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

Abstract

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.

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

“…Cho et al. (2020) used a Bayesian procedure to estimate an LRP for maize response to nitrogen. That study used priors to delineate lower and upper bounds on response parameters, which imposed theoretical restrictions with respect to parameter signs.…”

“…Intercepts, optimal N fertilizer rates, and their respective standard errors were collected from 12 studies on maize yield response to N estimated with linear response with plateau (LRP) models (Alotaibi et al., 2018; Cho et al., 2020) (Table 2; Crozier et al., 2014; Gentry et al., 2013; Halvorson & Bartolo, 2014; Jaynes, 2011; Kablan et al., 2017; Miller et al., 2017; Rajkovich et al., 2015; Ruark et al., 2018; Schmidt et al., 2002; Shroyer et al., 2011). The average of the maize yield intercepts was 6.12 Mg ha −1 , with minimum and maximum values of 2.78 and 9.33 Mg ha −1 .…”

Crop yield response functions in nutrient application: A review

“…Cho et al. (2020) modeled maize yield response to nitrogen using the Bayesian LRP approach. The Bayesian prior information on treatment yield can consider issues arising from under‐replication and unbalanced experimental design.…”

“…Findings suggest experimental design should have nitrogen levels reduced in consecutive years as more evidence is obtained. Cho et al (2020) modeled maize yield response to nitrogen using the Bayesian LRP approach. The Bayesian prior information on treatment yield can consider issues arising from under-replication and unbalanced experimental design.…”

“…A few studies have used Bayesian methods to model crop yield response to nutrients with stochastic plateau functions (Brorsen et al., 2019; Cho et al., 2020; Ng'ombe, 2019; Ouédraogo & Brorsen, 2018). The Bayesian technique appears to have several advantages (Moeltner et al., 2021).…”