4 Testing the DAG with causal constraints

This chapter covers

Using d-separation to reason about how causality constrains conditional independence
Using NetworkX and pgmpy to do d-separation analysis
Refuting a causal DAG using conditional independence tests
Refuting a causal DAG when there are latent variables
Using and applying causal discovery algorithm constraints

Our causal DAG, or any causal model, captures a set of assumptions about the real world. Often, those assumptions are testable with data. If we test an assumption, and it turns out not to hold, then our causal model is wrong. In other words, our test has “falsified” or “refuted” our model. When this happens, we go back to the drawing board, come up with a better model, and try to refute it again. We repeat this loop until we get a model that is robust to our attempts to refute it.

In this chapter, we’ll focus on using statistical conditional independence-based testing to test our causal DAG. As you learn more about the assumptions we can pack into a causal model, and the inferences those assumptions allow you to make, you’ll learn new ways to test and refute your model. The workflow you’ll learn for running conditional independence tests in this chapter can be applied to new tests you may come up with.

4.1 How causality induces conditional independence

4.1.1 Colliders

4.1.2 Abstracting independence with a causal graph

4.2 D-separation and conditional independence

4.2.1 D-separation: A gateway to simplified causal analysis

4.2.2 Examples of d-separating multiple paths

4.2.3 D-separation in code

4.3 Refuting a causal DAG

4.3.1 Revisiting the causal Markov property

4.3.3 Some tests are more important than others

4.4 Caveats with conditional independence testing