtılmaktadır

References

  • Adler, N., Raveh, A., Yazhemsky, E., 2006, Presenting dea graphically, The International Journal Of Management Science, 36, 715–729.
  • Atilgan, Y. K., 2016, Robust Coplot Analysis, Communications in Statistics - Simulation and Computation, 45, 1763-1775.
  • Borg, I., Groenen, P. J. F., 2005, Modern Multidimensional Scaling, New York: Springer.
  • Charnes, A., Cooper, W., Rhodes, E., 1978, Measuring the efficiency of decision making units, European Journal of Operational Research, 2, 429–444.
  • Charnes, A., Cooper, W., Li, S., 1989, Using Data Envelopment Analysis to Evaluate Efficiency in the Economic Performance of Chinese Cities, Socio-Econ, Plan, Sci., 23(6), 323–344.
  • Cooper W., Seiford L., Kaore, T., 2007, Data Envelopment Analysis A Comprehensive Text with Models, Applications, References, and DEA – Solver Software, Springer Books, New York.
  • Forero, P. A., Giannakis, G. B., 2011, Robust multi-dimensional scaling via outlier sparsity control, In:45th Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA., 1183–1187.
  • Huang, H., Liao, W. A., 2012, Co-Plot- based efficiency measurement to commercial banks, Journal of Software, 7(10), 2247–2251.
  • Kruskal, J. B., 1964, Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis, Psychometrika, 29, 1-27. [10] Nath, P., Mukherjee, A., Pal, M., 2001, Identification of Linkage Between Strategic Group and Performance of Indian Commercial Banks: A Combined Approach using DEA and Co-Plot, The International Journal of Digital Accounting Research, 1(2), 125–152.
  • Shevlyakov, G., Smirnov, P., 2011, Robust estimation of the correlation coefficient: An attempt of survey, Austrian Journal of Statistics, 40, 147–156.
  • Simar L 2003, Detecting Outliers in Frontier Models: A Simple Approach. Journal of Productivity Analysis 20, 391 – 424.
  • Söylemez, A., 2015, Veri Zarflama Analizinin Robust Coplot Yöntemi İle Grafiksel Gösterimi, Yüksek Lisans Tezi, http://hdl.handle.net/11655/2098.
  • Wilson, P.W., 1993, Detecting outliers in deterministic nonparametric frontier models with multiple outputs. Journal of Business and Economic Statistics, 11 (3), 319-323.

Robust Coplot: A graphic approach to visualize results of data envelopment analysis

Year 2016, Volume: 9 Issue: 2, 66 - 78, 25.12.2016

Abstract

The purpose of this study is to show how to combine and use two methodologies, available in the multi criteria decision making and exploratory data analysis fields. In the literature Data envelopment analysis(DEA) efficient units and variables can be visualized in the two dimensional space with the help of Coplot map.However, outliers make results of these analyses unreliable. Besides, there is no study which indicates the combination of DEA and Robust Coplot that would produce reliable graphs in the presence of outlier(s). Here, examination and interpretations of DEA results with the help of robust coplot is explained, and why robust methods should be preferred will be highlighted. Obtained map helps to detect suspicious observations and potentially negligible variables in the data set. Every step of graphing is given by means of a well known illustration. This study serves for usefull purpose in studying the implementation of this novel robust coplot method by providing a brief description of that software package (RobCop).

References

  • Adler, N., Raveh, A., Yazhemsky, E., 2006, Presenting dea graphically, The International Journal Of Management Science, 36, 715–729.
  • Atilgan, Y. K., 2016, Robust Coplot Analysis, Communications in Statistics - Simulation and Computation, 45, 1763-1775.
  • Borg, I., Groenen, P. J. F., 2005, Modern Multidimensional Scaling, New York: Springer.
  • Charnes, A., Cooper, W., Rhodes, E., 1978, Measuring the efficiency of decision making units, European Journal of Operational Research, 2, 429–444.
  • Charnes, A., Cooper, W., Li, S., 1989, Using Data Envelopment Analysis to Evaluate Efficiency in the Economic Performance of Chinese Cities, Socio-Econ, Plan, Sci., 23(6), 323–344.
  • Cooper W., Seiford L., Kaore, T., 2007, Data Envelopment Analysis A Comprehensive Text with Models, Applications, References, and DEA – Solver Software, Springer Books, New York.
  • Forero, P. A., Giannakis, G. B., 2011, Robust multi-dimensional scaling via outlier sparsity control, In:45th Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA., 1183–1187.
  • Huang, H., Liao, W. A., 2012, Co-Plot- based efficiency measurement to commercial banks, Journal of Software, 7(10), 2247–2251.
  • Kruskal, J. B., 1964, Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis, Psychometrika, 29, 1-27. [10] Nath, P., Mukherjee, A., Pal, M., 2001, Identification of Linkage Between Strategic Group and Performance of Indian Commercial Banks: A Combined Approach using DEA and Co-Plot, The International Journal of Digital Accounting Research, 1(2), 125–152.
  • Shevlyakov, G., Smirnov, P., 2011, Robust estimation of the correlation coefficient: An attempt of survey, Austrian Journal of Statistics, 40, 147–156.
  • Simar L 2003, Detecting Outliers in Frontier Models: A Simple Approach. Journal of Productivity Analysis 20, 391 – 424.
  • Söylemez, A., 2015, Veri Zarflama Analizinin Robust Coplot Yöntemi İle Grafiksel Gösterimi, Yüksek Lisans Tezi, http://hdl.handle.net/11655/2098.
  • Wilson, P.W., 1993, Detecting outliers in deterministic nonparametric frontier models with multiple outputs. Journal of Business and Economic Statistics, 11 (3), 319-323.
There are 13 citations in total.

Details

Primary Language Turkish
Journal Section Articles
Authors

Yasemin Kayhan Atılgan

Arslan Söylemez This is me

Publication Date December 25, 2016
Published in Issue Year 2016 Volume: 9 Issue: 2

Cite

IEEE Y. K. Atılgan and A. Söylemez, “Robust Coplot: Veri zarflama analizi sonuçlarının grafiksel gösterimi için bir yaklaşım”, JSSA, vol. 9, no. 2, pp. 66–78, 2016.