Analyzing the Relationship Between Missing Data Mechanisms and Bias in Maximum Likelihood Estimation Techniques

Posted: Mar 27, 2013

• Daniel Rivera
• Daniel Young
• David Allen

Abstract

The pervasive challenge of missing data represents one of the most fundamental obstacles in statistical inference and empirical research across scientific disciplines. Maximum likelihood estimation stands as a cornerstone methodology for parameter estimation in the presence of incomplete data, with its theoretical properties extensively studied under the Rubin framework of missing data mechanisms. Traditional statistical theory posits clear hierarchical relationships between missing completely at random (MCAR), missing at random (MAR), and missing not at random (MNAR) mechanisms in terms of their propensity to introduce bias in parameter estimates. However, the practical application of these theoretical distinctions often reveals complexities that transcend conventional classifications. This research addresses critical gaps in our understanding of how missing data mechanisms interact with estimation bias in maximum likelihood frameworks. While existing literature provides comprehensive treatments of missing data theory, there remains insufficient exploration of how complex dependency structures and high-dimensional contexts modulate the relationship between missingness mechanisms and bias propagation. Our investigation challenges several established assumptions, particularly the linear progression of bias severity from MCAR to MAR to MNAR scenarios, and reveals nuanced patterns that have significant implications for statistical practice.