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 

"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 
<>]: PC1 
with standard deviation, [Table/Fig-11 
<>] 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.


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