Skip to main content
Cross Validated

You are not logged in. Your edit will be placed in a queue until it is peer reviewed.

We welcome edits that make the post easier to understand and more valuable for readers. Because community members review edits, please try to make the post substantially better than how you found it, for example, by fixing grammar or adding additional resources and hyperlinks.

Required fields*

9
  • 1
    $\begingroup$ If you are using PCs from a PCA within some other procedure, their origin in PCA is immaterial for significance testing with that other procedure. That is a little contentious, as statistical people don't all agree on whether PCA is a multivariate transformation procedure or model estimation, but I think it is a good first approximation. If that argument is accepted, then your question is just about significance testing in whatever you are doing and covered by any standard account. Do you regard linear regression and PLS as equivalent? You seem unclear which you are using. $\endgroup$ Commented Nov 2, 2013 at 12:13
  • $\begingroup$ @NickCox Thanks, good comment. With PCA, do you think the description (as the first part of "significant" feature selection where the features have covariation) is correct? And for LinReg vs. PLS: I was indeed conflating linear regression for a single variate binary $Y$ variable as equivalent to PLS, but come to think of it, I'm not sure why (I guess I thought minimum square error would also be maximum margin discrimination)-- is it not true? $\endgroup$ Commented Nov 2, 2013 at 21:01
  • $\begingroup$ Sorry, but I don't understand what you are seeking here either from me or from the site. As you say, linear regression does not mean PLS, or vice versa. $\endgroup$ Commented Nov 3, 2013 at 10:16
  • $\begingroup$ 1) I am trying to get a good understanding of what type of significance testing procedure (from start to finish) is used when doing PCA-PLS (sometimes called PLS-DA). This is commonly used in processing metabolomic data (does not really describe the statistical testing). 2) From the Wikipedia article on Partial Least Squares: "it finds a linear regression model by projecting the predicted variables and the observable variables to a new space". I meant performing a linear regression in the transformed space ($PC_1$ and $PC_2$). $\endgroup$ Commented Nov 3, 2013 at 14:19
  • $\begingroup$ I can't say much more. Perhaps you need to ask in some chemometrics forum, so no expert here is biting on this yet. A significance testing procedure for the whole of what you do would need a probability model for the whole of what you do. On the face of it, that would be a lot of work to set up and evaluate. $\endgroup$ Commented Nov 3, 2013 at 16:08