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I'd like to illustrate my objective with an example:

Imagine we have collected data on the height, weight, and level of sports activity (represented as either a continuous or categorical variable) from a sample of approximately 100 individuals.

It's expected that weight and height will show some correlation. However, my goal is to comprehend the extent to which sports activity influences this correlation. My hypothesis is that highly active individuals might exhibit a different correlation compared to those who are less active, or vice versa.

While the example is straightforward, it aptly conveys the essence of what I aim to achieve.

I suspect that structured equation models, moderation analysis, or even graph theory might provide insights into addressing these questions.

I came across this link: link to Stack Exchange question, but I'm uncertain if this is the most suitable approach for my specific problem.

Any recommendations would be greatly appreciated.

Thank you in advance for your valuable insights.

Michele Scandola
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Your hypothesis:

My hypothesis is that highly active individuals might exhibit a different correlation compared to those who are less active, or vice versa.

is precisely the one addressed by moderation. I see no reason you would need more than that.

SEM is usually used when at least some of the variables are latent and measured by several variables.Graph theory also seems inapplicable.

Peter Flom
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  • Thank you very much for your prompt answer. I generally read of articles where they analyse the impact of a single moderator. What would happen if I have multiple moderators, such as eating behaviour, depression, ethnicity, sex, etc? – Michele Scandola Sep 15 '23 at 14:45
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    Graph theory does not seem applicable per se, especially the classic topics such as canonical isomorphism and planarity. Moderation analysis can be viewed from the perspective of Pearl's do-calculus which leverages a graph representation of the causal relationships between variables. Moderation analysis has been justified (retroactively I suspect) by do-calculus, so there is some applicable graph theory. – Galen Sep 15 '23 at 14:47
  • @MicheleScandola For multiple moderators I would draw the structural causal model and apply do-calculus to deduce what valid adjustment sets exist for the causal estimand of interest. – Galen Sep 15 '23 at 14:49
  • The simplest thing for mutliple moderators is to use multiple interactions. – Peter Flom Sep 15 '23 at 18:27