Bayesian Estimation of Mixed Effects Models of Fertilizer Response with Independent Skew-Normally Distributed Random Parameter

Abstract

The mixed effects model has been used for modelling the fertilizer response to predict the optimum doses.
However, a major restriction of this type of models is the normality assumption of the random parameter component.
The purpose of this paper is to investigate the performance of random parameter models of fertilizer dosing with
independent skew-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, Skew-normal, Skew-t, Skew-slash, and Skew-contaminated distributions and the random errors following
symmetric normal independent distributions. The method is applied to datasets of multi-location trials of potassium
fertilization of soybeans. The results show respectively that the Skew-t Model is the best Linear Plateau Response
Model, the Normal Model for Spillman-Mitscherlich Response Model, and the Skew-t Model for the Quadratic
Response Model. However, overall the normal Spillman-Mitscherlich Response Model is the best model for soybean
yield prediction.
Keywords: Bayesian estimation, Dose-response model, Random parameter model, Skew-normal independent
distributions.