A Bayesian Analysis Of Zero-inflated Count Data Regression Model

Count data exists widely in the field of biomedical, finance, insurance, public health and risk control, zero inflation is one of the characteristics of the data showed. So-called zero inflation, namely the proportion of zero observations in the far more than the range allowed by the fitting of distribution, zero at the bulging. Zero inflated Poisson regression model is generally choose the data fitting. In addition, count data often show characteristics of divergence is too large, if changes in the variance of the data is greater than the mean, said the data scatter is too large. Compared with the traditional zero inflated Poisson regression model in terms of, under the zero inflated negative binomial (ZINB) regression model can explain the bigger divergence of data structure is divergence analysis of partial high count data is a powerful tool. From the point of view of the existing research results, the existing methods and theories mostly concentrated on the aspect of the likelihood of count data analysis, by contrast, the Bayesian analysis of count data for real life are still exist a large research space, especially to the divergence of partial plans to count according to hierarchical regression model of Bayesian statistical inference research remains to be further improved. Compared with the maximum likelihood method and Bayesian method integrated in a sample of a priori information, for some distribution modeling is more flexible, especially for missing data and complex models, Bayesian method is especially advantage of computational feasibility and validity. Therefore, perspective in this paper, the Bayesian analysis, with zero inflation divergence and count data were studied.Firstly for count data of zero inflation problem, build probit model combined with the zero inflated Poisson regression model. At the same time to establish an combined with Gibbs sampling and metropolis hasting algorithm of MCMC techniques to obtain the Bayesian estimation of the parameters of the model, on this basis. In this paper the DIC information criterion for model comparison and selection of and further considering the partial posterior predictive p-values to reasonable evaluation model fitting goodness. In addition, due to the need of sampling procedures and questionnaire design, count data tend to show group related and independent of the characteristics, classical longitudinal count data analysis theory always of random effects and random error are considered normal distribution. However, in the practical application, the assumption that lack the flexibility of the statistical robustness and modeling, especially for with peak and fat tail and non symmetrical non normal state data, this assumption will lead to partial or even invalid statistical inferences. Therefore,this paper focuses on the Bias regression model to analyze the deviation normal under the ZINB level analysis. Specific, established a zero inflation count data of ZINB level regression model and the random error and random effects consider skew normal distribution, in the Bayesian posterior inference, based on data add thought and skew normal distribution random representation theory, set up the three levels of Bayesian analysis model and get the final model of the posterior distribution.Practical examples show that, the proposed method is effective.