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Scaling Issues

One’s first intuition when generating a composite measure of performance across multiple target variables, even if both say use R2 as the metric of interest, is to simply average them. In the case where these target variables are on roughly simmilar scales, that is to say, both similarly predictive in the best and worst cases, this might not be a bad choice. Consider on the other hand though when they are not on the same scale, for example let’s say our target variables are Waist Circumference (inches) and CBCL RuleBreak Syndrome Scale, which for the Elastic-Net Pipeline and with Random Parcellations scored:

Parcellation Waist Circumference (inches) R2 CBCL RuleBreak Syndrome Scale R2
Random 1000 Parcels 0.094893 0.016451
Random 10 Parcels 0.028499 0.007476

The mean R2 in this case is 0.055672 for Random 1000 Parcels and 0.017988 for Random 100 Parcels. The obvious problem is that the score from Waist Circumference (inches) contributes far more to this average score than CBCL RuleBreak Syndrome Scale, which introduces an unintended bias which says that performance predicting Waist Circumference (inches) is more important. Instead, we are more interested in that in this example the 1000 parcel solution does better than the 10 parcel solution in both cases (what we lose in order of magnitude when comparing between only 2 parcellations we re-gain by comparing 100+ parcellations). This issue of target variables having different scales of predictability is one of the main reasons we use Mean Rank as the metric of performance within this project.