A semiparametric Bayesian approach to simplex regression model with heterogeneous dispersion

ABSTRACT

Simplex regression model is often employed to analyze continuous proportion data in many studies. In this paper, we extend the assumption of a constant dispersion parameter (homogeneity) to varying dispersion parameter (heterogeneity) in Simplex regression model, and present the B-spline to approximate the smoothing unknown function within the Bayesian framework. A hybrid algorithm combining the block Gibbs sampler and the Metropolis-Hastings algorithm is presented for sampling observations from the posterior distribution. The procedures for computing model comparison criteria such as conditional predictive ordinate statistic, deviance information criterion, and averaged mean squared error are presented. Also, we develop a computationally feasible Bayesian case-deletion influence measure based on the Kullback-Leibler divergence. Several simulation studies and a real example are employed to illustrate the proposed methodologies.

KEYWORDS:

• Bayesian case-deletion diagnostics
• B-spline
• Continuous proportions
• Model comparison
• Simplex distribution
• Varying dispersion

MATHEMATICS SUBJECT CLASSIFICATION:

• 62F15
• 62G08

Additional information

Funding

The research was supported by grants from the National Natural Science Foundation of China (11501073, 11561074), the Applied Basic Research Project of Yunnan Province (2014FD051), the Scientific Research Foundation of Department of Education of Yunnan Province (2014Y447), the Science and Technology Foundation of Guizhou Province (LH[2014]7164) and the Natural Science Foundation of the Education Department of Guizhou Province (KY[2014]249).