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.

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>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 > > > > -- MORPHMET may be accessed via its webpage at http://www.morphometrics.org --- You received this message because you are subscribed to the Google Groups "MORPHMET" group. To unsubscribe from this group and stop receiving emails from it, send an email to morphmet+unsubscr...@morphometrics.org.