Regional Optimization of Fertilization Using a Hierarchical Linear Model

Abstract

Utilization of regional data for optimizing fertilizer strategy is considered. It is argued that a hierarchical mixed effects model is a reasonable, parsimonious way to model the data. Such models take into account the correlations between yield responses at the same site. Also, they conveniently let one model the differences between years, or between sites, as a function of year and site characteristics. We specifically develop the case of a linear (in the parameters) response model, but hierarchical models could also be based on nonlinear response functions. Given the estimated parameters, the calculation of an optimal fertilizer strategy (which depends on the site and year characteristics) is usually straightforward. A number of measures of the quality of this strategy are proposed. Among these are the risk, which measures yield loss caused by using estimated rather than true parameter values. Another measure of interest is the potential gain from having a model that explains all the between year, or all the between site variability. The effect of potassium on sown prairies in France is treated as an example.