Mediation analysis: Does the "mediation.two_stage_regression" method handle partial mediation?

[ShambaMondal]

In the discussion on mediation analysis
(https://www.pywhy.org/dowhy/v0.12/user_guide/causal_tasks/quantify_causal_influence/mediation_analysis.html), "mediation.two_stage_regression" is used as the only currently available method for estimating the effect.

The description of the estimator
(https://www.pywhy.org/dowhy/v0.12/dowhy.causal_estimators.html#module-dowhy.causal_estimators.two_stage_regression_estimator) says: "Compute treatment effect whenever the effect is fully mediated by another variable (front-door) or when there is an instrument available." (Emphasis on fully)

This case for full mediation seems true for the example shown in the mediation analysis link above, where the DAG represents the relationship: Treatment (T) ---> Mediator (M) ---> Outcome (Y). The only path from T to Y is via M.

My questions are: can I use the same effect estimation method (two stage regression) for mediation analysis -

1. when there is partial mediation? (The DAG would have the paths T ---> M, T ---> Y, and M ---> Y)

and

2. when the treatment variable is binary (0/1) ?

Thank you!

[0trm]

Yes to both. The "fully mediated" line in that docstring is about using the estimator for front-door identification of the total effect. For mediation you choose the estimand, and the natural direct effect is the T -> Y path, so partial mediation is the case it's built for. The graph in the docs example has both paths too.

from dowhy.causal_estimators.linear_regression_estimator import LinearRegressionEstimator

params = {"first_stage_model": LinearRegressionEstimator,
          "second_stage_model": LinearRegressionEstimator}

nie = model.identify_effect(estimand_type="nonparametric-nie", proceed_when_unidentifiable=True)
nde = model.identify_effect(estimand_type="nonparametric-nde", proceed_when_unidentifiable=True)
for estimand in (nie, nde):
    est = model.estimate_effect(estimand, method_name="mediation.two_stage_regression",
                                confidence_intervals=False, test_significance=False,
                                method_params=params)
    print(est.value)

On simulated data with a binary T, the graph W->T, W->M, W->Y, T->M, T->Y, M->Y, a true NIE of 6 and a true NDE of 1.5, this returned 6.05 and 1.49 (n = 20,000). A binary treatment is fine: T only enters both stages as a regressor. The catch is the method. The NIE is the product of the T -> M and M -> Y coefficients, and the NDE is the total effect minus that product (source). That holds when Y is linear in M and T with no T x M interaction. Checked on dowhy 0.14.