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

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 <i>φ</i>-divergence and present those computationally feasible formulas. Several simulation studies and a real example are presented to illustrate the proposed methodologies.

半参数再生散度混合模型（Semiparametric Reproductive Dispersion Mixed Model，SPRDMM）是再生散度模型与半参数混合模型的自然延伸。本文放宽了SPRDMM中随机效应的正态性假设，采用截断中心化狄利克雷过程先验对随机效应进行设定，并引入贝叶斯P样条（Bayesian P-spline）近似拟合平滑未知函数。本文采用结合分块吉布斯采样器与大都会-黑斯廷斯（Metropolis–Hastings）算法的混合采样算法，从后验分布中抽取样本。此外，本文基于φ-散度（φ-divergence）构建了SPRDMM的贝叶斯案例删除影响度量，并给出了计算可行的相关公式。文末通过多项模拟研究与一则实际案例，对所提出的方法论进行了验证与说明。