正态线形模型下缺失值的Bootstrap多重插补与比较

Bootstrap Multiple Imputation and Comparison of Missing Value Under the Normal Linear Model

缺失值是调查中普遍存在的问题,对缺失值进行插补是处理缺失值的较好方法。如果变量之间存在相关关系,可以通过正态线形模型利用不存在缺失值的变量对有存在缺失值的变量进行插补。较之单一插补,多重插补更能有效地估计总体方差,因此更多地被使用。文章借助Bootstrap法,让模型的参数和残差来自完全观测的Bootstrap样本的最小平法估计,可进一步准确估计总体方差。通过大量模拟试验,发现Bootstrap多重插补较之单一插补和一般多重插补能构建更宽的置信区间从而有更准确的总体参数覆盖率,这点在数据缺失比重很大时优势更明显。

Missing values always exist in survey data and the imputation methods can be used to deal with the missing values. If variables are correlated with each other, variables without missing values can be used to impute variables with missing values under normal linear model. Compared with singular imputation, multiple imputation especially Bootstrap multiple imputation can be used to estimate the population variance more efficiently, hence used more widely. A large number of simulation tests show that the proposed imputation method has wider confidence interval and more accurate population parameter coverage than singular and ordinary multiple imputation approaches, and its advantage is very distinct in the case of significant data-missing proportion.