A Bayesian approach for analyzing crop yield response data with limited treatments

Abstract This paper proposes a Bayesian multilevel modeling approach to incorporate response parameters from published studies into crop yield response estimation procedures when nonlimiting or limiting treatment levels are omitted or limited in agronomic experiments. Such circumstances may be encountered when data are from farmer‐led research, which may use nonstandardized experimental designs. The paper's focus is on maize yield response to nitrogen fertilizer, but the procedure is flexible enough to accommodate other factors that could affect crop yield response. A proof‐of‐concept Monte Carlo (MC) exercise supplements an empirical application. The MC simulation investigates the small sample properties of the proposed procedure. The empirical example uses field trial data for a maize planter experiment under different nitrogen (N) fertilizer rates. The planter trial compared mechanical planting methods to methods used in developing countries with limited access to mechanized planter technology. Some experiments had no check plots and all experiments lacked nonlimiting fertilizer rates. Linear and quadratic response functions with plateaus are used in the MC simulation and empirical application. MC results suggest that estimates were closest to true parameter values when priors for optimal N rates from published sources were used.

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