Use the link method twice to connect the data from African nations (continent 1 and continent 2). Subtract the results to get the extended difference of log GDP.

How to Build this Model

There is no raw data here. We are just building the model with existed models, then compared the difference. 
Although there might be a deeper reason for the log GDP in Africa, the association between log GDP and ruggedness might help us to come up with some methods to improve current situation.

Why We Say this Model is "Counter-factual"

In this model, we can see the PI is no longer 95%. Instead, it is 97%, which means we are talking about Bayesian statistics, and the posterior probability has changed.

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Thinking about how the symmetry is broken can be productive. It would help us to compare the interaction between two choices when we miss other information.

Symmetry of Interactions

McElreath, R. (2020). Statistical Rethinking: A Bayesian Course with Examples in R and STAN (2nd ed.). Chapman and Hall/CRC.

Statistical Rethinking: A Bayesian Course with Examples in R and STAN (2nd edition)

Example: Use Bayesian Methods to Find the Association between Ruggedness and log GDP of Nations in Africa

Simple interactions being symmetric indicates that the association between X1 and Y depends upon X2 just as much the association between the X2 and Y depends upon X1. When we reason casually about models, our mind usually prefers one of these interpretations over the other, but both of these interpretations are true. A continuation of the Africa example is shown below to demonstrate this concept.

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