基于联合模型法和完全条件法的分层多重插补方法研究

Research on Multilevel Multiple Imputation Method Based on Joint Modelling Method and Fully Conditional Method

大规模抽样调查常采用整群抽样、多阶段抽样等复杂抽样设计,得到的调查数据呈分层嵌套结构特征,其中不可避免会出现数据缺失的问题,本文将传统的对单一含缺失数据变量进行插补的方法推广到对多个含缺失数据变量进行插补,研究了两种基于分层模型的多元含缺失数据变量多重插补方法,即通过从一个多元分布中多次抽样,同时对所有含缺失值变量进行插补的联合模型法和通过一系列关于含缺失值变量的分布对各变量依次进行插补的完全条件法.本文针对分层结构含缺失调查数据集,给出了两种方法的插补步骤,通过理论推导和模拟实证,给出了两种方法的适用范围.

The large-scale sample survey often adopts complex sampling design such as cluster sampling and multi-stage sampling. The survey data obtained have a multilevel structure, and missing data problem is unavoidable. In this paper, the traditional imputation method for single variable with missing data is extended to the case of multiple variables with missing data, two multivariable multiple imputation methods based on multilevel model axe studied, that is, the joint modelling method simultaneously impute all the incomplete variables by making several draws of missing data from their joint distribution, and the fully conditional method specifies a series of separate imputation model for each incomplete variable and updates the missing data for each variable in turn. In this paper, the imputation steps of these two methods are given for the incomplete dataset with multilevel structure, and the scope of the application of the two methods is given through theoretical derivation and simulation.