Good afternoon all, I have a question about interpretation of PCs. I have come across several articles in orthodontic literature having to do with morphometric analysis of sagittal cephalograms that discuss warping a Procrustes analysis along a principal component axis. Essentially the authors discuss finding whatever principal components represent shape variance, then determining the standard deviation(s) of those PC's, and applying the standard deviations to the Procrustes shape to warp the average shape plus or minus. So if you have an average normodivergent Procrustes shape, one warp perhaps in the negative direction might give you a brachycephalic shape, while the opposite would give you a dolichocephalic shape. But I don't know where this idea comes from. I have been involved with 8 or 9 morphometrics projects over the last few years and I have never been able to figure this out or the rationale for performing such an application with the PC results.
As an example of what I am talking about here is a passage from the Journal of Clinical & Diagnostic research, doi: 10.7860/JCDR/2015/8971.5458 <https://dx.doi.org/10.7860%2FJCDR%2F2015%2F8971.5458> "Here, the first 2 PCs are shown & the Average shape (middle) was warped by applying each PC by amount equal to 3 standard deviations in negative (left) and positive (right) direction {[Table/Fig-10 <https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4347171/figure/F10/>]: PC1 with standard deviation, [Table/Fig-11 <https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4347171/figure/F11/>] PC 2 with standard deviation}." I did not include the graphs from the article but if it would help to answer this question I can supply them. What I do not quite understand is what exactly is the purpose of applying standard deviation(s) to the PCA and then warping the Procrustes average shape to these standard deviations? Maybe my understanding of PCA is limited, but I was under the impression that in GPA the principal components are only statistical variance, and don't represent something biologically real. So to see how an individual varies from the shape average you have to go back and look at whatever landmark(s) represent that specific individual and compare that shape to the Procrustes average. Maybe this is not correct? Thanks in advance, I appreciate any help you can give me. David -- MORPHMET may be accessed via its webpage at http://www.morphometrics.org --- 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 morphmet+unsubscr...@morphometrics.org.
