Correlation to ratio of two variables from individual correlation.

#1
I am trying to estimate the correlation between three parameters, from some know correlations between some of them.

I know the correlation of two variables Corr(k,1/a), Corr(k,1/(a+b)).

How can I calculate Corr(k, (1/(1-(b/a)))?

Also, if the two known correlations [Corr(k,1/a), Corr(k,1/(a+b)).] are very high, will it be wrong to assume the correlation I want to estimate [Corr(k, (1/(1-(b/a)))] would also be high?
 

hlsmith

Less is more. Stay pure. Stay poor.
#2
I haven't done this before, but I am a little familiar with meta-analyses - where your know the effect of a vs b and a vs c while wanting to know the effect of b vs c. I would imagine assumptions have to be made and SEs a little iffy. Two really strong correlations would be ideal in my mind. Is there also a plausible reason why they are correlated or is it ecological/macro?

@spunky - any input on this.
 

spunky

Doesn't actually exist
#3
If we know Corr(1/a, 1/(a+b)), Corr(1/a, (1/(1-(b/a))) and Corr(1/(a+b), (1/(1-(b/a))) we can work something out. Nevertheless, preliminary simulations show me that these various correlations are very, very, VERY close to 0 even if cor(a,b)=0.9999. If the OP can safely assume them to be 0, we can use the fact that the correlation matrix implied by these variables has to be positive definite to work something out using the equation of the determinant.