Bagging as a model averaging technique for estimating optimum nitrogen rates in agricultural crops

Abstract

For several (non-legume) crops, the addition of nitrogen (N) via fertilization is key to maximizing grain yield and farmers’ profit. The N rate balancing crop production and farmers' incomes is called the Economic Optimum N Rate (EONR). The process of finding the EONR is model-based, yielding different estimations depending on the data and the selected model. Therefore, in some cases, model averaging can be an appropriate tool to improve the accuracy (bias) and precision (variance) of the EONR estimation. In this study we propose for the first time the use of bagging, a simple machine learning algorithm, as a model averaging technique. The objectives of this study were to (i) evaluate the ability of bagging in estimating the EONR for different experimental designs (data quality) using simulated data, and (ii) apply this technique using data collected in a field experiment. In the simulation studies, we found that (beyond the model representing the true data generating process) bagging was able to reduce both bias and variance of the EONR estimation in comparison to individual models. This was more notorious as the number of observations and N rates increased (i.e. good data quality). For the real data example, bagging point estimation of the EONR was in between of the estimation of the individual models. Furthermore, beginning provided the wider confidence intervals of the EONR. Our framework for bagging grain yield response to N fertilization models provides researchers with a simple method to the estimation of the EONR (or other derived quantities), by considering a set of suitable candidate models.