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

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.

Monthly Pork Price Prediction Applying Projection Pursuit Regression: Modeling, Empirical Research, Comparison, and Sustainability Implications

“…Research has shown that it has the same nonlinear approximation ability as BPNN. Still, it is especially suitable for small and medium sample data modeling that does not obey the ordinary distribution law [20][21][22][41][42][43][44][45][46]. Due to PPR, the model of independent variable weight sum is equal to 1 for multiple independent variables with collaborative constraints.…”

“…The above monthly pork price normalization data and the current monthly price data of pork lagging 1-12 periods are imported into the PPA-based PPAR program compiled by Lou [20][21][22] and Mohamed et al [47]. In the PPAR program, the PPAR model based on the first linear PRF is established, and the actual global optimal solution is obtained.…”

“…The sample data of three predictors were imported into the PPA-based PPAR program compiled by Lou [20][21][22] to obtain the real global optimal solutions. The 1-1-PPAR model comprises two linear PRFs, and the 2-2-PPAR model comprises two quadratic PRFs.…”

“…According to Section 3.2, the normalized and monthly pork price data of the 12 independent variables above were imported into the PPA-based H-PPR program compiled by Lou [20][21][22]. First, the H-PPR model based on the linear ridge function was established, and the actual global optimal solution was obtained.…”

“…On the other hand, the research shows that the projection pursuit regression models have a good generalization ability and outperform SVR/SVM, BPNN, RF, etc., in suitability, applicability, and reliability [20][21][22] for small samples as well as large samples. The primary purpose of this article is split into four aspects.…”