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On‐farm precision experimentation (OFPE) is increasingly conducted using variable‐rate technology and precision agriculture (PA) equipment to measure the effect of changes in input application rates on yields and profits at specific fields. Classical linear regression models and new Bayesian and machine learning regressions for spatial data can be used to investigate site‐specific crop response from georeferenced data. The objective of this work was to compare statistical models that can be used by researchers analyzing OFPE data to estimate crop response and better describe its spatial within‐field variability. Three statistical models estimating the responses to N rates, seed rates, and site‐specific soil properties from eight OFPEs were compared: (a) linear regression (LR) for spatially correlated errors, (b) Bayesian regression (BR) with random site effects, and (c) random forest regression (RF) with kriged residuals. Models were adjusted to account for spatial variation in yield response, and with and without field characteristic covariates. Modeling spatial correlation and including plot covariates improved yield predictions. Differences among methods proved to be indistinguishable with respect to average explained variance, correlation between predicted and observed values, and mean square prediction errors (PEs). However, BR and RF outperformed LR in site‐specific prediction accuracy, with BR predictions having lower predictive uncertainty than RF predictions. The hierarchical Bayesian model for spatial data is a useful tool to process OFPE data, allowing direct derivation of linear coefficients and prediction uncertainty measures related to site‐specific yield responses. Core Ideas: On‐farm research encourages farmers' interest in adopting precision agriculture.Statistical models to estimate site‐specific crop response are compared.Spatial Bayesian models performed well in delivering site‐specific yield responses.Benefits and pitfalls of statistical analysis of variable‐rate trials are discussed. [ABSTRACT FROM AUTHOR]

Within-field variability of crop yield levels has been extensively investigated, but the spatial variability of crop yield responses to agronomic treatments is less understood. On-farm precision experimentation (OFPE) can be a valuable tool for the estimation of in-field variation of optimal input rates and thus improve agronomic decisions. Therefore, the objectives of this study were to investigate the spatial variability of optimal input rates in OFPE and the potential economic benefit of site-specific input management. Mixed geographically weighted regression (GWR) models were used to estimate local yield response functions. The methodology was applied to investigate the spatial variability in corn response to nitrogen and seed rates in four cornfields in Illinois, USA. The results showed that spatial heterogeneity of model parameters was significant in all four fields evaluated. On average, the RMSE of the fitted yield decreased from 1.2 Mg ha−1 in the non-spatial global model to 0.7 Mg ha−1 in the GWR model, and the r-squared increased from 10 to 68%. The average potential gain of using optimized uniform rates of seed and nitrogen was US$ 65.00 ha−1, while the added potential gain of the site-specific application was US$ 58.00 ha−1. The combination of OFPE and GWR proved to be an effective tool for testing precision agriculture's central hypothesis of whether optimal input application rates display adequate spatial variability to justify the costs of the variable rate technology itself. The reported results encourage more research on response-based input management recommendations instead of the still widespread focus on yield-based algorithms. [ABSTRACT FROM AUTHOR]