Logistic Regression Analysis Based on Multiple Imputation under Random Missing Covariates

在抽样调查研究中，针对含缺失数据集的总体参数估计问题，当前学术界的研究焦点呈现明显的不均衡性。现有方法体系主要集中于因变量缺失场景下的参数估计(如响应变量缺失下的回归分析)，而对协变量缺失情形下的统计推断方法探索研究较少。本文在协变量数据缺失机制为随机缺失的情形下，考虑用多重插补法来进行插补得到完整数据并建立Logistic回归模型，从多重插补估计量与设定模型参数的差异以及多重插补得到的方差估计来评估多重插补法的精度，并通过模拟实验对比了不同缺失率下多重插补估计量表现。最后对协变量存在随机缺失的德国信贷数据进行了多重插补后逻辑回归建模分析，比较了两种多重插补方法的效果。In sampling survey research, there is a significant imbalance in the current academic focus on the estimation of population parameters with missing datasets. Existing methods mainly focus on situations where the dependent variable data is missing (such as regression analysis in response variable missing scenarios), while relatively little research has been conducted on scenarios involving missing covariates. Under the condition of missing covariate missing data mechanism, this paper considered the multiple interpolation method to get the complete data and establish the Logistic regression model, evaluated the accuracy of the variance estimate obtained from the difference between the parameters and the multiple interpolation, and compared the performance of the multiple interpolation estimator under different missing rates through simulation experiments. Finally, multiple imputation logistic regression modeling analysis was conducted on German credit data with random missing covariates, and the effects of the two multiple imputation methods were compared.