Examining a counterfactual using a structural causal model involves three steps. The approach is valid regardless of the form of the model relationships (linear or otherwise).

 - Abduct
Apply abductive reasoning (logical inference that uses observation to find the simplest/most likely explanation) to estimate $u$, the proxy for the unobserved variables on the specific observation that supports the counterfactual.

 - Act
For a specific observation, use the do operator to establish the counterfactual (e.g., m=0), modifying the equations accordingly.

 - Predict
Calculate the values of the output (y) using the modified equations.

Use of SCM to Examine Counterfactuals

Structural equations provide truth values for counterfactuals. Counterfactual reasoning has been formalized for graphical representation. Thus, we can devise algorithms to determine individual outcomes based on a set of characteristics.

University of Michigan - Ann Arbor

The seven tasks the author thinks SCMs accomplish are : 
1. Encoding Causal Assumptions : Allow Transparency and Testability
2. Allows control for confounding and Do-calculus
3. Helps generate algorithms for counterfactuals
4. Mediation analysis and assessment of effects
5. Adaptability, sample selection, validity
6. Allows for missing data
7. Allows causal discovery

7 tasks accomplished by SCM

Pearl, Judea. “The Seven Tools of Causal Inference, with Reflections on Machine Learning.” Communications of the ACM, vol. 62, no. 3, 2019, pp. 54–60., doi:10.1145/3241036.

https://dl.acm.org/doi/pdf/10.1145/3241036

The Seven Tools of Causal Inference, with Reﬂections on Machine Learning

Discerning if assumptions made are plausible, and the necessity of additional assumptions.

Transparency

Allows assumptions to be tested against existing data to gauge their validity.

Testability

As we have seen in discussions, having a graphical representation allows us to find counterfactuals and if possible find ways to control for them.
If the backdoor criterion cannot be applied, we can also use Do calculus.

Control for Confounding and Do-Calculus

Algorithmizing Counterfactuals

Allows identification of mediators. Helps estimate effects - direct or indirect - of variables on one another using counterfactuals and the graphical representation.

Mediation Analysis and Assessment of Effects

Makes model more adaptable. Do-calculus allows for overcoming environmental bias i.e. bridges gaps between study sample and population, by allowing readjustment of learned parameters.

Adaptability, External Validity, Sample Selection

Causal models of 'missingness' allow for determining causal relationships between variables from the semi complete data. When data is complete, these models can generate realistic estimations.

Allows for Missing Data

Multiple methods exist that can be used to determine causal relationships between variables.

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