Causal Mediation Analysis with Multiple Uncausally Related Mediators – Asymptotic distribution of least square estimators for linear models with dependent errors
vendredi 23 novembre 2018, 9h30 - 10h30
Salle du conseil, espace Turing
Allan Jérolon
Titre : Causal Mediation Analysis with Multiple Uncausally Related Mediators
Causal mediation analysis is widely used in various domains such as biostatistics, epidemiology, psychology, legal and social sciences and public policy. The goal of such an analysis is to explain and quantify the effects of a variable on an outcome, directly and indirectly through other variables called mediators.
In 2010, Imaï and collaborators introduced a general framework to define, identify and estimate these effects and implemented their methods in the widely used R package « mediation ». When two or more mediators are considered, current approaches consists in repeating several simple mediator analysis in parallel. This could result in an estimation bias for quantities of interest effects.
In this work, contributions are threefold: First we show that conducting several simple mediator analysis in parallel, on data generating with multiple uncausally related mediators, result in a biased estimate. Then we propose a generalization of the approach by Imaï and collaborators in the case of multiple mediators uncausally related which lead to unbiased estimates. At last we implement our algorithm in R and apply it to simulate and real data.
In 2010, Imaï and collaborators introduced a general framework to define, identify and estimate these effects and implemented their methods in the widely used R package « mediation ». When two or more mediators are considered, current approaches consists in repeating several simple mediator analysis in parallel. This could result in an estimation bias for quantities of interest effects.
In this work, contributions are threefold: First we show that conducting several simple mediator analysis in parallel, on data generating with multiple uncausally related mediators, result in a biased estimate. Then we propose a generalization of the approach by Imaï and collaborators in the case of multiple mediators uncausally related which lead to unbiased estimates. At last we implement our algorithm in R and apply it to simulate and real data.
Emmanuel Caron
Titre : Asymptotic distribution of least square estimators for linear models with dependent errors
We consider the usual linear regression model in the case where the error process is assumed strictly stationary. We use a result from Hannan (1973), who proved a Central Limit Theorem for the usual least square estimator under general conditions on the design and on the error process. Whatever the design satisfying Hannan’s conditions, we define an estimator of the covariance matrix and we prove its consistency under very mild conditions. As an application, we show how to modify the usual tests on the linear model in this dependent context, in such a way that the type-I error rate remains asymptotically correct, and we illustrate the performance of this procedure through different sets of simulations.
