Dear Lv, you're right that analysing PCs of Procrustes shape coordinates one at a time is not a good idea. There will be very few cases (if any) when a single PC is a good summary of multivariate shape. In association studies, it is much more appropriate to look for the direction that maximizes covariation (with other variables) in the full multivariate space (multivariate regression, PLS etc.). PCs know nothing about covariates, as they just maximize total variance: they may or may not pick up some variation in the 'right' direction (the one where most covariation is), but are at best sub-optimal and more often inappropriate and misleading.
A few refs, in which you'll find more refs to older but more important papers: Adams D.C., Cardini A., Monteiro L.R., O’Higgins P., Rohlf F.J., 2011. Morphometrics and Phylogenetics: principal components of shape from cranial modules are neither appropriate nor effective cladistic characters. Journal of Human Evolution , 60: 240–243. Cardini A., 2020. Modern morphometrics and the study of population differences: good data behind clever analyses and cool pictures? Anatomical Record, 303: 2747–2765. DOI: 10.1002/ar.24397 Pdfs should be available in my webpage. All the best Andrea On 03/05/2022, lv xiao <[email protected]> wrote: > Dear all, > > I have the impression over the years that principal component scores of > shape along each axis after PCA cannot be analysed separately as if each > were idependent traits. However, I still come across such papers from time > to time (Fig 3 in R. Soc. open sci. 6: 181382; Fig 4 in PLoS Genet > 12:e1006174.). > > I would like to ask whether shape PC scores (like PC1 scores for all > specimens) could be used to investigate the association between explanatory > > variables and shape changes along that PC? > > If it is not possible, why and is there any references? Thanks. > > Lv > > -- > You received this message because you are subscribed to the Google Groups > "Morphmet" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To view this discussion on the web visit > https://groups.google.com/d/msgid/morphmet2/080177d0-e803-4857-a950-74edfae53b54n%40googlegroups.com. > -- E-mail address: [email protected], [email protected] WEBPAGE: https://sites.google.com/view/alcardini2/ or https://tinyurl.com/andreacardini -- You received this message because you are subscribed to the Google Groups "Morphmet" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/morphmet2/CAJ__j7OP%3DHRF2E9oDDLEGqtutmmaTMKHiAwHMOkgx-H5sBrRqg%40mail.gmail.com.
