Hi Jie

First, r=0.8 is usually not considered high correlation, more like
undetermined correlation. High correlation would be at least r=0.95 and
very high correlation r=0.99, somewhat depending on the studied effect
and assuming you refer to r as the linear correlation coefficient.

Second, If you want to extract the parts of V1 and V2 that don't
correlate you can e.g. use their respective principal components. But
then again, I'm not really sure I understand the problem. If V1 and V2
(or indirectly A/B/C) correlate it's in their nature to do so and a
direct comparison between the two reveal that they, well, correlates.

Just my 25 cents

/Nils

1st Research Engineer, Ph.D.
CMIV
Linköping University/US
SE-581 85 Linköping
Sweden
Nat : 013-22 89 96
Int : +46 - 13 22 89 96

----- Original Message -----
From: J Zhuang <[log in to unmask]>
Date: Thursday, November 22, 2007 8:17 pm
Subject: [SPM] How to reduce correlations between variables?
To: [log in to unmask]

> Dear SPMers,
>
> I plan to take two variables (V1, V2) as parametric modulators in
> an fMRI
> experiment. The two variables are ratios made from three original
> variables,A, B, and C, i.e., V1 = A/B, V2 = A/C. The correlation
> between B and C is
> not high, r = 0.3, but the correlation between V1 and V2 is very
> high, r =
> 0.8, in which case I can not put V1 and V2 as modulators in a
> design matrix
> together (The modulators should not be highly correlated with each
> other in
> a same model). However, it is my research interest to make a direct
> comparison between V1 and V2 in a same model. Is there a way to
> reduce the
> correlation between V1 and V2 to a quite low level? I have tried to
> mean-correct each original variables (subtract each individual
> item in A, B,
> and C with its goup mean value, respectively), and got a quite low
> correction between V1 and V2, r = 0.2. The thing here is I do not know
> whether the mean-correction has changed the nature of the original
> correlation. Is this kind of transformation acceptable? Can I put
> the three
> original variables, A, B, C, into a model directly, and then make
> furtheranalysis to get V1 and V2? If possible, how to do it? Is
> there any other
> better method to reflect the change from V1 to V2, while avoiding
> the high
> correlation between them?
>
> Any help is greatly appreciated!
>
> Cheers,
> Jie
>