# [MORPHMET] Interpreting PCA results

```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?

David

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