Questions on rCCA Functionality in mixOmics

Support
1

Dear mixOmics Development Team,

Thank you for developing the mixOmics package. The rCCA functionality has been incredibly helpful in my research. However, I have a few basic questions I hope you can assist with, as my mathematical understanding is somewhat limited:

1. Obtaining ( R^2 ) and Adjusted ( R^2 )

Is it possible to calculate ( R^2 ) or adjusted ( R^2 ) for the overall rCCA model? These metrics are often used in traditional CCA to quantify the model’s explanatory power, but I couldn’t find a direct way to extract them in mixOmics.

2. Testing Model and Canonical Variate Significance

How can I assess the significance of the rCCA model and individual canonical variates? For example:

  • Are there built-in methods for testing the reliability of the model (e.g., permutation or bootstrap)?
  • Can I test the significance of canonical correlations or individual variable contributions?

3. Examples or Tutorials

Given my concerns about model reliability and interpretation, could you kindly share any practical examples or tutorials that demonstrate how to evaluate the robustness and significance of an rCCA model? This would greatly help users like me who are less mathematically inclined but eager to use the tool correctly.

Thank you again for creating such a powerful and versatile tool. I greatly appreciate your work and look forward to your advice on these questions.

Best regards,
Zhaopeng Lv

2

hi @lvzhaopeng,

  1. Obtaining ( R^2 ) and Adjusted ( R^2 )

Not really in our package. For large datasets we use rCCA and I am not sure if these metrics would be relevant.

You can have a look at this paper:
González I, Déjean S, Martin P, Gonçalves O, Besse P, Baccini A: Highlighting relationships between heteregeneous biological data through graphical displays based on regularized Canonical Correlation Analysis. J Biol Syst. 2009, 17 (2): 173-199. 10.1142/S0218339009002831.
from the original authors of the method (Ignacio has left the team unfortunately).

  1. Testing Model and Canonical Variate Significance

This would require a bit of coding, but you could recalculate the predicted variates based on a test data set (this is pretty much what is done in the tuning function of rcca in this example, or permute the data and calculate the canonical correlation for a permutation test. None of this is implemented in mixOmics though as we consider rCCA as an exploratory tool.

  1. Examples or Tutorials
    Beside the examples we have on our website, we also have a chapter in our book dedicated to rCCA where we present the method and an example similar to the website.