Bayesian Analysis of Tweedie Compound Poisson Partial Linear Mixed Models for Longitudinal Semicontinuous Data
Under the Bayesian framework,this paper develops a Tweedie compoundPoisson partial linear mixed model on the basis of Bayesian P-spline approximation to nonparametric function for longitudinal semicontinuous data.It is quite difficult to directly implement Bayesian computation because the probability density function for Tweedie compound poisson distribution is not analytically tractable.Therefore,inspired by the data-augmentation strategy,we introduce a latent variable to obtain the joint probability density function of a semi-continuous random variable and the latent variable,and conduct the Bayesian statistical inference based on this joint probability density function.Furthermore,a hybrid algorithm combining the block Gibbs sampler and the Metropolis-Hastings algorithm is proposed for producing the joint Bayesian estimates of unknown parameters,random effects and nonparametric function,as well as the predicted value of latent variables.Finally,several simulation studies and a real example are presented to illustrate the proposed methodologies.
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