- "to deconfound two variables X and Y, we need only block every noncausal path between them without blocking or perturbing any causal paths" (2018, Pearl, p. 158)
- on page 157-162, Pearl gives an overview of the rules and follows the explanation with examples


University of Michigan - Ann Arbor

Here is an example of how the collaboration between students, over the last semester, helped the class learn difficult concepts, which were not clearly explained in two of the required textbooks of the course: An Introduction to Statistical Learning (ISL) and The Book of Why (TBW):
We started with ISL, where we learned regression analysis and dimensionality reduction methods like PCA, shrinkage, step-wise, ... Then, we continued with TBW that clearly explains how to identify "confounders," "colliders," and "mediators," but very superficially explains how to deconfound a confounder. 

Initially, a student created a node that states, based on TBW, that in regression models, one should control for confounders. But TBW doesn’t say how to control for confounders.

So a different student linked that node to a node that previously been created, based on material in the ISL textbook. That linked node explains how to control for an independent variable in a regression model.

Two other students took the idea that we should not include "colliders" and "mediators" in our regression models that they learned from TBW and drew links between this reasoning and the cluster of dimensionality reduction methods taken from ISL. They explained that the dimensionality reduction methods only make sense for the purpose of prediction and classification where we care about improving the prediction accuracy. For causal inference, these methods fail and we should employ causal diagrams and the procedures explained in TBW to identify "confounders," "colliders," and "mediators;" and only include confounders, but never "colliders" or "mediators," in our regression model.

Later on, other students further completed these explanations and links, based on TBW, by reasoning for why common methods that are usually advised by statisticians and economists to "control for as many variables as possible" and "use dimensionality reduction methods" fail in causal inference, as they may open back-door paths and introduce new confounders in our analysis.

Collaboratively Learning Deconfounding in Causal Inference on 1Cademy

Pearl, J., & Mackenzie, D. (2018). $\mathit{The \ Book \ of \ Why: \ The \ New \ Science \ of \ Cause \ and \ Effect.}$ Basic Books.

The Book of Why

- "Why not controll for a descent of x?"
- "Controlling for everything is misguided"
- Explanations of the games discussed in the book

Specific Nodes that were Helpful in Learning Deconfounding

Explanations from "The Book of Why" About Deconfounding

These interactions with the students showed that the system has allowed students to create connections between the two books. The system allowed them to compare the overlapping concepts between the two books and think critically about the distinctions and usages of the concepts. 

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