零频数过多模型在亚健康状态研究中的应用

Application of zero-inflated models on regression analysis of count data： a study of sub-health symptoms

探讨零频数过多（ZI）模型在亚健康症状数研究中的应用.应用Stata 11.0软件拟合ZI模型分析亚健康症状数的危险因素,并用d系数、Vuong检验、O检验、似然比拟合优度检验比较ZI模型与传统负二项回归模型、Poisson回归模型的拟合效果.α=0.939,Vuong检验Z=32.08,P＜0.0001,表明此数据的零频数过多.亚健康症状数的（-x）=2.90,s=3.85,过度离散统计量0=308.011,P＜0.001,s2＞（-x）,表明存在过度离散.从4个模型中的拟合优度看,零频数过多的负二项回归（ZINB）模型log likelihood最大,AIC最小,说明ZINB模型的拟合效果最佳.当计数资料中出现过多的零频数时（如亚健康症状数资料）,应用ZINB模型能够获得最佳的拟合效果.

To explore the goodness of fit about the zero-inflated （ZI） models in analyzing data related to sub-health symptoms in which the counts are non-negative integers. ZI models are conducted with Stata 11.0. The coefficient of a, Vuong test, O test and likelihood test are used to compare the goodness of fit for ZI models with the common used models such as passion model,negative binomial model. When a is 0.939, and the Z statistic of Vuong test is 32.08, P〈0.0001,which shows that there are too many zeros. The mean number of sub-health symptoms is 2.90, s=3.85, 0=308.011, P〈0.001, s2〉（-x）, indicating that the data are over-dispersed. In addition, the optimum goodness of fit is found in zero-inflated negative binomial （ZINB） model with the largest log likelihood and the smallest AIC. ZINB seems the optimal model to study those over-dispersed count data with too many zeros.