Parameter Estimation And Hypothesis Testing For The Multilevel Zero-inflated Count Data

Count data has a very important application in many areas (such as bio-medicine, actuarial, public health, etc.). To analyze this data, many scholars have adapted Pois-son distribution for its simple form. However, the stringent requirement that its sample variance should be equal to the mean can not be met by most pragmatic data. Actual-1y, this data always occurs with excess zeroes and the analysis result using a Poisson distribution will not be satisfying. Adding a dispersion parameter to the standard Poisson distribution and mixed with a zero-degradation distribution, the zero-inflated generalized Poisson distribution could be a good choice to analyze this data.This paper is aimed at choosing an appropriate model for a health-care utiliza-tion data set, which kept the using times of health-care utilization in some 6 years and the basic information of 180 individuals form 48 different families. Because the data is a repeated kept result of different individuals form different families, we set our model as a three-level regression model. In this paper, we first discuss the parameter estimating method for the most complicated model:multilevel zero-inflated general-ized Poisson regression. An expectation-maximization algorithm in conjunction with restricted maximum likelihood estimates are used here to obtain the results of param-eter estimate. Afterwards, we present significance tests for zero-inflated parameter and dispersion parameter in the regression model, and obtain the score test statistics. In addition, we represent a large amount of simulation study to prove the effective of our parameter estimating method and the score statistics. At last, we choose an ap-propriate model to analyze the health-care utilization data with the using of score test and likelihood ratio test. Some statistics, such as negative logarithm likelihood, de-viance and scoring rules statistics are also obtained to illustrate the correctness of our choice. The analysis result using our selected model is proper and common-sensible, which further illustrate the methodology and validity of our parameter estimation and hypothesis test method.