The estimation of controlled direct effects can be carried out by fitting a marginal structural model and using inverse probability of treatment weighting. To use marginal structural models to estimate natural direct and indirect effects, 2 marginal structural models can be used: 1 for the effects of the treatment and mediator on the outcome and 1 for the effect of the treatment on the mediator. Unlike marginal structural models typically used in epidemiologic research, the marginal structural models used to estimate natural direct and indirect effects are made conditional on the covariates.
"The final purpose of our study is to contribute to the literature on the use of multilevel mediation analyses in randomized field trials in education settings. Mediation analyses are commonly applied in other fields to identify mechanisms through which interventions achieve their effects such as health related interventions (Stigler, Kugler, Komro, Leshabari, & Klepp, 2006), and in psychological research (MacKinnon, Fairchild, & Fritz, 2007) and epidemiological studies (VanderWeele, 2009). Fewer applications are found in experimental studies of educational interventions when three levels are present e students, classrooms, and schools e in part because this statistical technique is not widely known (Pituch, Murphy, & Tate, 2010; Raudenbush, 2011). "
"Structure equation model (SEM) is a popular approach to perform mediation analysis, which assesses the extent of the effect passing through M , see Baron and Kenny (1986) and MacKinnon et al. (2007). This topic has been studied in the statistical literature, see for example Holland (1988); Robins and Greenland (1992); Angrist et al. (1996); Ten Have et al. (2007); Jo (2008); Albert (2008); Gallop et al. (2009); VanderWeele (2009); Imai et al. (2010); Daniels et al. (2012). A popular assumption to infer causal effects is to assume the ignorability of the mediator (Imai et al., 2010). "
[Show abstract][Hide abstract] ABSTRACT: Mediation analysis assesses the effect passing through a intermediate
variable (mediator) in a causal pathway from the treatment variable to the
outcome variable. Structure equation model (SEM) is a popular approach to
estimate the mediation effect. However, causal interpretation usually requires
strong assumptions, such as ignorability of the mediator, which may not hold in
many social and scientific studies. In this paper, we use mediation analysis in
an fMRI experiment to assess the effect of randomized binary stimuli passing
through a brain pathway of two brain regions. We propose a two-layer SEM
framework for mediation analysis that provides valid inference even if
correlated additive errors are present. In the first layer, we use a liner SEM
to model the subject level fMRI data, where the continuous mediator and outcome
variables may contain correlated additive errors. We propose a constrained
optimization approach to estimate the model coefficients, analyze its
asymptotic properties, and characterize the nonidentifiability issue due to the
correlation parameter. To address the identifiability issue, we introduce a
linear mixed effects SEM with an innovation to estimate the unknown correlation
parameter in the first layer, instead of sensitivity analysis. Using extensive
simulated data and a real fMRI dataset, we demonstrate the improvement of our
approach over existing methods.
"This requires estimators for the conditional mean of Y given D, M, X and the conditional density of M given D, X. In the literature, parametric methods have been most commonly used, see for instance Pearl (2011) and VanderWeele (2009). 6 They, however, appear unattractive due to their severe functional form restrictions and the potentially difficult interpretability of direct and indirect effects under non-linear modeling (e.g., when both the outcome and the mediator are binary). "
[Show abstract][Hide abstract] ABSTRACT: This paper demonstrates the identification of causal mechanisms of a binary treatment under selection on observables, (primarily) based on inverse probability weighting. I.e., we consider the average indirect effect of the treatment, which operates through an intermediate variable (or mediator) that is situated on the causal path between the treatment and the outcome, as well as the (unmediated) direct effect. Even under random treatment assignment, subsequent selection into the mediator is generally non-random such that causal mechanisms are only identified when controlling for confounders of the mediator and the outcome. To tackle this issue, units are weighted by the inverse of their conditional treatment propensity given the mediator and observed confounders. We show that the form and applicability of weighting depend on whether some confounders are themselves influenced by the treatment or not. A simulation study gives the intuition for these results and an empirical application to the direct and
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