Statistical test for consistent estimation of causal effects in linear non-Gaussian models
Doris Entner, Patrik Hoyer, Peter Spirtes ; JMLR W&CP 22: 364-372, 2012.
In many fields of science researchers are faced with the problem of estimating causal effects from non-experimental data. A key issue is to avoid inconsistent estimators due to confounding by measured or unmeasured covariates, a problem commonly solved by 'adjusting for' a subset of the observed variables. When the data generating process can be represented by a directed acyclic graph, and this graph structure is known, there exist simple graphical procedures for determining which subset of covariates should be adjusted for to obtain consistent estimators of the causal effects. However, when the graph is not known no general and complete procedures for this task are available. In this paper we introduce such a method for linear non-Gaussian models, requiring only partial knowledge about the temporal ordering of the variables: We provide a simple statistical test for inferring whether an estimator of a causal effect is consistent when controlling for a subset of measured covariates, and we present heuristics to search for such a set. We show empirically that this statistical test identifies consistent vs inconsistent estimates, and that the search heuristics outperform the naive approach of adjusting for all observed covariates.