When one conduct a Canonical correlation analysis many function are extracted (the lower data set n) the First function has high correlation and contribute much to the variation. While the other have very low contribution. Can the researcher select the function who sum 90 percent variance.
See a statistical consultant at your university for a suggestion on doing your research. That person should be available to help you with that question.
Hello Abdulmuhsin,
Canonical correlation analysis (CCA) is not designed to maximize the variance accounted for within and across the two sets of variables. Instead, it generates roots/functions (up to k - 1, where k is the smaller of the number of variables in the two variable sets) that have the strongest possible linear associations between the composite variates represented by the roots. So, extracting roots until 90% of variance is accounted for seems like an odd criterion to apply in CCA.
You are correct in noting that the first extracted root/function always captures the largest amount of explained variance (this is true in a number of methods, including factor analysis, principal component analysis, discriminant analysis/manova). As subsequent roots have to be contrived so as to be independent of previously generated roots, they will continue to account for successively lower amounts of explained variation.
I agree with Professor Booth that you would likely be well served by consulting with someone at your institution with statistical expertise. It may be the case that a different approach or implementation would better help to address your research aims.
Good luck with your work.
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