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An Exploration of Prediction Performance Based on Projection Pursuit Regression in Conjunction with Data Envelopment Analysis: A Comparison with Artificial Neural Networks and Support Vector Regression

Author

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  • Xiaohong Yu

    (College of Humanities and Law, Shanghai Business School, Shanghai 200235, China
    College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China)

  • Wengao Lou

    (School of Information Management, Shanghai Lixin University of Accounting and Finance, Shanghai 201209, China)

Abstract

Data envelopment analysis (DEA) is a leading approach in performance analysis and discovering newer benchmarks, and the traditional DEA models cannot forecast the future efficiency of decision-making units (DMUs). Machine learning, such as the artificial neural networks (ANNs), support vector machine/regression (SVM/SVR), projection pursuit regression (PPR), etc., have been viewed as beneficial for managers in predicting system behaviors. PPR is especially suitable for small and non-normal distribution samples, the usual cases in DEA analysis. This paper integrates DEA and PPR to cover the shortcomings we faced while using DEA and DEA-BPNN, DEA-SVR, etc. This study explores the advantages of combining these complementary methods into an integrated performance measurement and prediction model. Firstly, the DEA approach is used to evaluate and rank the efficiency of DMUs. Secondly, we establish two DEA-PPR combined models to describe the DEA efficiency scores (also called the production function) and the DEA-efficient frontier function. The first combined model’s input variables are input–output indicators in the DEA model, and the output variable is the DEA efficiency. In the second model, its input variables are input or output indicators in the DEA model, and the output variable is the optimal input indicator for input-oriented DEA or the output indicator for output-oriented DEA. We conducted positive research on two examples with actual data and virtual small, medium-sized, and large samples. Compared with the DEA-BPNN and DEA-SVR models, the results show that the DEA-PPR combined model has more vital global optimization ability, better convergence, higher accuracy, and a simple topology. The DEA-PPR model can obtain robust results for both small and large cases. The DEA-BPNN and DEA-SVR models cannot obtain robust results for small and medium-sized samples due to overfitting. For large samples, the DEA-PPR model outperforms DEA-BPNN, DEA-SVR, etc. The DEA-PPR combined model possesses better suitability, applicability, and reliability than the DEA-BPNN model, the DEA-SVR model, etc.

Suggested Citation

  • Xiaohong Yu & Wengao Lou, 2023. "An Exploration of Prediction Performance Based on Projection Pursuit Regression in Conjunction with Data Envelopment Analysis: A Comparison with Artificial Neural Networks and Support Vector Regressio," Mathematics, MDPI, vol. 11(23), pages 1-29, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:23:p:4775-:d:1288140
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    References listed on IDEAS

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    1. Reza Sanei & Farhad Hosseinzadeh lotfi & Mohammad Fallah & Farzad Movahedi Sobhani, 2022. "An Estimation of an Acceptable Efficiency Frontier Having an Optimum Resource Management Approach, with a Combination of the DEA-ANN-GA Technique (A Case Study of Branches of an Insurance Company)," Mathematics, MDPI, vol. 10(23), pages 1-21, November.
    2. Kwon, He-Boong, 2017. "Exploring the predictive potential of artificial neural networks in conjunction with DEA in railroad performance modeling," International Journal of Production Economics, Elsevier, vol. 183(PA), pages 159-170.
    3. Abdel Latef M. Anouze & Imad Bou-Hamad, 2019. "Data envelopment analysis and data mining to efficiency estimation and evaluation," International Journal of Islamic and Middle Eastern Finance and Management, Emerald Group Publishing Limited, vol. 12(2), pages 169-190, April.
    4. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
    5. E G Gomes & M P E Lins, 2008. "Modelling undesirable outputs with zero sum gains data envelopment analysis models," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(5), pages 616-623, May.
    6. Gecheng Chen & Rui Tuo, 2023. "Projection pursuit Gaussian process regression," IISE Transactions, Taylor & Francis Journals, vol. 55(9), pages 901-911, September.
    7. Zhang, Guoqiang & Eddy Patuwo, B. & Y. Hu, Michael, 1998. "Forecasting with artificial neural networks:: The state of the art," International Journal of Forecasting, Elsevier, vol. 14(1), pages 35-62, March.
    8. R. D. Banker & A. Charnes & W. W. Cooper, 1984. "Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis," Management Science, INFORMS, vol. 30(9), pages 1078-1092, September.
    9. Reza Yazdanparast & Reza Tavakkoli-Moghaddam & Razieh Heidari & Leyla Aliabadi, 2021. "A hybrid Z-number data envelopment analysis and neural network for assessment of supply chain resilience: a case study," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 29(2), pages 611-631, June.
    10. Carlos Pestana Barros & Peter Wanke, 2014. "Insurance companies in Mozambique: a two-stage DEA and neural networks on efficiency and capacity slacks," Applied Economics, Taylor & Francis Journals, vol. 46(29), pages 3591-3600, October.
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