2020/08/08 by F Richard Guo, Guo, F. Richard, Emilija Perković +2 · 1 citation
Computer Science · #Bayesian Modeling and Causal Inference
paper · pdf · doi:10.48550/arxiv.2008.03481
Recursive linear structural equation models are widely used to postulate\ncausal mechanisms underlying observational data. In these models, each variable\nequals a linear combination of a subset of the remaining variables plus an\nerror term. When there is no unobserved confounding or selection bias, the\nerror terms are assumed to be independent. We consider estimating a total\ncausal effect in this setting. The causal structure is assumed to be known only\nup to a maximally oriented partially directed acyclic graph (MPDAG), a general\nclass of graphs that can represent a Markov equivalence class of directed\nacyclic graphs (DAGs) with added background knowledge. We propose a simple\nestimator based on recursive least squares, which can consistently estimate any\nidentified total causal effect, under point or joint intervention. We show that\nthis estimator is the most efficient among all regular estimators that are\nbased on the sample covariance, which includes covariate adjustment and the\nestimators employed by the joint-IDA algorithm. Notably, our result holds\nwithout assuming Gaussian errors.\n