Simpson's Paradox in Behavioral Curves: How Aggregation Distorts Parametric Models of User Dynamics

Abstract:Behavioral curve modeling -- fitting parametric functions to engagement-versus-exposure data -- is standard practice in recommendation, advertising, and clinical dosing. We show that aggregation introduces a systematic distortion: Simpson's paradox in behavioral curves. On Goodreads (3.3M users, 9 genres), individual users peak at n* approximately 11 exposures while the aggregate peaks at n* approximately 34 -- a 3x gap driven by survival bias. Amazon Electronics (18M reviews) shows a 5.3x distortion. MovieLens-25M (D approximately 1) serves as a negative control, confirming that survival bias -- not aggregation per se -- is the operative mechanism. The distortion is robust to category granularity, engagement operationalization, and classifier calibration. We develop Synthetic Null Calibration to address a 32% false positive rate in per-user classification. Our findings apply wherever individual behavioral parameters are estimated from aggregate curves under differential attrition.

Withdrawn by the authors: the central empirical result does not reproduce under reanalysis; the reported curve peaks are artifacts of fitting a peaked model to near-flat data. Withdrawn pending a corrected analysis

Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Information Retrieval (cs.IR)

arXiv:2605.11017 [cs.LG]

(or arXiv:2605.11017v2 [cs.LG] for this version)