Using SAEM to estimate parameters of models of response to applied fertilizer

Many nonlinear functions have been used to predict crop yield response to applied fertilizer. Accurate estimates of the parameter values are required for the formulation of satisfactory fertilizer dose recommendations. In fertilizer trials, several yield measurements for different fertilizer doses are usually made at the same site and in the same year. Model errors are therefore unlikely to be independent for the same site-year. Nonlinear mixed effects models can be used for yield response data. We evaluated the performance of a recently proposed stochastic approximation of the EM algorithm (SAEM) for estimating the parameters of nonlinear mixed effects models. We used the SAEM method to estimate the parameters of four different nonlinear models, using a real dataset including 37 site-years of yield measurements.. We then carried out simulations, to determine the bias and the root mean squared errors of the estimators. We compared the results obtained with SAEM with those obtained using a first-order conditional method. SAEM gave better results in most cases. The estimates produced by SAEM were less biased and less affected by initial values.