Model Deconstruction and Hill Causality

• Activity Number: 612
• Type: Contributed
• Date/Time: Thursday, August 2, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Graphics
• Author(s): William Heavlin*+
• Companies: Google
• Keywords: Austin Bradford Hill ; cumsum charts ; Frisch-Waugh-Lovell theorem ; internal validity ; meta-analysis ; regression diagnostics

Abstract

Hill (1965, 1971) articulates several criteria for inferring causality: (1) the magnitude of the effect (its strength), (2) consistency across multiple studies,(3)specificity of association, (4) respect for temporal ordering, (5)monotonicity of the dose-response relationship, (6)plausibility with respect to theory, and (7) coherence with respect to experiments. Most commonly applied within epidemiology, Hill's criteria give us a framework for meta-analysis over a body of research.

Here we adapt Hill's criteria (1)-(6) to the case of a single dataset and model. Our main graphical tool is a modest generalization of the cumsum chart called the numerator-denominator (ND) plot. Each ND plot is motivated by a Hill criterion, and corresponds also to a relatively more familiar regression diagnostic plot. Whereas regression diagnostic plots concentrate on residual patterns, ND plots focus on model coefficients. By showing how subsets of data contribute to estimated coefficients, ND plots both deconstruct any estimated model and assess its terms with respect to Hill's criteria.