Abstract
Many linear and nonlinear mixed response models are proposed to predict the optimum dose of fertilizer. However, a major restriction of this class of models is the normality assumption of the random parameter component. The purpose of this paper is to analyze the performance of linear and nonlinear mixed models of fertilizer dosing with independent normally distributed random parameter components. We compare the Linear Plateau, Spillman-Mitscherlich, and Quadratic random parameter models with different random effects distribution assumption, i.e. the normal, Student-t, slash, and contaminated normal distributions and the random errors following their symmetric normal independent distributions. The method is applied to datasets of multi-location trials of potassium fertilization of soybeans. The results show that the Student-t Spillman-Mitscherlich Response Model is the best model for soybean yield prediction.
Highlights
Many linear and nonlinear response models are commonly used to predict the optimum dose of fertilizer
Linear plateau response models Based on the expected Akaike information criterion (EAIC) and the expected Bayesian information criterion (EBIC) in table 1, we find that among the Normal independent (NI) models the Student-t (t-t) Model gives the best fit, followed by the contaminated normal (CN-CN), slash (SL-SL), and normal (N-N) Model
Spillman-Mitscherlich response models Based on the EAIC and EBIC in table 2 we find the following rankings of the NI models: t-t < N-N < SL-SL < CN-CN
Summary
Many linear and nonlinear response models are commonly used to predict the optimum dose of fertilizer. One modeling approach is to fit a general quadratic form to the data by means of least squares under the assumption of a fixed effects model with independent normally distributed random error term with constant variances ([1]-[2]). This approach is unrealistic because it neglects the variability that probably exists between sites and/or years. [7] and [9] showed that the stochastic linear plateau model and the Mitscherlich exponential type functions outperform the quadratic form. In a similar vein, [8] showed that the stochastic linear plateau function is more adequate than the stochastic quadratic plateau function for corn response to Nitrogen fertilizer
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