Comparing the magnitude of two different associations (same IV, different DV, from same dataset/sample)

#1
Hallo,

I'm wondering if there is a way to compare the magnitude of two different associations, each with the same predictor variable (and covariates) but different dependent variables. To give a (fictional) example:

Imagine that I have some survey data in which participants were asked how much they liked cats (scale of 1 to 10), how much chocolate they ate (grams per month), how much orange juice they drank (litres per month), and some covariates (age and gender).

First I want to see if liking cats is cross-sectionally associated with eating chocolate. To do that, my plan is to run a multiple linear regression including liking cats, eating chocolate, and the covariates. [Apologies if I've already gone wrong at this step!]

I also want to see if liking cats is associated with drinking orange juice. To do that, my plan is to run a regression including liking cats, drinking orange juice, and age and gender. So the same model, except this time with orange juice instead of chocolate as the dependent variable.

Finally (the focus of my question), I want to see if liking cats is *more strongly* associated with eating chocolate than it is with drinking orange juice.

Is there a way to do that?

My idea was to compare standardised regression coefficients for each (cats*chocolate and cats*orange juice) - however I'm not sure if this is valid at all (ie to note that one is larger than the other), and even if it is, I'm not sure how to test for a statistical difference between the two.

This seems to be easily done with correlation coefficients, but I can't find a clear explanation as to whether it's feasible, and if so how to do it, with regression coefficients (or some other way to do it when you want to include covariates). Is it doable? Or is there another analysis to find out if the effect there is a difference in the magnitude of the associations?

Apologies if this is a stupid question. Many thanks in advance for any help anyone can give.
 
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hlsmith

Less is more. Stay pure. Stay poor.
#2
How do you know which variable came first? I get this is a toy example, but cross-sectional surveys don't necessarily order variable occurrences.

Yeah, I think historically people would state these are two different models, thus can't be compared. I could be wrong - though I know that I haven't come across this or done it. I wonder if some type of approach like MANOVA could be applicable?
 
#3
How do you know which variable came first? I get this is a toy example, but cross-sectional surveys don't necessarily order variable occurrences.

Yeah, I think historically people would state these are two different models, thus can't be compared. I could be wrong - though I know that I haven't come across this or done it. I wonder if some type of approach like MANOVA could be applicable?
Thanks for the reply.

I don't follow the importance of variable order for this type of analysis, sorry - could you explain?

Thanks - yes I was also wondering if MANOVA, or multivariate regression, might help somehow. I'm not really familiar with either of them but will do some reading.
 

hlsmith

Less is more. Stay pure. Stay poor.
#4
I was referring to whether your dependent variable was actually your DV or if the two DVs could be treated like IVs and you flip it into one model (likes cats = juice + Chocolate).

Is your name a reference to Futurama? If so, awesome!
 
#6
I was referring to whether your dependent variable was actually your DV or if the two DVs could be treated like IVs and you flip it into one model (likes cats = juice + Chocolate).
Ah yes of course, thanks - that makes sense. Yes in the toy example I gave there's just an association and no particular reason to treat liking cats as the IV and eating chocolate as the DV, good point. However in real world examples I am thinking of/would like to apply this to, the hypothesis is that one does precede/influence the other, and not the other way round. Sorry, should have thought of that when coming up with the example.

Is your name a reference to Futurama? If so, awesome!