The more data, the better? Demystifying deletion-based methods in linear regression with missing data.

Pub Date : 2022-01-01 DOI:10.4310/21-sii717
Tianchen Xu, Kun Chen, Gen Li
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Abstract

We compare two deletion-based methods for dealing with the problem of missing observations in linear regression analysis. One is the complete-case analysis (CC, or listwise deletion) that discards all incomplete observations and only uses common samples for ordinary least-squares estimation. The other is the available-case analysis (AC, or pairwise deletion) that utilizes all available data to estimate the covariance matrices and applies these matrices to construct the normal equation. We show that the estimates from both methods are asymptotically unbiased under missing completely at random (MCAR) and further compare their asymptotic variances in some typical situations. Surprisingly, using more data (i.e., AC) does not necessarily lead to better asymptotic efficiency in many scenarios. Missing patterns, covariance structure and true regression coefficient values all play a role in determining which is better. We further conduct simulation studies to corroborate the findings and demystify what has been missed or misinterpreted in the literature. Some detailed proofs and simulation results are available in the online supplemental materials.

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数据越多越好?揭示缺失数据线性回归中基于删除的方法。
我们比较了两种基于删除的方法来处理线性回归分析中观测值缺失的问题。一种是完全案例分析(CC,或列表删除),它抛弃所有不完整的观察结果,只使用普通最小二乘估计的共同样本。另一种是可用情况分析(AC,或成对删除),它利用所有可用数据来估计协方差矩阵,并应用这些矩阵来构造正态方程。我们证明了两种方法的估计在完全随机缺失(MCAR)下是渐近无偏的,并进一步比较了它们在一些典型情况下的渐近方差。令人惊讶的是,在许多情况下,使用更多的数据(即AC)并不一定会导致更好的渐近效率。缺失模式、协方差结构和真实回归系数值都在决定哪个更好。我们进一步进行模拟研究,以证实这些发现,并揭开文献中被遗漏或误解的神秘面纱。一些详细的证明和模拟结果可在网上补充材料。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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