98,657 research outputs found
Causal Consistency of Structural Equation Models
Complex systems can be modelled at various levels of detail. Ideally, causal
models of the same system should be consistent with one another in the sense
that they agree in their predictions of the effects of interventions. We
formalise this notion of consistency in the case of Structural Equation Models
(SEMs) by introducing exact transformations between SEMs. This provides a
general language to consider, for instance, the different levels of description
in the following three scenarios: (a) models with large numbers of variables
versus models in which the `irrelevant' or unobservable variables have been
marginalised out; (b) micro-level models versus macro-level models in which the
macro-variables are aggregate features of the micro-variables; (c) dynamical
time series models versus models of their stationary behaviour. Our analysis
stresses the importance of well specified interventions in the causal modelling
process and sheds light on the interpretation of cyclic SEMs.Comment: equal contribution between Rubenstein and Weichwald; accepted
manuscrip
Identification and Estimation of Causal Effects Using non-Gaussianity and Auxiliary Covariates
Assessing causal effects in the presence of unmeasured confounding is a
challenging problem. Although auxiliary variables, such as instrumental
variables, are commonly used to identify causal effects, they are often
unavailable in practice due to stringent and untestable conditions. To address
this issue, previous researches have utilized linear structural equation models
to show that the causal effect can be identifiable when noise variables of the
treatment and outcome are both non-Gaussian. In this paper, we investigate the
problem of identifying the causal effect using auxiliary covariates and
non-Gaussianity from the treatment. Our key idea is to characterize the impact
of unmeasured confounders using an observed covariate, assuming they are all
Gaussian. The auxiliary covariate can be an invalid instrument or an invalid
proxy variable. We demonstrate that the causal effect can be identified using
this measured covariate, even when the only source of non-Gaussianity comes
from the treatment. We then extend the identification results to the
multi-treatment setting and provide sufficient conditions for identification.
Based on our identification results, we propose a simple and efficient
procedure for calculating causal effects and show the -consistency of
the proposed estimator. Finally, we evaluate the performance of our estimator
through simulation studies and an application.Comment: 16 papges, 7 Figure
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