GRADIENT BOOSTING-BASED RESPONSE SURFACE METHODOLOGY WITH APPLICATION IN MODELLING POTATO POST-HARVEST LOSSES

Abstract

Modelling the complex nonlinear systems is one of the most challenging problems in statistics and the conventional response surface models are generally not sufficient in capturing the intricate nonlinear relationship and higher order interaction and advanced machine learning models are highly predictive but have generally not been developed to have statistical interpretability and optimization properties. Therefore, there is no single modelling tool that allows for accurate predictions, interpretable inferences and response optimization of nonlinear data. To overcome this methodological limitation, this study introduced a novel Gradient Boosting Based Response Surface Methodology (GB-RSM) framework, combining the optimization and interpretability properties of Response Surface Methodology (RSM) with the nonlinear learning ability of Gradient Boosting. Specifically, the study aimed at identifying important storage factors that affect potato post-harvest losses using Response Surface Methodology (RSM); Modeling the potato post-harvest losses by a Gradient Boosting model to model nonlinear relationship; Developing a hybrid Gradient Boosting-Response Surface Methodology (GB-RSM) model for better nonlinear modelling; and comparing the performance of the developed model with the standalone RSM and Gradient Boosting models. A mixed method research design was used that combined experimental simulation and a cross-sectional survey. A four factor rotatable Central Composite Design (CCD) experiment was simulated to develop and test the proposed modelling framework and fieldwork was conducted among 628 potato value-chain actors who were sampled using stratified sampling in Nakuru and Nyandarua Counties, which were purposively selected as they are among the major potato growing counties in Kenya and intensive production activities as well as a high number of post-harvest handling activities exists, providing an appropriate setting for the evaluation of the proposed methodology. Data preprocessing was done using K-Nearest Neighbor imputation and normalization. A second order response surface model was fitted to the residuals and a Gradient Boosting model trained on the residuals to create a hybrid GB-RSM model to capture nonlinear structures not accounted for by the polynomial approximation. Furthermore, a multilevel beta regression technique was used to find factors influencing proportional post-harvest losses and Principal Component Analysis (PCA) was used to build a Composite Loss Index (CLI) for integrated modelling. The GB-RSM model was the best among the three models in terms of predictive performance (RMSE = 0.0896 and 𝑅 2 = 0.993) and more model interpretable and optimized with response capability as compared to the other two models. Storage methods, storage duration, market distance, chemical use, transport method and extension training were identified as factors that significantly affect post-harvest losses, but formal education was not significant. The integrated modelling also confirmed that storage duration, potato variety, relative humidity and temperature were the most important factors influencing the Composite Loss Index, and that the curing time did not have a significant effect in the range of the experiment. The study demonstrates that the proposed GB-RSM framework can be a powerful and precise and interpretable method for modelling complex nonlinear systems, while utilizing the complementary strengths of classical statistical modelling and machine learning. The framework is suggested to be implemented for the modelling and optimization of problems with strong nonlinearity in a variety of application areas and to be extended to other machine learning algorithms, high￾dimensional data and adaptive experimental designs in the future.