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From: Sophia on 18 Apr 2010 14:49
Hello,

I am using canoncorr to compute canonical correlations between two sets of variables, and I have several questions pertaining to interpreting the results in my analysis.

First, how do I evaluate the statistical significance of each canonical root?

Secondly, I'd like to compute the redundancy, for which I need the factor loadings, i.e the correlations between the canonical variates and the variables in each set. I have the canonical correlation coefficents (A, B), the canonical variates (U, V), and the canonical correlations (r). How do I compute the factor loadings?

Thirdly, there are two fields in the stats structure that are not described in the MATLAB doc page for canoncorr: stats.p, and stats.dfe. What do each of these represent? Is p just the p-value, where lower values mean greater significance? If I am getting stats.p = [0 0], should I be happy that my results are significant, and does this mean that both canonical roots are statistically significant?

Thanks,

Sophia
From: Peter Perkins on 19 Apr 2010 11:42
On 4/18/2010 2:49 PM, Sophia wrote:

> First, how do I evaluate the statistical significance of each canonical
> root?

There are two sets of p-values in the Stats output argument, both relating to the sequence of hypothesis tests that I think you care about. See the documentation, or one of the references cited in the doc.


> Secondly, I'd like to compute the redundancy, for which I need the
> factor loadings, i.e the correlations between the canonical variates and
> the variables in each set. I have the canonical correlation coefficents
> (A, B), the canonical variates (U, V), and the canonical correlations
> (r). How do I compute the factor loadings?

Canonical correlation is not factor analysis, but presumably what you mean by "factor loadings" is the coefficients.

> Thirdly, there are two fields in the stats structure that are not
> described in the MATLAB doc page for canoncorr: stats.p, and stats.dfe.

They are not documented becasue they are deprecated. Use the fields containing the statistics for the chi-squared and F tests, as in the documentation.
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