Pearl's D-Separation: One More Step Into Causal Thinking

Abstract

It is frequently claimed that experiments can attest to causal assertions, whereas cross-sectional survey research cannot underwrite similar causal claims. Some logical deficiencies with deriving causal claims from correlation data have been addressed through model testing, the estimation of reciprocal effects, and admonitions to seek sparse models, but the foundations for making specifically causal structural equation modeling claims remain elusive. The body of work collected in Pearl's (2000) book, Causality: Models, Reasoning, and Inference, makes substantial progress toward elucidating a logical structure capable of distinguishing evidence-supported causal claims from unsupported SEM causal claims. Pearl's approach is sufficiently laden with notation, definitions, axioms, and theorems that most SEM users are likely to respond to by saying, "just looking, thanks." Our objective in this article is to provide a relatively accessible entry into Pearl's thinking because we feel this work is worth more than a cursory glance. We tackle one fundamental component of Pearl's conceptualization, something he calls d-separation. Our hope is that once SEM practitioners begin to see the structure of Pearl's thinking, they will strive to discover more of Pearl's pearls of wisdom. Pearl does not attempt to defend an entire structural equation model, but instead seeks to determine which specific effect coefficients within a model do, and which do not, garner causal support through demonstration of consistency with the data. This article explains how d-separation connects to control variables, partial correlations, causal structuring, and even to a potential mistake in regression.