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Stepwise regression data envelopment analysis for variable reduction. (English) Zbl 1338.62193

Summary: We develop stepwise regression data envelopment model to select important variables. We formulate null hypothesis to understand the importance of each variable and use Kruskal-Wallis test for this purpose. If the Kruskal-Wallis test does not reject the null hypothesis then we can conclude that all the variables are of equal importance as their presence and on the other hand absence of other variable does not create huge fluctuations in efficiency scores in fact give a complete ranking relative to base model. If the Kruskal-Wallis test does reject the null hypothesis this will imply there is significant fluctuation in the efficiency score relative to base model. And therefore we have to further check the pair of variables that causes the fluctuation in order to determine its importance using Conover-Inman test. The results of the proposed models are compared with the results of previously published models of the same dataset. The proposed models helps understand the extent of misclassification decision making units as efficient/inefficient when variables are retained or discarded alongside provides useful managerial prescription to make improvement strategies.

MSC:

62P20 Applications of statistics to economics
90C08 Special problems of linear programming (transportation, multi-index, data envelopment analysis, etc.)
Full Text: DOI

References:

[1] Chong, I.; Jun, C., Performance of some variable selection methods when multicollinearity is present, Chemom. Intell. Lab. Syst., 78, 103-112 (2005)
[2] Friedman, L.; Sinuany-Stern, Z., Combining ranking scales and selecting variables in the DEA context: the case of industrial branches, Comput. Oper. Res., 25, 781-791 (1998) · Zbl 1042.90574
[3] Sengupta, J., Tests of efficiency in data envelopment analysis, Comput. Oper. Res., 17, 2, 123-132 (1990) · Zbl 0681.62103
[4] Jenkins, L.; Anderson, M., A multivariate statistical approach to reducing the number of variables in data envelopment analysis, Eur. J. Oper. Res., 147, 51-61 (2003) · Zbl 1011.90528
[5] Charnes, A.; Cooper, W. W.; Rhodes, E., Measuring the efficiency of decision-making units, Eur. J. Oper. Res., 3 (1979), 339-339 · Zbl 0425.90086
[6] Wagner, J. M.; Shimshak, D., Stepwise selection of variables in data envelopment analysis: procedures and managerial perspectives, Eur. J. Oper. Res., 180, 57-67 (2007) · Zbl 1114.90040
[7] Zhu, J., Data envelopment analysis vs. principal components analysis: an illustrative study of economic performance of chinese cities, Eur. J. Oper. Res., 111, 50-61 (1998) · Zbl 0938.91018
[8] Ueda, T.; Hoshiai, Y., Application of principal component analysis for parsimonious summarization of DEA inputs and/or outputs, J. Oper. Res., 40, 4, 466-478 (1997) · Zbl 0905.90002
[9] Lewin, A. Y.; Morey, R. C.; Cook, T. J., Evaluating the administrative efficiency of courts, OMEGA, 10, 4, 401-411 (2001)
[10] Norman, M.; Stoker, B., Data Envelopment Analysis: The Assessment of Performance (1991), John Wiley and Sons: John Wiley and Sons Chichester, England
[11] Banker, R., Maximum likelihood, consistency and data envelopment analysis: a statistical foundation, Manage. Sci., 39, 10, 1265-1273 (1993) · Zbl 0798.90009
[12] Banker, R., Hypothesis tests using data envelopment analysis, J. Prod. Anal., 7 (1996), 1395-159
[13] Pastor, J. T.; Ruiz, J. L.; Sirvent, I., A statistical test for nested radial DEA models, Oper. Res., 50, 4, 728-735 (1991) · Zbl 1163.90563
[14] Lutjohann, H., The stepwise regression algorithm seen from the statician’s point of view, Metrika, 15, 1, 110-125 (1970) · Zbl 0207.49702
[15] Conover, W. J., Practical Nonparametric Statistics (1999), John Wiley
[16] Ragsdale, C. T., Spreadsheet Modeling and Decision Analysis (2004), South-Wester: South-Wester Mason
[17] Cooper, W.; Tone, K.; Seiford, L., Introduction to Data Envelopment Analysis and its Uses: with DEA-Solver Software and References (2006), Springer
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.