Estimating Causal Effects from Nonparanormal Observational Data

Mahdi Mahmoudi Seyed () and Wit Ernst C. ()
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Mahdi Mahmoudi Seyed: Department of Statistics, Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran
Wit Ernst C.: Johann Bernoulli Institute (FWN), Rijksuniversiteit Groningen Faculteit voor Wiskunde en Natuurwetenschappen, Groningen, Netherlands

The International Journal of Biostatistics, 2018, vol. 14, issue 2, 15

Abstract: One of the basic aims of science is to unravel the chain of cause and effect of particular systems. Especially for large systems, this can be a daunting task. Detailed interventional and randomized data sampling approaches can be used to resolve the causality question, but for many systems, such interventions are impossible or too costly to obtain. Recently, Maathuis et al. (2010), following ideas from Spirtes et al. (2000), introduced a framework to estimate causal effects in large scale Gaussian systems. By describing the causal network as a directed acyclic graph it is a possible to estimate a class of Markov equivalent systems that describe the underlying causal interactions consistently, even for non-Gaussian systems. In these systems, causal effects stop being linear and cannot be described any more by a single coefficient. In this paper, we derive the general functional form of a causal effect in a large subclass of non-Gaussian distributions, called the non-paranormal. We also derive a convenient approximation, which can be used effectively in estimation. We show that the estimate is consistent under certain conditions and we apply the method to an observational gene expression dataset of the Arabidopsis thaliana circadian clock system.

Keywords: causal effects; directed acyclic graph (DAG); nonparanormal distribution; PC-algorithm; Gaussian copula (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1515/ijb-2018-0030

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