Statistical Methods for Predicting Responses to Applied Nitrogen and Calculating Optimal Nitrogen Rates

Abstract

Models of response to applied N can be useful for deriving improved N dose recommendations. Here we show how response model parameters can be estimated and how model predictions and model N dose recommendations can be evaluated. For parameter estimation, we use a statistical approach based on random parameter models. Two methods for evaluating models are applied. The first method is to calculate mean squared error of prediction (MSEP) by cross validation, and the second is to perform nonparametric regressions to evaluate the profitability of calculated optimal N rates. The proposed methods are used with a data set consisting of 37 winter wheat (Triticum aestivum L.) experiments. Different functions taking into account end‐of‐winter mineral soil N are evaluated. The results show that the different functions all have similar MSEP values for predictions of yield and grain protein content and lead to N recommendations of similar profitability. However, there are substantial differences in MSEP for residual mineral N at harvest. One of these models is then compared with a model that does not include any site‐year characteristic and with a model that does not have random parameters. We find that using the model without a site‐year characteristic leads to predictions that are less accurate and optimal N rates that are less profitable by F 17 to F 105 ha−1. Another result is that the gross margin obtained with the optimal N rates calculated using the model without random parameters is lower by F 438 to F 550 ha−1.