Subtle but potentially important update to RRPP

[Mike Collyer]

Dear Colleagues,

I uploaded a new version of RRPP to GitHub that corrects a problem, that was thankfully revealed by Carlo Meloro. The bug was subtle and only affected linear models with GLS estimation for which the number of variables (p) exceeds the number of observations (n). This would have impact on procD.pgls in geomorph, for example. The issue was only in the calculation of SS, not the estimation of coefficients. For calculating SS with high-high-diemnsional (p > n) data, it makes sense to project data on the n - 1 possible principal components (PCs) of the data, which makes computation faster over many permutations. SS calculations follow coefficient calculations, which are performed on GLS-transformed data (not PCs). Therefore, the criterion was if p > n, reduce the transformed data to n - 1 dimensions. However, this produces slightly different results than first reducing the untransformed data to n - 1 PCs and then transforming the PC projections.

Although this should be an obvious problem, it evaded checks using other software, which requires univariate data or (n > p). I believe it was introduced, incidentally, with RRPP 2.0.

If it sounds like I am describing an analytical situation similar to one you might have, please update RRPP. Unfortunately, this issue does not cause any errors. Of course, re-installing RRPP or geomorph from Github every now and then is just a good practice to be most up to date.

Regards!
Mike