Dear Morphmet list, first, thank you all for the very interesting and stimulating posts.

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`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 timeto reply to my questions: I didn't think I would generated such aninteresting discussion! As an amateur morphometrician I am trying tokeep up and have started reading some of the literature you all havecited.From what I understand so far, the PCA is a statistical result thatdescribes the variance in a shape, and the warp visualization that isextrapolated from the PCs is one method to describe the statisticalvariance. I think this is what I was getting at by saying that thePCA didn't have a "real" biological basis (sorry for my inaccuratelanguage). James you identified my main problem, in that how doesone move from this virtuality into the real world? Or more to thepoint, how does the reader, who is not necessarily well versed ingeometric morphometrics, interpret PCA results in real-world shapespaces, perhaps without this visualization?The replies from Profs. MacLeod and Rohlf also get a bit at what I wasafter, in that how does one decide which axes in PCA are of interestin the first place, or indeed which landmarks are of interest, andavoid the trap of mechanically displaying a warp (of whatever extreme)simply to provide a visualization? That question about the way we usethese spaces is also important to know, as one of the questions Iusually get from my residents or faculty colleagues is what clinicalapplication the PCA has; I usually find that I have to explain that itdoesn't have a clinical significance or application, as by itself itis not a description of a real clinical situation.What they seem to want me to say is, can the PCs derived from GPA beused as a predictive tool to describe how an individual shape willchange over time. My usual answer is no, it cannot be used that way.I think that the warped PCA, whatever criteria are selected, mighthelp to visually explain how an individual differs from the Procrustesshape, but in the average orthodontic reader I am not sure it isinterpreted this way. This may be a quirk of our specialty, since wehave been using landmark-based linear and angular analyses as growthpredictive tools since the 1940's.I don't want to say that we are wrong to do this, but the issue comesin trying to apply those long-used clinical tools to geometricmorphometrics, and I don't think they mesh very well. And as we getcloser to 3 dimensional analysis those older tools won't be able toapply anymore. From a standard cephalometric approach I might be ableto claim that cranial base angle (Nasion-Sella-Basion) has somecorrelation with mandibular prognathism, but I am not sure that thisis true from a geometric morphometric perspective, as I can't (yet)answer what the covariance is between the cranial base and themandible, for example.Anyway thank you all again, this is a very interesting thread and Iappreciate all the input so far. I have been sharing it with myresidents who are in the midst of working on their research, I hope itwill 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 -- MORPHMET may be accessed via its webpage at http://www.morphometrics.org ---You received this message because you are subscribed to the GoogleGroups "MORPHMET" group.To unsubscribe from this group and stop receiving emails from it, sendan email to morphmet+unsubscr...@morphometrics.org<mailto:morphmet+unsubscr...@morphometrics.org>.

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