-------- Original Message -------- Subject: Re: Interpreting 2B-PLS results Date: Wed, 27 May 2009 02:25:25 -0700 (PDT) From: Chris Klingenberg <[email protected]> Reply-To: [email protected] Organization: University of Manchester To: [email protected] References: <[email protected]> Dear Claire The difference in the results of the permutation tests comes from the difference in the null hypotheses they use. MorphoJ uses the "global" null hypothesis of total independence of the two sets of variables for all permutation tests, even those of individual singular values and the correlations between pairs of PLS axes. (In the permutations, the entire sets of variables are permuted, the PLS analysis is run in each iteration, and the correlation is computed from the scores.) As far as I can determine, the permutation test for the correlations in tpsPLS uses the more "local" null hypothesis that the pairs of scores are uncorrelated. (Therefore, this is a permutation test just for the bivariate correlation of the scores.) I agree with you that the behaviour of the correlation between the PLS scores is counterintuitive, particularly if the number of variables is approaching the number of specimens (you have 26 variables in each block for the 45 observations). Even if the two blocks of variables are totally independent of each other, you will get high correlation between the scores of the two first PLS axes if your sample sizes are similar to the numbers of variables. See Figure 3 of Mitteroecker & Bookstein (Syst. Biol. 56:818-836, 2007) for a graph showing this behaviour. Accordingly, by taking a sufficient number of semilandmarks for a given sample size, you can more or less guarantee a high correlation of the PLS scores, no matter how the two structures actually covary. My rationale for using the "global" null hypothesis for all the permutation tests associated with PLS analyses in MorphoJ was to avoid declaring singular values or correlations of scores significant in such cases. The cost of this is that even high correlations of scores often are not declared significant. It might be useful to recall that PLS is primarily an exploratory technique. Therefore, perhaps it is not very useful to worry too much whether this or that statistic is significant or not. (This is a little bit like principal component analysis, which has proven a most useful tool in multivariate statistics for over 100 years, but where there is no agreement about how to determine how many PCs should be considered "significant".) Best wishes, Chris morphmet wrote:
On Thu, May 21, 2009 at 12:21 PM, Claire Terhune <[email protected] <mailto:[email protected]>> wrote: Hello all- I need a bit of assistance with interpreting the results of my 2B-PLS analyses. I am looking at the covariance between two curves with the same number of points and specimens (15 2D pts and 45 specimens). I first slid the landmarks in tpsrelw, and then took the aligned coordinates and performed 2B-PLS analyses in tpsPLS and in MorphoJ, simply to compare the results. Generally, the values that both programs return are the same, but I’m unsure of the significance of the results since they seem to differ substantially. In TPS, the observed correlation for dimension 1 is 0.912348, and the permutation test (1000 iterations) indicates that no permuted values exceeded the test value, which (if I am interpreting this correctly) should indicate a p-value of <0.001 for that dimension. In MorhoJ, I get the same general correlation value (0.91225) for the first dimension, but the permuted p-value (also from 1000 iterations) is 0.6290 (although the reported p-value for the singular value for the same dimension is <0.001). Given that the correlation is so high, it would surprise me if the p-value was not significant, particularly since the RV coefficient reported by MorphoJ is 0.7537 with a permuted p-value of <0.001. I must be misinterpreting something here, but I’m not sure what exactly that is, so any help that could be provided would be greatly appreciated! Thanks, Claire -- Claire E. Terhune Ph.D. Candidate School of Human Evolution and Social Change Arizona State University PO Box 872402 Tempe, AZ 85287-2402 [email protected] <mailto:[email protected]>
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