Reproduce “Comparing Two Proxy Methods for Causal Identification” on OpenResearch

About this paper

Helen Guo, Elizabeth L. Ogburn, Ilya Shpitser

Researchers compared two major nonparametric proxy variable methods for causal identification, bridge equation methods and array decomposition methods, under shared conditional independence assumptions. The analysis revealed that while specific array decomposition methods can be nested within bridge equation methods, the more general array decomposition framework is non-nested with bridge equation approaches, defining distinct scopes of applicability.

Key insights

• Specific array decomposition methods (e.g., Kuroki and Pearl, 2014) can be a special case, nested within the bridge equation framework (Miao et al., 2018) in discrete settings.
• The more general array decomposition approach based on Kruskal's theorem and bridge equation methods are non-nested, operating under distinct sets of sufficient assumptions for identification.
• Bridge equation methods primarily identify a specific causal effect, while array decomposition methods aim to recover the full joint law of hidden and observed variables, offering broader utility.

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