The Statistical Inference Of Zero-inflated Negative Binomial Regression Model With Missing Data

In real life, count data exist widely in the financial data, insurance, clinical medicine, biological genetics and sampling survey, and other fields, Scholars at home and abroad on such questions did windly analysis research, thus set up the count data model of under the background of all kinds of application. In the above model, Poisson regression model is the important research count data analysis model, is also the most basic model. Poisson model requirements events independent, the conditions of the events is equal to the conditions mean variance, However, in the actual research analysis, often do not accord with the premise, in this case, negative binomial regression is an extension of the Poisson regression.But in actual count data analysis study, often because all sorts of reasons cause observation data, there are a lot of zero, the proportion is far more than Poisson regression or negative binomial regression prediction ability, showing zero inflation phenomenon (zero-inflated). Classic zero inflation count data model, through to the zero count and the zero count build mixed regression model, very good solution to the existing in the data of zero problems too. This paper on the basis of Greene (1994) proposed zero inflation negative binomial regression model (zero-inflated negative binomial, ZINB), system discussed the basic idea of count data modeling, single level ZINB model, double horizontal band ZINB model with random effects, and the ZINB model with missing data. Now in this paper, the main research contents are as follows:First, we discusses the characterizations of the commonly used data count distribution, the numerical characteristics, application scope of the introduction of the system, and introduced the basic thoughts of the count data modeling, especially to the existence of the expansion of the count zero data modeling method.Second, In the completely data mode, According to different condition, we discussed the single level ZINB model, and double horizontal band of ZINB model with random effects, and are given respectively for zero inflation Score test statistics and the corresponding amount of sampling distribution and potential.Finally, Based on the Little Rubin and put forward in 2002 missing data model and the lack of the mechanism, we analyzed the ZINB model with missing data, established ML estimation of model parameters procedure and model selection standard, and in the end of paper are given a simulation.To sum up, in view of the count data with zero inflation and missing data, this paper mainly based on the ZINB model was given the ZINB model in completely data and the corresponding Score test statistics, The model parameter estimation and model selection criteria of ZINB model with missing data and the corresponding simulation.