## Abstract

Random parameter models have been found to outperform fixed parameter models to estimate dose-response relationships with independent errors. A major restriction, however, is that the responses are assumed to be normally and symmetrically distributed. The purpose of this paper is to analyze Bayesian inference of random parameter response models in the case of independent responses with normal and skewed, heavy-tailed distributions by way of Monte Carlo simulation. Three types of Bayesian estimators are considered: one applying a normal, symmetrical prior distribution, a second applying a Skew-normal prior and, a third applying a Skew-t-distribution. We use the relative bias (RelBias) and Root Mean Squared Error (RMSE) as valuation criteria. We consider the commonly applied linear Quadratic and the nonlinear Spillman-Mitscherlich dose-response models. One simulation examines the performance of the estimators in the case of independent, normally and symmetrically distributed responses; the other in the case of independent responses following a heavy-tailed, Skew-t-distribution. The main finding is that the estimator based on the Skew-t prior outperforms the alternative estimators applying the normal and Skew-normal prior for skewed, heavy-tailed data. For normal data, the Skew-t prior performs approximately equally well as the Skew-normal and the normal prior. Furthermore, it is more efficient than its alternatives. Overall, the Skew-t prior seems to be preferable to the normal and Skew-normal for dose-response modeling.

Original language | English |
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Pages (from-to) | 27-50 |

Number of pages | 24 |

Journal | Journal of the Indonesian Mathematical Society |

Volume | 24 |

Issue number | 1 |

Publication status | Published - Apr-2018 |

## Keywords

- Dose-response model
- Bayesian estimation
- Gibbs sampler
- Random parameter model
- Skew-normal distribution
- Skew-t distribution
- LINEAR MIXED MODELS
- FERTILIZER
- INFERENCE
- NITROGEN