Graphical Criteria for Efficient Total Effect Estimation via Adjustment in Causal Linear Models

Abstract

Covariate adjustment is a commonly used method for total causal effect estimation. In recent years, graphical criteria have been developed to identify all valid adjustment sets, that is, all covariate sets that can be used for this purpose. Different valid adjustment sets typically provide total effect estimates of varying accuracies. Restricting ourselves to causal linear models, we introduce a graphical criterion to compare the asymptotic variances provided by certain valid adjustment sets. We employ this result to develop two further graphical tools. First, we introduce a simple variance reducing pruning procedure for any given valid adjustment set. Second, we give a graphical characterization of a valid adjustment set that provides the optimal asymptotic variance among all valid adjustment sets. Our results depend only on the graphical structure and not on the specific error variances or edge coefficients of the underlying causal linear model. They can be applied to directed acyclic graphs (DAGs), completed partially directed acyclic graphs (CPDAGs) and maximally oriented partially directed acyclic graphs (maximal PDAGs). We present simulations and a real data example to support our results and show their practical applicability.

arXiv comment63 pages, 17 figures

References in corpus (15)

• Causal Inference and Causal Explanation with Background Knowledge
• Estimating high-dimensional intervention effects from observational data
• Characterization and Greedy Learning of Interventional Markov Equivalence Classes of Directed Acyclic Graphs
• Causal Networks: Semantics and Expressiveness
• On the Validity of Covariate Adjustment for Estimating Causal Effects
• A generalized back-door criterion
• Permutation-based Causal Inference Algorithms with Interventions
• Causal discovery of linear acyclic models with arbitrary distributions
• A Complete Generalized Adjustment Criterion
• Complete Graphical Characterization and Construction of Adjustment Sets in Markov Equivalence Classes of Ancestral Graphs
• On efficient adjustment in causal graphs
• Cyclic Causal Discovery from Continuous Equilibrium Data
• Interpreting and using CPDAGs with background knowledge
• Efficient adjustment sets in causal graphical models with hidden variables
• The Variance of Causal Effect Estimators for Binary V-structures

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