Dear Dr. Jombart,<br>Thank you for the link for the DAPC-paper.<br>I found it quite interesting.<br><br>But the question about the formal criterion to determine a number of PC axes that should be retained is still opened.<br>
Maybe it has sense to use the Horn’s Parallel Analysis (see Glorfeld)?<br>It’s already implemented in R package paran by Alexis Dinno, and according to Peres-Neto it performed quite well in comparative tests with other criteria.<br>
<br>But the big disadvantage of PA is its speed - even with 500 iterations it's slow.<br>And maybe it's too conservative.<br>Taking example from your paper: for the island model (a) PA retained only 25 principal components (around 77,5% of variance). And with it, observed proportions of overall correct assignment and correct assignment per group are higher then in the example (with 100 PCs retained).<br>
<br> library(adegenet)<br> library(paran)<br> data(dapcIllus)<br> attach(dapcIllus)<br> <br> dim <- paran(a@tab, iterations=500, centile=95, graph=TRUE)<br> clust.a_PA <- find.clusters(a, n.pca=dim$Retained, n.clust=6)<br>
dapc.a_PA <- dapc.genind(x = a, pop = clust.a_PA$grp, n.pca=dim$Retained, n.da = 5)<br> <br> summary(dapc.a_PA)<br> scatter.dapc(dapc.a_PA)<br><br><br>Well, I almost sure that you already thought about the dimension-reduction problem.<br>
Anyway criterion choice is up to researcher.<br><span style="color: rgb(102, 102, 102);"><br>
</span>Best regards,<br>Vladimir<span style="color: rgb(102, 102, 102);"><br></span><br><br>References:<br><br>Glorfeld L.W. An Improvement on Horn's Parallel Analysis Methodology for Selecting the Correct Number of Factors to Retain // Educ Psychol Meas. 1995. V. 55. № 3. P. 377-393.<br>
<br>Peres-Neto P.R., Jackson D.A., Somers K.M. How many principal components? stopping rules for determining the number of non-trivial axes revisited // Comput Stat Data An. 2005. V. 49. № 4. P. 974-997.<br><span style="color: rgb(102, 102, 102);"><br>
<br>--</span><br><font style="color: rgb(102, 102, 102);" color="#888888">Vladimir Mikryukov<br>
</font><span style="color: rgb(102, 102, 102);">PhD student</span><br style="color: rgb(102, 102, 102);">
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<span style="color: rgb(102, 102, 102);">Institute of Plant & Animal Ecology UD RAS,</span><br style="color: rgb(102, 102, 102);">
<span style="color: rgb(102, 102, 102);">Lab. of Population and Community Ecotoxicology</span><br style="color: rgb(102, 102, 102);"><span style="color: rgb(102, 102, 102);">[8 Marta 202, 620144, Ekaterinburg, Russia]</span></font></font></font></font></font><br style="color: rgb(102, 102, 102);">
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