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,


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.


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:

    "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
    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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