I am working on analyzing volumetric information extracted from the brain. In particular we would like to compare the strength of effects across three different regions (say x, y, and z). However, the three regions grossly differ in size (say y is 10 times larger than x, and z is 20 times larger than x). We would like to know if these three regions decline differentially with advancing age.
The differences in scale seem to introduce significant regional interactions by themselves. If I take the data from x and simply generate a fake y and z (by scaling x by 10 and 20, call them $y'$ and $z'$) I get significant interactions even though the underlying relationships are identical. This is clear when you look at B weights if you compute separate models for x, $y'$, and $z'$.
This does not appear to be an issue commonly addressed in studies that examine brain volume. Currently we are using partial correlations and then Steiger's Z to compare the effects of age across regions.
- Are there suggestions for dealing with such a problem with a more elegant approach?
- How can we compare the effect of age on brain volume across different brain regions when the regions are of different sizes?