Statistically comparing the strength of two different associations


This is a cross-post of sorts, as I already asked a similar question here on the regression forum - I hope that's OK (if not, apologies, and mods please remove). I will use a different, psychology-focused example here, not asking specifically about regression (as maybe there's a different/better way to do this).

Let's say I'm interested in whether conscientiousness is cross-sectionally associated with some health-related behaviours. I measure conscientiousness, alcohol consumption, cannabis consumption, and some covariates (let's say age and gender). I want to know if conscientiousness (after adjusting for covariates) is associated with each of (separately) alcohol consumption and cannabis consumption. But, assuming it is indeed associated with each of them, I *also* want to know if it is *more strongly associated* with one or the other.

Is there a way to do this - and if so how?

(If it makes a difference - and I'm not sure it does - my underlying hypothesis is that conscientiousness determines alcohol and drug consumption, and not vice-versa).

If I did not want to include the covariates, I could run correlations for conscientiousness*alcohol and conscientiousness*cannabis, and if I understand correctly (perhaps not!), these can be compared straightforwardly. But I am unclear how to do it once I include the covariates and more complicated models/techniques are required.

My idea is to run the same regression twice, albeit once with alcohol in it and once with cannabis in it, and then compare the regression coefficients, or change in R2, across the two models - but I cannot find much info on whether this is a reasonable thing to do and if so how to go about it. Or is there another way to do it (partial-correlations?) - or no way at all? It seems like quite a simple question, conceptually at least, but I am struggling to come up with an analysis that covers it.

Many thanks in advance for any help.
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