Statistical models of yield in on-farm precision experimentation

Abstract

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.