Causal Inference Primer — Beyond Correlation

The single biggest leap from analytics to data science. Correlation ≠ causation, and how to reason about WHY. FIND_VIDEO: search 'causal inference confounders DAG' — recommended channel: StatQuest / 3Blue1Brown. Aim for 11 min or under.

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Key moments

Ladder Introduction — The discussion begins with a question about Judea Pearl's ladder of causation: association, intervention, and counterfactual.
Causal Modeling Difficulty — A common confusion is noted: effective causal modeling seems to require prior knowledge of the expected outcome.
Process vs. Data — Causality asks you to model the data generating process and state assumptions, rather than just manipulating the data itself.
Rung 1: Association — Level one is defined as plain old vanilla statistics and correlation.
Rung 2: Intervention — Level two involves asking 'what if' questions, such as emulating an experiment to determine causal effect.
Rung 3: Counterfactual — Level three questions imagine what might have been different, conditioning on observed facts that contradict the hypothetical.
Defining Counterfactual — A counterfactual is defined by the conflict between the hypothetical condition or outcome and the data actually observed.
Role of DAGs — Answering causal questions requires additional causal assumptions, which can often be specified using a Directed Acyclic Graph (DAG).
Beyond DAGs — More complex questions require assumptions beyond DAGs, such as assuming monotonicity in the relationship between variables.

PDF notes

Bottom line: You will be able to distinguish between the three levels of causal inference, moving beyond simple correlation to understand intervention and counterfactual reasoning. You will learn that effective causal modeling requires explicitly stating assumptions about the underlying data generating process, often using tools like Directed Acyclic Graphs (DAGs).

This lesson on Causal Inference Primer — Beyond Correlation is hands-on and example-driven. You will be able to distinguish between the three levels of causal inference, moving beyond simple correlation to understand intervention and counterfactual reasoning. You will learn that effective causal modeling requires explicitly stating assumptions about the underlying data generating process, often using tools like Directed Acyclic Graphs (DAGs).

What You'll Be Able To Do

Differentiate the three rungs of Judea Pearl's ladder of causation.
Explain why causal inference requires modeling the data generating process, not just the data.
Formulate an intervention question suitable for the second rung of causation.
Identify the additional conditioning required for a level three counterfactual question.
Specify the role of a Directed Acyclic Graph (DAG) in defining causal assumptions.

Topics Covered in Causal Inference Primer — Beyond Correlation

Ladder Introduction (0:00 - 0:30) — The discussion begins with a question about Judea Pearl's ladder of causation: association, intervention, and counterfactual.
Causal Modeling Difficulty (0:30 - 1:15) — A common confusion is noted: effective causal modeling seems to require prior knowledge of the expected outcome.
Process vs. Data (1:15 - 2:45) — Causality asks you to model the data generating process and state assumptions, rather than just manipulating the data itself.
Rung 1: Association (2:45 - 3:15) — Level one is defined as plain old vanilla statistics and correlation.
Rung 2: Intervention (3:15 - 3:45) — Level two involves asking 'what if' questions, such as emulating an experiment to determine causal effect.
Rung 3: Counterfactual (3:45 - 5:00) — Level three questions imagine what might have been different, conditioning on observed facts that contradict the hypothetical.
Defining Counterfactual (5:00 - 5:45) — A counterfactual is defined by the conflict between the hypothetical condition or outcome and the data actually observed.
Role of DAGs (5:45 - 6:30) — Answering causal questions requires additional causal assumptions, which can often be specified using a Directed Acyclic Graph (DAG).
Beyond DAGs (6:30 - 7:00) — More complex questions require assumptions beyond DAGs, such as assuming monotonicity in the relationship between variables.

SQL Cheat Sheet

Association (Rung 1) — Plain old statistics and correlation land
```
SELECT CORR(A, B) FROM data;
```
Intervention (Rung 2) — Asking 'what if' questions about potential actions
```
SELECT outcome FROM experiment WHERE action = 'vaccinate';
```
Counterfactual (Rung 3) — Imagining what might have been different given observed facts
```
SELECT outcome FROM observed_data WHERE NOT action AND outcome;
```
Data Generating Process — The underlying mechanism creating the observed data
Causal Assumptions — Explicit statements required to move up the hierarchy
```
SELECT * FROM assumptions_table WHERE level = 3;
```
DAG (Directed Acyclic Graph) — Visual tool to specify some causal assumptions
```
SELECT * FROM graph_nodes WHERE type = 'cause';
```

Comparison Table

Level	Question Type	Required Assumptions
Level 1 (Association)	What is the correlation?	Vanilla statistics
Level 2 (Intervention)	What if I do X?	Causal effect assumptions
Level 3 (Counterfactual)	Would Y have happened?	Conditioning on observed facts

Common Pitfalls

Mistake: Treating correlation (Rung 1) as proof of causation (Rung 2). Avoid: Explicitly state assumptions about the data generating process before modeling.
Mistake: Confusing an intervention question with a counterfactual question. Avoid: Rung 3 questions condition on observed facts that conflict with the hypothetical.
Mistake: Focusing only on manipulating the data itself (transforms). Avoid: Causal modeling requires stating assumptions about the underlying generating process.
Mistake: Believing you must know the answer before running any analysis. Avoid: Causal modeling asks you to state assumptions, not know the final outcome.

FAQs

What is the difference between Rung 2 (Intervention) and Rung 3 (Counterfactual)? Rung 3 is Rung 2 plus conditioning on observed facts that contradict the hypothetical action or outcome. It asks what might have been, given what is.
Why is causal modeling harder in industry than in academia? In industry, data scientists often have less control over how the data is collected. This makes it challenging to model the data generating process effectively.
What makes a counterfactual question 'counterfactual'? The hypothetical condition (e.g., taking the vaccine) or the hypothetical outcome conflicts with data that was actually observed.
Can a DAG specify all necessary causal assumptions? No. While DAGs specify structure, additional assumptions about mechanism, like monotonicity, are often required for complex questions.

Common pitfalls

Mistake: Treating correlation (Rung 1) as proof of causation (Rung 2). Avoid: Explicitly state assumptions about the data generating process before modeling.
Mistake: Confusing an intervention question with a counterfactual question. Avoid: Rung 3 questions condition on observed facts that conflict with the hypothetical.
Mistake: Focusing only on manipulating the data itself (transforms). Avoid: Causal modeling requires stating assumptions about the underlying generating process.
Mistake: Believing you must know the answer before running any analysis. Avoid: Causal modeling asks you to state assumptions, not know the final outcome.

Let's jump now into some of the audience questions. We've got one here from Dr. Doug McLane. He's got a PhD in applied math and works as the lead data scientist at a food company in the UK called Greggs, which is famous for its delicious pastries. Though uh they have lots of other foods as well. But uh anyway, uh so Doug, technical guy, he's got a good technical question here. He says, could you make sure Robert comments on Judea Pearl's ladder of causation? So rung one is association. Rung two is intervention (doing). And rung three is counterfactual. Um and so there's some terms there that you might you mentioned counterfactual uh in some of your other responses but you might need to uh dig into the definition of that a bit for our audience. And so the reason why he's asking you to comment on this ladder of causation, again, rung one is association, which I think is kind of like correlation. Rung two is intervention, so the kind of uh, you know, being able to make some assumptions about causal effect. And then rung three is counterfactual. He says, to be blunt, I'm really stumped when it comes to causal modeling. It seems you need to know what to expect first before running any analysis. Um, so he's I I guess he's kind of basically saying here that, you know, to like these kinds this ladder of causation or the way that you set up causal models, there seems to be like often to set up the model effectively, you already have to have some understanding of what's going on and that he finds that confusing. Yeah, and so, uh to answer that last point directly is that, you know, I'd say that you want to model, I think oftentimes the way that people are trained to think about data, uh particularly again in industry where we unfortunately often have less control over how the data is collected. Um, so causality is kind of asking you to think more about the data generating process than the data. And so when you don't actually have control over that process, it can get a little bit frustrating because it's, you know, it's kind of out of your hands, right? And but, you know, so typically we kind of get some data set, we're thinking about like, okay, well, you know, what are the transforms I should apply to this, which, you know, how should I maybe I should discretize this, maybe I should apply a log transform to that. Right? And so we're thinking directly in manipulating the data to make it more amenable to the models that we want to use. And causality is saying like, you know, data aside, you need to tell me what your assumptions are about the underlying data generating process. So, now going into the causal hierarchy. Uh I I go into it very extensively in the book, I'd say probably more so than any other book. Um the, you know, and so we're really, you know, so again at level one of association, we're just kind of in kind of plain old vanilla statistics and correlation land. Um and then level two intervention, uh this this is, you know, this is what we've been we're talking about say with when we're trying to emulate a an experiment, when we're asking what if questions, like what if I were to uh take this vaccine, would it prevent me from getting sick? And then and then the level three is uh is counterfactuals and here we're asking questions where we're imagining what might have been different. Uh so say for example, I didn't get vaccinated and I got sick, would I have gotten sick had I uh been vaccinated? So this is actually the same as kind of level two, which is say, what if, what if I had taken the vaccine? What what if I take the vaccine, would I would I get sick? But now we're going to condition on two, uh two pieces of additional information. The fact that I didn't take the vaccine and the fact that I did get sick having not taken the vaccine. Right? So in what, so in level two, I'm saying, um, uh, uh, I uh, what if I take the vaccine, will I get sick? And level three I'm saying, what if I take the vaccine and what, you know, putting aside tense, putting aside, you know, uh present tense, past tense, say, A, take the vaccine, B, you know, get sick, yes or no. But now we're going to condition, and so that's the same as the first case, but now we're going to condition on two extra things, the facts that we that that had you not, if you that's given not A, that not B happens. Right? And so the counterfact, and the reason we call it a counterfactual is because the, um, the either the hypothetical condition, taking the vaccine, or the hypothetical outcome, getting sick or not, is in conflict with some data that we've actually observed. Um, which just makes it a bit more challenging to model, but at the same time we're just we're still just conditioning on um some some some some extra evidence. Uh, and so, in terms of like, does that what is required to make those types of assumptions, those types of answer those kinds of questions? Requires um very generally speaking, uh some additional causal assumptions. Um, um, some of those assumptions can be specified entirely in the form of a DAG. Uh and then some of them can't often, they're more frankly the more interesting ones can't rely on DAG-based assumptions alone. We need to we need to make additional assumptions about mechanism. Um, but if, you know, him being a a mathematician who understands things like, for example, you might make, you know, so not only that A cause B, which you represent with a graph, but maybe you make the additional assumption that that B is monotonic in A. Right? That's that's for a change in A, uh there's a corresponding uh change in B and it's and it's in that change is constant um or that that that that that change is going one direction no matter where you're at with A. And so like, um uh, you know, so it can so it's it's just asking for more assumptions. Uh but it's not asking you to know the answer, it's just asking you to uh say like, well, you know, for certain questions, you can get away with lesser assumptions. For certain questions, uh you need to make a few more. And so like, you know, we can think about our assumptions as falling out on different levels of the hierarchy, um and and so you can, you know, you might sometimes for some interesting questions, you need to make a level three counterfactual assumptions.

Frequently asked questions

What is the difference between Rung 2 (Intervention) and Rung 3 (Counterfactual)?

Rung 3 is Rung 2 plus conditioning on observed facts that contradict the hypothetical action or outcome. It asks what might have been, given what is.

Why is causal modeling harder in industry than in academia?

In industry, data scientists often have less control over how the data is collected. This makes it challenging to model the data generating process effectively.

What makes a counterfactual question 'counterfactual'?

The hypothetical condition (e.g., taking the vaccine) or the hypothetical outcome conflicts with data that was actually observed.

Can a DAG specify all necessary causal assumptions?

No. While DAGs specify structure, additional assumptions about mechanism, like monotonicity, are often required for complex questions.