中文摘要：

基于EM算法和Laplace逼近，本文给出了研究ZI（即含0较多的）纵向计数数据模型的影响分析方法．为了识别含0较多的分组计数数据中的强影响点，本文将ZI纵向数据模型中取值为0的数据赋予一定的权重；而把随机效应看作缺失数据；在此基础上引入EM算法，从而应用完全数据对数似然函数的条件期望以及相应的Q距离函数进行影响分析；并进一步应用Laplace逼近方法简化EM算法中的积分计算．在此基础上，基于数据删除模型和局部影响分析方法导出了适用于ZI纵向计数数据模型的诊断统计量．本文也通过实际计数数据的例子验证了诊断统计量的有效性．

英文摘要：

Based on the EM algorithm and Laplace approximation, this paper presents a method of influence analysis for zero inflated longitudinal count data models. To detect the influential observations in clustered COUllt data with excess zeros, we regard the random effects as the missing data and put certain weight to the data with zero values in ZI longitudinal data models. According to this fact. we develop the influence method for the model based on the conditional expectation of the complete-data log-likelihood function and the associated Q-distance function under the EM algorithm. The Laplace approximation is also employed for integral computing in E-step. Then the case-deletion model and the local influence analysis are investigated for the model and several diagnostic measures are obtained. Finally, a numerical example of the real count data is given to illustrate the results in this paper.