Bayesian semiparametric reproductive dispersion mixed models for non-normal longitudinal data: estimation and case influence analysis

ABSTRACT

Semiparametric reproductive dispersion mixed model (SPRDMM) is a natural extension of the reproductive dispersion model and the semiparametric mixed model. In this paper, we relax the normality assumption of random effects in SPRDMM and use a truncated and centred Dirichlet process prior to specify random effects, and present the Bayesian P-spline to approximate the smoothing unknown function. A hybrid algorithm combining the block Gibbs sampler and the Metropolis–Hastings algorithm is implemented to sample observations from the posterior distribution. Also, we develop Bayesian case deletion influence measure for SPRDMM based on the φ-divergence and present those computationally feasible formulas. Several simulation studies and a real example are presented to illustrate the proposed methodologies.

KEYWORDS:

• Bayesian case deletion diagnostics
• truncated and centred Dirichlet process
• Gibbs sampler
• Metropolis–Hastings algorithm
• Bayesian P-spline

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research was supported by grants from the National Natural Science Foundation of China [11501073], the Applied Basic Research Project of Yunnan Province [2014FD051] and the Scientific Research Foundation of Department of Education of Yunnan Province [2014Y447].