GitHub

Getting Started

We will show the basic usage of this package via directed acyclic graphs (DAGs).

Constructing a graph

Let's build a DAG with a confounder A that affects both X and Y, and a mediator M between X and Y:

using CausalStructures
using CairoMakie
using Sugiyama

dag = DAG("A --> X + Y, X --> M --> Y")
DAG with 4 nodes and 4 edges:
  nodes: A, M, X, Y
  edges:
    A --> X, A --> Y, X --> M, M --> Y
Validation on construction

All graphs you construct are validated on construction to be a valid graph according to your graph class. For a DAG this means all edges are directed edges (-->), and there are no cycles. Let's try to create a DAG with a cycle:

julia> invalid_dag = DAG("A --> B --> C --> A")
ERROR: ArgumentError: Invalid DAG:
  - directed cycles are not allowed in DAG

Since, a picture is worth a thousand words[1] let's plot our DAG:

plot(dag)

For more plotting details and customization options, see the Plotting guide.

Testing conditional independence

A central question in causal inference is whether two variables are conditionally independent. For DAGs, this is determined using d-separation.

Are X and Y independent?

d_separated(dag, :X, :Y)
false

No, there is a directed path X --> M --> Y.

If we condition on the mediator M, does that make them independent?

d_separated(dag, :X, :Y, :M)
false

Still no, the backdoor path via A: X <-- A --> Y remains open.

What if we condition on both A and M?

d_separated(dag, :X, :Y, [:A, :M])
true

Yes, now all paths are blocked.

Finding adjustment sets

Now suppose we want to estimate the causal effect of X on Y. The backdoor path X <-- A --> Y introduces confounding bias, so we need to block it by conditioning on a valid adjustment set.

Let's find one automatically:

adjustment_set(dag, :X, :Y)
1-element Vector{Symbol}:
 :A

We can also verify that a specific set is valid:

is_valid_adjustment(dag, :X, :Y, :A)
true

And enumerate all minimal valid adjustment sets:

all_adjustment_sets(dag, :X, :Y)
1-element Vector{Vector{Symbol}}:
 [:A]

In this case, {A} is the only minimal set that blocks the confounding.

Next steps

This small quick guide barely scratched the surface of what you can do with this package:

  • 1Especially with causal graphs