Index: Imai Keele Yamamoto 2010 - Causal Mediation Analysis

Imai Keele Yamamoto 2010 - Causal Mediation Analysis

Routing Summary

This folder fully captures Imai, Keele & Yamamoto (2010), Identification, Inference and Sensitivity Analysis for Causal Mediation Effects (Statistical Science 25(1): 51-71): natural direct/indirect effects, sequential ignorability and Theorem 1, the Baron-Kenny LSEM interpretation, nonparametric estimation, the $\rho$ sensitivity analysis (Theorem 4, Corollary 1) and the media-framing application. It contains 7 notes plus this index.

• Need the paper on one page or the section-to-note map? → Imai 2010 - Causal Mediation Analysis - Overview
• Need ${\delta }_i(t)$, ACME, sequential ignorability or Theorem 1 with proof? → Imai 2010 - Potential Outcomes Mediation Effects and Sequential Ignorability
• Need how this compares with Pearl, Robins, Petersen, Rubin? → Imai 2010 - Identification Compared with Pearl Robins and Principal Strata
• Need Baron-Kenny as a causal estimator, interaction, or estimators and variances? → Imai 2010 - LSEM Baron-Kenny Interaction and Estimation
• Need the $\rho$ sensitivity analysis, Theorem 4, Corollary 1, $R^2$ forms or nonparametric bounds? → Imai 2010 - Sensitivity Analysis with Error Correlation Rho
• Need Tables 1-3, Figs. 1-2 or the Monte Carlo study? → Imai 2010 - Media Framing Application and Simulation
• Need a Bayesian PyMC sketch for marketing halo effects (E35) or the paper’s limitations? → Imai 2010 - Bayesian Mediation Sketch for Halo Effects

Concept Map

Concept	Note	Type	Depends On	Key Result
ACME / natural direct effect	Imai 2010 - Potential Outcomes Mediation Effects and Sequential Ignorability	definition	Potential Outcomes Framework	$\tau =\delta (t)+\zeta (1-t)$
Sequential ignorability	Imai 2010 - Potential Outcomes Mediation Effects and Sequential Ignorability	definition	randomised $T$ + ignorable $M	T,X$
Theorem 1	Imai 2010 - Potential Outcomes Mediation Effects and Sequential Ignorability	theorem	Asm. 1	ACME nonparametrically identified
Identification comparison	Imai 2010 - Identification Compared with Pearl Robins and Principal Strata	concept	Thm 1	trade-off: post-treatment confounders vs no-interaction
Theorem 2 (LSEM)	Imai 2010 - LSEM Baron-Kenny Interaction and Estimation	theorem	Thm 1	ACME $={\beta }_2\gamma$
Assumption 2	Imai 2010 - LSEM Baron-Kenny Interaction and Estimation	definition	Thm 2	$\bar{\delta }(1)=\bar{\delta }(0)$
Theorem 3	Imai 2010 - LSEM Baron-Kenny Interaction and Estimation	theorem	Eq. 18	asymptotic variance of NP estimator
Theorem 4	Imai 2010 - Sensitivity Analysis with Error Correlation Rho	theorem	Thm 2	$\bar{\delta }={\beta }_2\frac{{\sigma }_1}{{\sigma }_2}\{\tilde{\rho }-\rho \sqrt{(1-{\tilde{\rho }}^2)/(1-{\rho }^2)}\}$
Corollary 1	Imai 2010 - Sensitivity Analysis with Error Correlation Rho	theorem	Thm 4	$\rho \in (-1,1)$, ACME $\in (-\infty ,\infty )$
Media framing results	Imai 2010 - Media Framing Application and Simulation	example	Thms 2,4	ACME $-0.51$; sign holds unless $\rho <-0.68$
Bayesian halo sketch	Imai 2010 - Bayesian Mediation Sketch for Halo Effects	example	Eq. 20	counterfactual propagation from posterior draws

Notes

• Imai 2010 - Causal Mediation Analysis - Overview — CONTAINS: research question, contributions, Source Map, E35 link, worked example.
• Imai 2010 - Potential Outcomes Mediation Effects and Sequential Ignorability — CONTAINS: Def. ACME/NDE/total; Asm. 1; Thm 1 and Appendix A proof; discrete-$M$ formula; binary example; Python.
• Imai 2010 - Identification Compared with Pearl Robins and Principal Strata — CONTAINS: Sec. 3.3 table: Pearl (6)-(7), FRCISTG (8)-(9), Petersen (10), Hafeman, Rubin principal strata, Sobel.
• Imai 2010 - LSEM Baron-Kenny Interaction and Estimation — CONTAINS: Eqs. 11-20: BK model, Thm 2 + proof, Asm. 2, interaction model, Delta/Goodman variances, NP estimators, Thm 3, Python.
• Imai 2010 - Sensitivity Analysis with Error Correlation Rho — CONTAINS: Eq. 24, Thm 4 + proof, Cor. 1, Appendix C, $R^2$ interpretation, nonparametric bounds (Eq. 29), simulation check, Python.
• Imai 2010 - Media Framing Application and Simulation — CONTAINS: Sec. 2, 4.3, 6: Tables 1-3, Figs. 1-2, Monte Carlo design and Table 2, Python.
• Imai 2010 - Bayesian Mediation Sketch for Halo Effects — CONTAINS: Sec. 7 limitations; mapping to Meta-search halo; PyMC NB sketch; Bayesian sensitivity.

Sources

• Imai Keele Yamamoto 2010 - Identification Inference and Sensitivity Analysis for Causal Mediation — Imai K, Keele L, Yamamoto T (2010), Stat. Sci. 25(1): 51-71, arXiv:1011.1079; 21 pp. Sole source. (Substituted for the suggested Imai-Keele-Tingley 2010 Psych. Methods paper, which has no stable open copy found.)

See Also

• Cinelli Hazlett 2020 - Making Sense of Sensitivity - Overview — OVB-style sensitivity for regression.
• Instrumental Variables and Principal Stratification, Potential Outcomes Framework, DAGs and Causal Identification, Sensitivity Analysis in Observational Studies.