Quadratic-plateau geographically weighted regression model for estimating site-specific economically optimal input rates

• QP-GWR model addresses limitations of traditional GWR yield-input models. • Simulations demonstrate QP-GWR’s enhanced statistical and economic performance. • Model rankings show a gap between statistical accuracy and economic viability. • Dual metric evaluation is crucial for agricultural decision-making tools. • User-friendly QP-GWR Python implementation promotes on-farm precision strategies. In precision agriculture, site-specific input management is crucial for optimizing input rates according to unique field conditions allowing farmers to maximize their profits. However, traditional yield-input models like Geographically Weighted Regression (GWR) are hindered by the yield response functions misspecification problem, leading to biased input recommendations. This study develops a Quadratic-Plateau Geographically Weighted Regression (QP-GWR) model to estimate site-specific economically optimal input rates (EOIR), overcoming limitations in existing GWR models by adequately handling quadratic-plateau yield responses. Focused on corn nitrogen management, the study validates QP-GWR’s effectiveness through extensive simulations and on-farm trials, demonstrating its superior statistical and economic performance. Notably, compared to existing GWR models, QP-GWR achieves smaller bias and Root Mean Square Error (RMSE) in EOIR estimation, and enhances profits by $0.60 to $13.90 per ha, underscoring the critical role of this novel QP-GWR in modeling crop yield responses to management inputs. Additionally, the observed discrepancies between statistical and economic metrics underline the importance of evaluating both aspects in agricultural decision-making. Overall, these findings demonstrate our developed QP-GWR’s capability to enhance on-farm precision experimentation recommendations, particularly when dealing with plateauing yield responses. The user-friendly Python implementation of QP-GWR is available at: https://github.com/rssiuiuc/QP-GWR to facilitate broader adoption and application in precision agriculture.