An Empirical Study of Bayesian Hierarchical Models in Analyzing Multi-Level and Nested Data Structures

Posted: Sep 23, 2020

• Alexander Hill
• Alexander Martin
• Alexander Wilson

Abstract

Bayesian hierarchical models have emerged as powerful statistical tools for analyzing data with complex dependency structures, particularly in situations where observations are naturally grouped or nested. The theoretical foundations of these models are well-established in statistical literature, with applications spanning diverse fields including education, epidemiology, ecology, and social sciences. However, despite their theoretical appeal and increasing adoption, comprehensive empirical evaluations of BHMs under realistic data conditions remain surprisingly limited. This research gap is particularly pronounced for scenarios involving deeply nested structures, unbalanced designs, and complex correlation patterns that frequently characterize real-world data. The current study addresses this methodological void through a systematic empirical investigation of BHMs across a spectrum of data complexity conditions. Our investigation builds upon existing theoretical work while introducing several methodological innovations. We developed a comprehensive simulation framework that systematically varies key data characteristics including nesting depth, intra-class correlation, sample size distribution across levels, and missing data mechanisms.