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

This paper has been withdrawn by Chao Zhou

[Submitted on 10 May 2026 (v1), last revised 23 Jul 2026 (this version, v2)]

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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.

Submission history

From: Chao Zhou [view email]
[v1] Sun, 10 May 2026 14:44:13 UTC (100 KB)
[v2] Thu, 23 Jul 2026 21:52:57 UTC (1 KB) (withdrawn)