Assessing the Role of Random Effects Modeling in Accounting for Unobserved Heterogeneity Across Data Groups

Posted: Dec 23, 2023

• Theodore Baker
• Luna Adams
• Liam Lee

Abstract

Random effects modeling has long been a cornerstone of statistical methodology for analyzing data with hierarchical or grouped structures. The fundamental premise of these models is that they can account for unobserved heterogeneity by introducing group-specific random intercepts or slopes. However, the conventional application of random effects models often relies on strong parametric assumptions that may not hold in practice, particularly when dealing with complex, real-world data from diverse sources. This paper challenges the adequacy of traditional random effects approaches and proposes a novel framework that better captures the intricate nature of unobserved heterogeneity in modern datasets. Contemporary data collection practices frequently yield information from multiple sources with varying characteristics, protocols, and latent structures. Educational institutions gather student performance data using different assessment tools, healthcare systems record patient outcomes with disparate measurement instruments, and environmental monitoring networks deploy heterogeneous sensors across geographical regions. In all these scenarios, the standard random effects model assumption of normally distributed random effects with constant variance may be overly restrictive and potentially misleading. Our research addresses several critical gaps in the current literature. First, we question the universality of the normality assumption for random effects and explore alternative distributional forms that may better represent the underlying heterogeneity. Second, we investigate whether the common practice of assuming homogeneous variance across groups adequately captures the variability.