Causal models for qualitative and mixed methods inference

Exercise 4: Mixed methods

Author

Macartan Humphreys and Alan Jacobs

Choose your exercise. If you brought your own data, now please try to Part 1 A otherwise do Part 1 B.

1 Part 1 A: Own data exercise

  1. Define your model
  2. Update your model on your data
  3. Compute a query using posteriors and compare to inferences based on priors
  4. Figure out what inferences you might draw for a case conditional on different within case observations you might observe

see hoop_example

OR:

2 Part 1 B: A hoop test anda smoking gun test justified with data

(60 minutes)

2.1 Hoops

Sometimes we treat the absence of an expected mediator as strong evidence against a proposition. In this exercise we will try to justify a claim of this form:

  1. Define a model in which \(X \rightarrow M \rightarrow Y\) but do not impose any other restrictions
  2. Imagine you saw 20 cases in which \(X\) and \(M\) are very highly correlated and \(M\) and \(Y\) are very highly correlated. Generate data like this and update the model.
  3. Now imagine you saw a case in which \(X=1\) and \(Y=1\). What should you believe about the probability that \(X\) caused \(Y\)?
  4. Now imagine you saw in addition that \(M=1\). What should you believe about the probability that \(X\) caused \(Y\)?
  5. Now imagine you saw instead that \(M=0\). What should you believe about the probability that \(X\) caused \(Y\)?

2.2 Smoking guns

Can you construct another model and background data that lets you treat \(K\) as a smoking gun evidence for the \(X\) causing \(Y\)?

Try to generate a model and data structure that would justify smoking gun inferneces. Demonstrate on an updated model that these inferences are valid.

3 Closing discussion

(30 minutes)