procD.pgls - Warning message: Singular phylogenetic covariance matrix. Proceed with caution

[Sergio Ferreira Cardoso]

Dear all,

I'm getting a warning message with the comparative methods.

> procD.pgls(shape ~ log(cs), phy = phy, data = gdfPGLS, iter = 9999, RRPP = FALSE,print.progress = FALSE)

Call:
procD.pgls(f1 = shape ~ log(cs), phy = phy, iter = 9999, RRPP = FALSE,      data = gdfPGLS, print.progress = FALSE)

Type I (Sequential) Sums of Squares and Cross-products
Randomization of Raw Values used
10000 Permutations

           Df         SS         MS     Rsq      F         Z Pr(>F)
log(cs)     1 0.00037645 0.00037645 0.22198 46.791 -0.064039 0.5185
Residuals 164 0.00131941 0.00000805                                
Total     165 0.00169586                                           
Warning message:
In procD.pgls(shape ~ log(cs), phy = phy, data = gdfPGLS, iter = 9999,  :
  Singular phylogenetic covariance matrix. Proceed with caution

Do you know what does this warning mean? Does it mean I have only 1 tree and that I should use a multiPhylo? I tried multiPhylo and it didn't work, as only phylo works.
I did this with a different tree before but I don't understand which could be the difference.

Thanks in advance.

Best regards,
Sérgio Cardoso.

[Mike Collyer]

Sergio,

It is simply a warning message, not an error message.  It means that the phylogenetic covariance matrix is not full rank.  When calculating this matrix, some of the covariances that should be positive are near 0 (maybe because of tree polytomies).

The analysis worked but alerted you that you covariance matrix was singular, just in case that is a surprise.

Mike

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[Sergio Ferreira Cardoso]

Hello Mike,

Thank you for your answer. Well, it's probably due to politomies because all my tips have politomies (several specimens per terminal branch).
I should probably use mean shape per species while using comparative methods with GMM.

Thank you.

Cheers,

Sérgio.

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[Mike Collyer]

Sérgio,

Just so you are aware, if you have a balanced design (same number of tips per species), using species means should give you about the same answer.  We are able to handle singular matrices by using a phylogenetic projection matrix, derived from eigen-analysis.  (The projection matrix has lower rank than the number of tips, and should have rank that is about or exactly the same as the number of species.)  If your design in imbalanced, the result might change.

Normally, PGLS is done with tips equal to the number of species, perhaps using species means.  You have stumbled into a reality that exists but has not been explored, theoretically (although we are in the process of doing that).  If you know what you are doing, you can use weighted species means rather than just means, if imbalance is a concern.  Again, the theoretical justification of this using the permutation procedures we use has not been explored.  But also the polytomy approach you are using has not been explored.  One might argue that using this approach is tantamount to pseudoreplication, as statistical power might increase simply by over-representing species (without really increasing the effect size).

In your case you have a large F but a small effect size (Z) and the effect is not significant.  This is a strange result and makes me wonder if RRPP is actually robust to attempted pseudoreplication.  Regardless, for your empirical results, I’m not sure adding polytomies helped much.

Cheers!

Mike

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[Sergio Ferreira Cardoso]

Hello Mike,

Once again, thank you for your answer. I have an unbalanced design so I will go for the regular arithmetic mean. As I'll compute a mean shape per each species, I don't think weighted means would help a lot (I guess it would be more useful to create a mean shape of the species of a group, given an unbalanced design). In fact I ran the analysis with a brlen=1 (and no politomies) and the result is completely different.

Once again, thank you for your advice and for the clarification about the warning message.

Cheers,
Sérgio.