Dear Morphmet list,
first, thank you all for the very interesting and stimulating posts.
In my humble opinion, not being PCA a "predictive" tool, it can be
easily misused as such. Personally, I most frequently use PCA to have a
quick look at what my data looks like. In other words, to look at
obvious patterns in multivariate data, which would be otherwise very
hard to visualize. I often don't feel the need to mechanically (to echo
Dr. Rohlf) describe what shape change each PC axis (especially after the
first) explains. In most cases, there are other tools for hypothesis
testing, modeling and so on. But the immediate first look that I get
from simply plotting ordinations is very hard to obtain in other ways.
Trying to use PCA as a predictive tool, in my opinion, can equal to
"forcing" it for a use that it is not perfectly fit for. It does work in
some cases, but if that is reasonable or not is more of a case-by-case
decision. This point is hardly original as most, if not all, the people
who answered this far have raised it, but phrased it differently.
I also found the question by Dr. MacLeod very stimulating. I imagine
that PCA, in its use as a dimensionality reduction tool (as
controversial as it might be), and in conjunction with other techniques,
can be used to produce realistic morphospaces. In other words, by
"separating the wheat from the chaff" first and then modeling shape in
this subspace (for instance, explicitly as a vector of shape in a
certain direction) we can perhaps get an outcome that is realistic, with
reduced amounts of variation in directions that are not of interest
(perhaps because we consider them noise). The use of PCA in this context
might not be strictly necessary, but would probably still useful when it
comes to thinking about and visualizing the morphospace.
To be clear, I'm not advocating a generalized use of dimensionality
reduction, just its potential in certain contexts.
Best wishes,
Carmelo
On 16/05/2017 10:55 PM, dsbriss_dmd wrote:
Good morning all,
I would like to thank everyone so far for generously taking the time
to reply to my questions: I didn't think I would generated such an
interesting discussion! As an amateur morphometrician I am trying to
keep up and have started reading some of the literature you all have
cited.
From what I understand so far, the PCA is a statistical result that
describes the variance in a shape, and the warp visualization that is
extrapolated from the PCs is one method to describe the statistical
variance. I think this is what I was getting at by saying that the
PCA didn't have a "real" biological basis (sorry for my inaccurate
language). James you identified my main problem, in that how does
one move from this virtuality into the real world? Or more to the
point, how does the reader, who is not necessarily well versed in
geometric morphometrics, interpret PCA results in real-world shape
spaces, perhaps without this visualization?
The replies from Profs. MacLeod and Rohlf also get a bit at what I was
after, in that how does one decide which axes in PCA are of interest
in the first place, or indeed which landmarks are of interest, and
avoid the trap of mechanically displaying a warp (of whatever extreme)
simply to provide a visualization? That question about the way we use
these spaces is also important to know, as one of the questions I
usually get from my residents or faculty colleagues is what clinical
application the PCA has; I usually find that I have to explain that it
doesn't have a clinical significance or application, as by itself it
is not a description of a real clinical situation.
What they seem to want me to say is, can the PCs derived from GPA be
used as a predictive tool to describe how an individual shape will
change over time. My usual answer is no, it cannot be used that way.
I think that the warped PCA, whatever criteria are selected, might
help to visually explain how an individual differs from the Procrustes
shape, but in the average orthodontic reader I am not sure it is
interpreted this way. This may be a quirk of our specialty, since we
have been using landmark-based linear and angular analyses as growth
predictive tools since the 1940's.
I don't want to say that we are wrong to do this, but the issue comes
in trying to apply those long-used clinical tools to geometric
morphometrics, and I don't think they mesh very well. And as we get
closer to 3 dimensional analysis those older tools won't be able to
apply anymore. From a standard cephalometric approach I might be able
to claim that cranial base angle (Nasion-Sella-Basion) has some
correlation with mandibular prognathism, but I am not sure that this
is true from a geometric morphometric perspective, as I can't (yet)
answer what the covariance is between the cranial base and the
mandible, for example.
Anyway thank you all again, this is a very interesting thread and I
appreciate all the input so far. I have been sharing it with my
residents who are in the midst of working on their research, I hope it
will also be able to help them.
Best,
David
On Sunday, May 14, 2017 at 2:22:10 PM UTC-4, dsbriss_dmd wrote:
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
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