7 Dealing with complex graphs

 

This chapter covers

  • A mathematical definition of a causal model
  • Deriving conditional independencies between variables with d-separation
  • Using the back-door criterion to decide which variables to put in the adjustment formula
[Note]  Note

If you are wondering what you will learn regarding the adjustment formula, look at the diagram explained in Chapter 2, here as Figure 7.1. This chapter is the central core of step (5a).

Figure 7.1. Applying the adjustment formula
ch2 map7

We now know that one way to remove the effect of confounders is by using the adjustment formula. But in real-life DAGs, it is not always clear which variables we need to adjust for. Let’s see an example.

7.1 Altering the correlation between two variables conditioning on a third one

7.1.1 Breaking a Causal Model into independent modules

7.1.2 The bricks of DAGs: Factorizing probability distributions

7.1.3 What’s the d-separation about?

7.1.4 Defining d-separation

7.2 Back-door criterion

7.2.1 The importance of the back-door criterion

7.3 Good & Bad Controls

7.3.1 Good Controls

7.3.2 Neutral Controls

7.3.3 Bad Controls

7.4 Revisiting previous chapters

7.4.1 Propensity Score

7.4.2 Linear Models

7.5 Efficient Controls

7.6 An advances tool for identifying causal effects: the do-calculus

7.7 Summary