Evaluating the Use of Generalized Linear Models in Modeling Complex Non-Normal Data Relationships

Posted: Apr 20, 2017

• Chloe Harris
• Chloe Johnson
• Chloe Robinson

Abstract

Generalized Linear Models (GLMs) have served as fundamental tools in statistical analysis since their introduction by Nelder and Wedderburn in 1972. These models extend ordinary linear regression to accommodate response variables following distributions from the exponential family, providing a unified framework for analyzing diverse data types including binary, count, and continuous outcomes. The theoretical elegance and computational tractability of GLMs have established them as workhorse methods across numerous scientific disciplines. However, the increasing complexity of contemporary datasets presents significant challenges to traditional GLM formulations. Modern applications in computational biology, network science, and environmental informatics frequently generate data with intricate dependency structures, multi-scale patterns, and non-Euclidean relationships that violate standard modeling assumptions. The conventional GLM framework assumes that observations are independent and identically distributed, with relationships adequately captured by linear predictors on a transformed scale. While this approach has proven remarkably successful in many contexts, its limitations become apparent when confronted with data exhibiting complex geometric structures or hierarchical dependencies. Recent advances in topological data analysis and geometric statistics have revealed that many real-world phenomena possess intrinsic structural properties that conventional statistical methods fail to capture. This gap between methodological capability and data complexity motivates our investigation into enhanced GLM frameworks that incorporate geometric and topological considerations.