零膨胀集群数据层次回归模型的贝叶斯推断

Bayesian Inference of Hierarchical Regression Model for zero-Inflated Clustered Count Data

摘要: 零膨胀Poisson回归模型是研究零观测值过多的计数数据的常用工具, 本文提出了一类拟合具有这类特征的集群数据的层次零膨胀泊松回归模型, 并给出了相应的贝叶斯推断方法, 参数估计通过Gibbs抽样获得, 模型比较与选择则通过拟合优度检验与BIC准则实现. 最后, 利用一个船舶受损事故数据来展示本文方法的实现及应用.

Abstract: Zero-inflated Poisson (ZIP) regression model is a popular tool for analyzing count data with excess zeros. In this paper, a flexible hierarchical ZIP regression model is proposed to handle with such data with cluster and Bayesian approach is develop. A Gibbs sampler is employed to produce the Bayesian estimate, a goodness-of-fit and a Bayesian information criterion (BIC) are used for model comparison and selection. Finally, an application of data from a ship damage incident study illustrates the proposed method.