Methodology for calculating critical values of relevance measures in variable selection methods in data envelopment analysis

The selection of input and output variables is a key step in evaluating the relative efficiency of decision- making units (DMUs) in data envelopment analysis (DEA). In this paper, we present a methodology based on Monte Carlo simulations and bootstrapping for calculating the critical values of relev...

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Autores:: Villanueva-Cantillo, Jeyms
Munoz-Marquez, Manuel

Tipo de recurso:

Fecha de publicación:: 2021

Institución:: Universidad Simón Bolívar

Repositorio:: Repositorio Digital USB

Idioma:: eng

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dc.title.eng.fl_str_mv	Methodology for calculating critical values of relevance measures in variable selection methods in data envelopment analysis
title	Methodology for calculating critical values of relevance measures in variable selection methods in data envelopment analysis
spellingShingle	Methodology for calculating critical values of relevance measures in variable selection methods in data envelopment analysis Data envelopment analysis Variable selection Critical values Monte Carlo simulations
title_short	Methodology for calculating critical values of relevance measures in variable selection methods in data envelopment analysis
title_full	Methodology for calculating critical values of relevance measures in variable selection methods in data envelopment analysis
title_fullStr	Methodology for calculating critical values of relevance measures in variable selection methods in data envelopment analysis
title_full_unstemmed	Methodology for calculating critical values of relevance measures in variable selection methods in data envelopment analysis
title_sort	Methodology for calculating critical values of relevance measures in variable selection methods in data envelopment analysis
dc.creator.fl_str_mv	Villanueva-Cantillo, Jeyms Munoz-Marquez, Manuel
dc.contributor.author.none.fl_str_mv	Villanueva-Cantillo, Jeyms Munoz-Marquez, Manuel
dc.subject.eng.fl_str_mv	Data envelopment analysis Variable selection Critical values Monte Carlo simulations
topic	Data envelopment analysis Variable selection Critical values Monte Carlo simulations
description	The selection of input and output variables is a key step in evaluating the relative efficiency of decision- making units (DMUs) in data envelopment analysis (DEA). In this paper, we present a methodology based on Monte Carlo simulations and bootstrapping for calculating the critical values of relevance measures in variable selection methods in DEA. Additionally, we define a set of metrics to study the methods’ performance when using such critical values. We conducted an extensive simulation study, applying the proposed methodology to two variable selection methods in 28 single-output model specifications (i.e., different number of inputs and DMUs in the DEA model) under multiple scenarios, varying factors related to the functional form of the production function, the probability of an input being relevant in the model, the probability distribution of the inputs, and the theoretical efficiencies of the DMUs. The simulation study shows that (i) our proposed methodology yields consistent results for the two methods studied, in terms of the generated critical values and the performance metrics, and (ii) for most model specifications, the critical values can be estimated with a linear model with a high adjusted R 2 , using factors related to the input probability distribution and the probability of an input being relevant as independent variables. Furthermore, we describe and compare the performance of the two methods studied, provide guidelines for using our methodology and the results presented in this paper, and propose suggestions for future research.
publishDate	2021
dc.date.accessioned.none.fl_str_mv	2021-07-22T17:01:41Z
dc.date.available.none.fl_str_mv	2021-07-22T17:01:41Z
dc.date.issued.none.fl_str_mv	2021
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dc.type.spa.spa.fl_str_mv	Artículo científico
dc.identifier.issn.none.fl_str_mv	03772217
dc.identifier.uri.none.fl_str_mv	https://hdl.handle.net/20.500.12442/8028
dc.identifier.doi.none.fl_str_mv	https://doi.org/10.1016/j.ejor.2020.08.021
dc.identifier.url.none.fl_str_mv	https://www.sciencedirect.com/science/article/pii/S0377221720307293
identifier_str_mv	03772217
url	https://hdl.handle.net/20.500.12442/8028 https://doi.org/10.1016/j.ejor.2020.08.021 https://www.sciencedirect.com/science/article/pii/S0377221720307293
dc.language.iso.eng.fl_str_mv	eng
language	eng
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dc.format.mimetype.spa.fl_str_mv	pdf
dc.publisher.spa.fl_str_mv	Elsevier
dc.source.eng.fl_str_mv	European Journal of Operational Research (EJOR) Vol. 290, Issue 2 (2021)
institution	Universidad Simón Bolívar
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spelling	Villanueva-Cantillo, Jeymscc24ee3e-2338-481d-a97e-f01eba6c5173Munoz-Marquez, Manuelba8b0a04-9bc6-4c96-bc5d-df83de1be1022021-07-22T17:01:41Z2021-07-22T17:01:41Z202103772217https://hdl.handle.net/20.500.12442/8028https://doi.org/10.1016/j.ejor.2020.08.021https://www.sciencedirect.com/science/article/pii/S0377221720307293The selection of input and output variables is a key step in evaluating the relative efficiency of decision- making units (DMUs) in data envelopment analysis (DEA). In this paper, we present a methodology based on Monte Carlo simulations and bootstrapping for calculating the critical values of relevance measures in variable selection methods in DEA. Additionally, we define a set of metrics to study the methods’ performance when using such critical values. We conducted an extensive simulation study, applying the proposed methodology to two variable selection methods in 28 single-output model specifications (i.e., different number of inputs and DMUs in the DEA model) under multiple scenarios, varying factors related to the functional form of the production function, the probability of an input being relevant in the model, the probability distribution of the inputs, and the theoretical efficiencies of the DMUs. The simulation study shows that (i) our proposed methodology yields consistent results for the two methods studied, in terms of the generated critical values and the performance metrics, and (ii) for most model specifications, the critical values can be estimated with a linear model with a high adjusted R 2 , using factors related to the input probability distribution and the probability of an input being relevant as independent variables. Furthermore, we describe and compare the performance of the two methods studied, provide guidelines for using our methodology and the results presented in this paper, and propose suggestions for future research.pdfengElsevierAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2European Journal of Operational Research (EJOR)Vol. 290, Issue 2 (2021)Data envelopment analysisVariable selectionCritical valuesMonte Carlo simulationsMethodology for calculating critical values of relevance measures in variable selection methods in data envelopment analysisinfo:eu-repo/semantics/articleArtículo científicohttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_2df8fbb1Adler, N., & Golany, B. (2001). Evaluation of deregulated airline networks using data envelopment analysis combined with principal component analysis with an ap- plication to western europe. European Journal of Operational Research, 132 (2), 18–31. https://doi.org/10.1016/S0377-2217(0 0)0 0150-8 .Adler, N., & Golany, B. (2002). Including principal component weights to improve discrimination in data envelopment analysis. Journal of the Operational Research Society, 53 (9), 985–991. https://doi.org/10.1057/palgrave.jors.2601400 .Adler, N., & Yazhemsky, E. (2010). Improving discrimination in data envelopment analysis: PCA-DEA or variable reduction. European Journal of Operational Re- search, 202 (1), 273–284. https://doi.org/10.1016/j.ejor.2009.03.050 .Amirteimoori, A., Despotis, D., & Kordrostami, S. (2012). Variable reduction in data envelopment analysis. Optimization, 63 (5), 735–745. https://doi.org/10. 1080/02331934.2012.684354Banker, R. D. (1996). Hypothesis tests using data envelopment analysis. The Journal of Productivity Analysis, 7 (2/3), 139–159. https://doi.org/10.10 07/BF0 0157038 .Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European Journal of Operational Research, 2 (6), 429–4 4 4. https:// doi.org/10.1016/0377-2217(78)90138-8 .Daraio, C. , & Simar, L. (2007). Advanced robust and nonparametric methods in effi- ciency analysis: methodology and applications (1st). Springer Science + Business Media .Dyson, R. G., Allen, R., Camanho, A. S., Podinovski, V. V., Sarrico, C. S., & Shale, E. A. (2001). Pitfalls and protocols in DEA. European Journal of Operational Research, 132 , 245–259. https://doi.org/10.1016/S0377-2217(0 0)0 0149-1 .Eskelinen, J. (2017). Comparison of variable selection techniques for data envelop- ment analysis in a retail bank. European Journal of Operational Research, 259 (2), 778–788. https://doi.org/10.1016/j.ejor.2016.11.009 .Fanchon, P. (2003). Variable selection for dynamic measures of efficiency in the computer industry. International Advances in Economic Research, 9 (3), 175–188. https://doi.org/10.1007/BF02295441 .Fernandez-Palacin, F., Lopez-Sanchez, M. A., & Munoz-Marquez, M. (2017). Step- wise selection of variables in DEA using contribution loads. Pesquisa Operacional, 38 (1), 31–52. https://doi.org/10.1590/0101-7438.2018.038.01.0031 .Holland, D., & Lee, S. (2002). Impacts of random noise and specification on es- timates of capacity derived from data envelopment analysis. European Journal of Operational Research, 137 (1), 10–21. https://doi.org/10.1016/S0377-2217(01) 0 0 087-X .Jenkins, L., & Anderson, M. (2003). A multivariate statistical approach to reducing the number of variables in data envelopment analysis. European Journal of Oper- ational Research, 147 (1), 51–61. https://doi.org/10.1016/S0377- 2217(02)00243- 6 .Jitthavech, J. (2016). Variable elimination in nested DEA models: a statistical ap- proach. 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Industrial & Engi- neering Chemistry Research, 57 (30), 9866–9878. https://doi.org/10.1021/acs.iecr. 7b05284 .Lin, T.-Y., & Chiu, S. H. (2013). Using independent component analysis and network DEA to improve bank performance evaluation. Economic Modelling, 32 (1), 608–616. https://doi.org/10.1016/j.econmod.2013.03.003 .Liu, J. S., Lu, L. Y., & Lu, W. M. (2016). Research fronts in data envelopment analysis. Omega, 58 , 33–45. https://doi.org/10.1016/j.omega.2015.04.004 .Madhanagopal, R., & Chandrasekaran, R. (2014). Selecting appropriate variables for dea using genetic algorithm (ga) search procedure. International Journal of Data Envelopment Analysis and ∗Operations Research ∗, 1 (2), 28–33. https://doi.org/10. 12691/ijdeaor- 1- 2- 3 .Morita, H., & Avkiran, N. K. (2009). Selecting inputs and outputs in data envelop- ment analysis by designing statistical experiments. Journal of the Operations Re- search Society of Japan, 52 (2), 163–173. https://doi.org/10.15807/jorsj.52.163 .Nataraja, N. R., & Johnson, A. L. (2011). Guidelines for using variable selection tech- niques in data envelopment analysis. European Journal of Operational Research, 215 (3), 662–669. https://doi.org/10.1016/j.ejor.2011.06.045 .Pastor, J. T., Ruiz, J. L., & Sirvent, I. (2002). A statistical test for nested radial DEA models. Inmaculada Operations Research, 50 (4), 728–735. https://doi.org/10.1287/ opre.50.4.728.2866 .Perelman, S., & Santín, D. (2009). How to generate regularly behaved production data? a monte carlo experimentation on DEA scale efficiency measurement. Eu- ropean Journal of Operational Research, 199 (1), 303–310. https://doi.org/10.1016/j. ejor.2008.11.013 .R Core Team (2017). R: A language and environment for statistical computing, Vienna, Austria . https://www.R-project.org/Ruggiero, J. (2005). Impact assessment of input omission on DEA. 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Journal of the Operations Research Society of Japan, 40 (4), 466–478. https://doi.org/10.15807/jorsj.40.466 .Wagner, J. M., & Shimshak, D. G. (2007). Stepwise selection of variables in data en- velopment analysis: Procedures and managerial perspectives. 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Methodology for calculating critical values of relevance measures in variable selection methods in data envelopment analysis

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