I am learning CCA and I have come across a question that I do not know how to answer. Suppose we have the following 2 sets of variables:
X as psychology traits (control, concept, motivation) Y as academic achievements (read, write, math, science)
And suppose that all variables are real valued numbers, but use different scales:
control: [-1, 1] concept: [0, 100] motivation: [0, 1.0] read: [-9, 9] write: [-9, 9] math: [0, 100] science: [0,100]
If I want to do a CCA analysis on these two sets of variables, do I need to transform each variable into a uniform scale? For example, by scaling all variables into the [0,1] range, before doing the CCA?
The reason I am asking, is that CCA attempts to find the max correlation between two canonical variates CX, CY. And CX CY are each the weighted sum of their variables, and these weights are canonical weights. But if the variables are on different scales (e.g., read and math), would the canonical weights for them still be comparable (e.g., if 'read' has a weight of 0.5 and 'math' also 0.5, should these two values be interpreted the same way?)
Many thanks in advance.