Bayesian Estimation of Random Parameter Models of Responses with Normal and Skew-t Distibutions Evidence from Monte Carlo Simulation

Mohammad Masjkur; Henk Folmer

doi:10.22342/jims.24.1.516.27-50

Mohammad Masjkur ⁽¹⁾ , Henk Folmer ⁽²⁾

(1) Bogor Agricultural University, Indonesia,

(2) University of Groningen, Netherlands

https://doi.org/10.22342/jims.24.1.516.27-50

Issue
Volume 24 Number 1 (April 2018)

Submitted
May 19, 2017

Accepted
September 4, 2017

Published
January 21, 2018

Keywords:

Dose-response model, Bayesian estimation, Gibbs sampler, Random parameter model, Skew-normal distribution, Skew-t distribution.

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Abstract

Random parameter models have been found to outperform xed pa-rameter models to estimate dose-response relationships with independent errors. Amajor restriction, however, is that the responses are assumed to be normally andsymmetrically distributed. The purpose of this paper is to analyze Bayesian infer-ence of random parameter response models in the case of independent responseswith normal and skewed, heavy-tailed distributions by way of Monte Carlo simu-lation. Three types of Bayesian estimators are considered: one applying a normal,symmetrical prior distribution, a second applying a Skew-normal prior and, a thirdapplying a Skew-t-distribution. We use the relative bias (RelBias) and Root MeanSquared Error (RMSE) as valuation criteria. We consider the commonly applied lin-ear Quadratic and the nonlinear Spillman-Mitscherlich dose-response models. Onesimulation examines the performance of the estimators in the case of independent,normally and symmetrically distributed responses; the other in the case of indepen-dent responses following a heavy-tailed, Skew-t-distribution. The main nding isthat the estimator based on the Skew-t prior outperforms the alternative estima-tors applying the normal and Skew-normal prior for skewed, heavy-tailed data. Fornormal data, the Skew-t prior performs approximately equally well as the Skew-normal and the normal prior. Furthermore, it is more ecient than its alternatives.Overall, the Skew-t prior seems to be preferable to the normal and Skew-normal fordose-response modeling.

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Authors

Mohammad Masjkur

Bogor Agricultural University

masjkur@gmail.com (Primary Contact)

Henk Folmer

University of Groningen

Author Biographies

Mohammad Masjkur, Bogor Agricultural University

Department of Statistics, Faculty of Mathematics and Natural Sciences

Henk Folmer, University of Groningen

Faculty of Spatial Sciences

Masjkur, M., & Folmer, H. (2018). Bayesian Estimation of Random Parameter Models of Responses with Normal and Skew-t Distibutions Evidence from Monte Carlo Simulation. Journal of the Indonesian Mathematical Society, 24(1), 27–50. https://doi.org/10.22342/jims.24.1.516.27-50