Propose making mediation and moderation notebooks more causal

[drbenvincent]

I propose moving the Bayesian mediation analysis and Bayesian moderation analysis notebooks from the Case Studies section to the Causal Inference section of the docs.

Both notebooks would be heavily edited to incorporate more of a causal flavour. Important changes could include:

• need to express caution over unobserved confounding variables
• coverage of the kinds of tests you can do (e.g. implied independence or conditional independence from the causal DAG structure)

This would also help trim down the bloat of the currently rather large size of the Case Studies section.

Definitely open to recommendations or feedback about this idea.

Plans for Moderation notebook updates [update 2024 May 13th]

• Add in the introduction that we will make a distinction between statistical and causal ideas.
• Clarify that we are focussing on observational data and don't consider experimental/interventional approaches
• We currently have a “statistical” diagram, but we should add a causal DAG
• Discuss the DAG. If this is our entire causal DAG then we have no real complexities in terms of backdoor paths etc. We can simply collect data and make inferences about the strengths of the causal relationships given the DAG and assumptions (e.g. linearity of relationships).
• ConstantData -> Data nodes in the pymc model
• Clarify that the “Related issues: mean centering and multicollinearity” section comes from the statistical literature
• Definitely bring in insights from Rohrer, J. M., Hünermund, P., Arslan, R. C., & Elson, M. (2022). That’sa lot to process! Pitfalls of popular path models. Advances in Methods and Practices in Psychological Science, 5(2), 25152459221095827.
• Maybe bring in insights from Wu, A. D., & Zumbo, B. D. (2008). Understanding and using mediators and moderators. Social Indicators Research, 87, 367-392.
• Almost certainly add this reference as a good primer for causal thinking with observational data: Rohrer, Julia M. "Thinking clearly about correlations and causation: Graphical causal models for observational data." Advances in methods and practices in psychological science 1.1 (2018): 27-42.
• Another useful resource: Rohrer, J. M., & Arslan, R. C. (2021). Precise answers to vague questions: Issues with interactions. Advances in Methods and Practices in Psychological Science, 4(2).
• Check updates to style guide

[drbenvincent]

It will presumably break any external inbound links because of the URL change.

[OriolAbril]

It will presumably break any external inbound links because of the URL change.

It should not be the case. We already have "rediraffe" extension set up, so we should add the "path movement mapping" to https://github.com/pymc-devs/pymc-examples/blob/main/examples/conf.py#L155 for sphinx to set up redirects automatically