The More Data, the Better? Demystifying Deletion-Based Methods in Linear Regression with Missing Data

TL;DR

This paper compares complete-case and available-case deletion methods in linear regression with missing data, revealing that more data does not always mean better estimates and highlighting the influence of data patterns and structure.

Contribution

It provides a theoretical comparison of deletion-based methods, clarifies misconceptions about data usage, and offers simulation evidence on their asymptotic properties.

Findings

Available-case analysis does not always outperform complete-case analysis in efficiency.

Missing data patterns and covariance structures significantly influence method performance.

Both methods are asymptotically unbiased under certain conditions.

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 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.