儿童抑郁症调查中数据缺失情形下logistic回归模型参数的最大似然估计

摘要

Because of various reasons, data missing exists in most medical surveys. Wecould not use the method to analyze such missing data as the way we handle the complete observed data. How to handle these missing data is becoming one of the focuses of the statisticians in recent years.The original method of solving this problem is the rejection of the missing data, it means only modeling and parameter estimation of the observed data. Obviously, this method will result in the losing of information of the model. Many statisticians have suggested various methods to the problem. Rubin (1974, 1976, 1978) and Little (1987)presented the basic approaches of analysis of the incomplete data. Dempster, Laird and Rubin (1977) systematically described the EM algorithm under incomplete situation. These all applied the thought of solving missing data for us.This paper is based on the data of Shanghai Children Depression Survey. The outcome of the model is missing. We intend to use aimed data to reset the data, and model the logistic regression model, present the parameter estimation method. And according to the real background of the case, modify the model, to obtain the influence of the covariance to the outcomes.

目录

英文文摘

第一章简介

1.1 儿童抑郁症简介

1.2上海儿童抑郁症情况调查

1.3以往缺失数据处理的研究成果

1.4针对上海儿童抑郁症调查中数据缺失的处理方法

第二章列联表的独立性检验

2.1单因素列联表检验

2.2多因素列联表检验

第三章响应变量数据缺失情形下logistic回归模型参数最大似然估计

3.1分组还原缺失的响应变量数据

3.2对于logistic回归参数估计

3.3对上海儿童抑郁症调查的logistic回归模型的参数估计

3.4随机模拟结果分析

参考文献

附录一、上海儿童抑郁症调查问卷

附录二、改进前logistic回归模型参数估计值收敛情况

附录三、改进后logistic回归模型参数估计值收敛情况

后记

论文独创性声明和论文使用授权声明