Bayesian random parameter models of fertilizer dosing with independent skew-normally distributed random components

Random parameter models have been found to better predict the optimum dose of fertilization than fixed parameter models. However, a major restriction of this class of models is that the random parameter components are normally distributed. This paper introduces random parameter models of fertilizer dosing with independent skew-normally distributed random components using Bayesian
estimation. We compare the Linear Plateau, Spillman-Mitscherlich, and Quadratic random parameter models with random parameter components with different distributions, i.e. the Skew-normal, Skew-t, Skew-slash, and Skew-contaminated normal distributions and also their counterparts, i.e., the normal, Student-t, slash and the contaminated normal distributions,with the errors following symmetric normal independent distributions. The method is applied to a dataset 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.