Bayesian Estimation and Economic Analysis of Under-Replicated Field Trials With a Linear Response Plateau Function

The linear response with plateau (LRP) is widely used in agronomic and agricultural economic studies of crop yield response. This empirical example uses data from an under-replicated experiment to compare maize (Zea maize L.) yield response to nitrogen under different plant and corridor row spacing. Not all replications received a 0-nitrogen rate, making estimation of the LRP difficult because data for the intercept terms is absent. We leverage information from other treatments using Bayesian methods to estimate the yield response of each treatment using a LRP function, given limited replication and absence of check plots for some treatments. We use a linearized LRP, which bypasses using the “min” operator typically required to estimate LRP functions. Economically optimal nitrogen rates were determined and net returns from treatments compared from the perspective of risk-averse producers. The wide plant/narrow row treatment was most profitable when the decision rule was to apply nitrogen. The statistical procedure used here may be useful for exploratory analyses of pilot agronomic trials that may include unbalanced and under-replicated treatments.