# Identification and Sensitivity Analysis for Average Causal Mediation Effects with Time-Varying Treatments and Mediators: Investigating the Underlying Mechanisms of Kindergarten Retention Policy

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## Abstract

Considering that causal mechanisms unfold over time, it is important to investigate the mechanisms over time, taking into account the time-varying features of treatments and mediators. However, identification of the average causal mediation effect in the presence of time-varying treatments and mediators is often complicated by time-varying confounding. This article aims to provide a novel approach to uncovering causal mechanisms in time-varying treatments and mediators in the presence of time-varying confounding. We provide different strategies for identification and sensitivity analysis under homogeneous and heterogeneous effects. Homogeneous effects are those in which each individual experiences the same effect, and heterogeneous effects are those in which the effects vary over individuals. Most importantly, we provide an alternative definition of average causal mediation effects that evaluates a partial mediation effect; the effect that is mediated by paths other than through an intermediate confounding variable. We argue that this alternative definition allows us to better assess at least a part of the mediated effect and provides meaningful and unique interpretations. A case study using ECLS-K data that evaluates kindergarten retention policy is offered to illustrate our proposed approach.

## Keywords

causal mediation analysis time-varying treatment and mediator time-varying confounding variable homogeneous effects heterogeneous effects sensitivity analysis## Notes

### Acknowledgements

This research was supported by a grant from the American Educational Research Association which receives funds for its “AERA Grants Program” from the National Science Foundation under Grant #DRL-0941014. Opinions reflect those of the author and do not necessarily reflect those of the granting agencies.

## Supplementary material

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