Semiparametric Bayesian analysis of nonlinear reproductive dispersion mixed models for longitudinal data

In the development of nonlinear reproductive dispersion mixed models, it is commonly assumed that distribution of random effects is normal. The normality assumption is likely violated in many practical applications. In this paper, we assume that distribution of random effects is specified by a Dirichlet process prior for relaxing this limitation. A semiparametric Bayesian approach combining the stick-breaking prior and the blocked Gibbs sampler as well as the Metropolis-Hastings algorithm is developed for simulating observations from the posterior distributions and producing the joint Bayesian estimates of unknown parameters and random effects. Two goodness-of-fit statistics are presented to assess the plausibility of the posited model, and the procedures for computing the Bayes factor, pseudo-Bayes factor and deviance information criterion for model comparison are given. Also, we propose two Bayesian case deletion influence measures including the ϕ-divergence and Cook's posterior mean distance. Four simulation studies and a real example are presented to illustrate the newly developed Bayesian methodologies.