yeah, your inference makes absolute sense.Thanks for the quick response, Carmelo.

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On Mon, May 15, 2017 at 12:10 PM, Carmelo Fruciano <c.fruci...@unict.it> wrote: > Dear Mahediran, > > to my understanding from David's phrasing, it is just a way to visualize > shape variation along a given PC axis (as the value at 0 is the mean). One > could use some other criterion (for instance the maximum and minimum scores > along that given PC). > > But, of course, all the other considerations of whether or not it makes > sense to interpret (or at least explore) the patterns predicted along a > given PC axis still apply. > > Best, > > Carmelo > > Il 15/05/2017 4:30 PM, mahendiran mylswamy ha scritto: > > Dear all, > I read interesting comments and the attached manuscript as well. > I find David question us interesting. > If any one could answer David question in a simple way? > I am quoting his question below?. > "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? " > > > On 15 May 2017 6:08 a.m., "F. James Rohlf" <f.james.ro...@stonybrook.edu> > wrote: > >> I agree with these comments but would like to add another point. I prefer >> to think that the purpose of the PCA is to produce a low-dimension space >> that captures as much of the overall variation (in a least-squares sense) >> as possible. Within that space there is no need to limit the visualizations >> to the extremes of each axis – one can investigate any direction within >> that space if there is a pattern in the data that suggests an interesting >> direction. The directions of the axes are mathematical constructs and not >> bases on any biological principles. Perhaps one sees some clusters in the >> PCA ordination but the variation within or between clusters need not be >> parallel to one of the PC axes. One can then look in other directions. That >> is why the tpsRelw program allows one to visualize any point in the >> ordination space – not just parallel to the axes. That means for >> publication one has to decide which directions are of interest – not just >> mechanically display the extremes of the axes. >> >> >> >> ---------------------- >> >> F. James Rohlf *New email: f.james.ro...@stonybrook.edu >> <f.james.ro...@stonybrook.edu>* >> >> Distinguished Professor, Emeritus. Dept. of Ecol. & Evol. >> >> & Research Professor. Dept. of Anthropology >> >> Stony Brook University 11794-4364 >> >> WWW: http://life.bio.sunysb.edu/morph/rohlf >> >> P Please consider the environment before printing this email >> >> >> >> *From:* K. James Soda [mailto:k.jamess...@gmail.com] >> *Sent:* Sunday, May 14, 2017 7:28 PM >> *To:* dsbriss_dmd <orthofl...@gmail.com> >> *Cc:* MORPHMET <morphmet@morphometrics.org> >> *Subject:* Re: [MORPHMET] Interpreting PCA results >> >> >> >> Dear David, >> >> Great question! I disagree with the statement that the samples' variance >> in shape space is not biologically real or, perhaps more accurately, is >> less real than the variance in any other space. As far as I see it, the >> basic strategy in any biostatistical study, be it GM or otherwise, is that >> a researcher represents a real biological population as an abstract >> statistical population. They then use this abstract statistical population >> as a proxy for the real one so that inferences in the statistical space >> have implications for the real world. >> >> For example, a PCA finds a direction in the statistical space in which >> the statistical population tends to be spread out. This is interesting to >> the researcher because this direction has a correspondence to certain real >> world variables. As a result, the PCA tells the researcher in what ways >> the real population tends to vary. The key point, though, is that the >> researcher transitioned from the statistical space to the real world. >> >> Moving from shape space to the real world is no different in principle. >> We have a real population of specimens, whose shape are of interest to us, >> and we represent them using vectors of shape variables. The vectors are >> abstractions; it is not as if we can hold a vector in our hands. However, >> this is irrelevant because they are just proxies, no less real than any >> other quantitative representation. What matters is if we can tie them back >> to the real world. This is why morphometricians implement a visualization >> step. In a PCA, the PCs describe how our proxies vary, and we visualize in >> order to see how this variation appears in the real world. It is >> infeasible to visualize every point along this axis, so we instead >> visualize a handful. Since the core goal in PCA (at least in this context) >> is to describe variance, we generally describe the locations where a >> visualization occurs in units of standard deviations from the mean. We >> could use absolute distances along an axis, but this is probably more >> arbitrary than standard deviation units. The standard deviations come from >> the data's distribution, whereas the absolute distance is really only >> well-defined in the mathematical space. >> >> To summarize: i) Nearly all quantitative analyses involve an abstraction >> to a mathematical space. ii) The description of points in a mathematical >> space is useful to the researcher because the researcher is able to >> translate the abstract mathematical space into a real world >> interpretation. iii) In GM, the shape variables are traditionally >> translated into the real world via visualization. Ergo, morphometricians >> often interpret PCA results via visualizations along individual PCs. To >> aid in interpretation, this tends to occur in standard deviation units >> because the standard deviation is more easily tied to the real world >> relative to arbitrary selecting a unit of distance. >> >> Perhaps some of these points are up for debate, but remember that >> statistics is largely the study of VARIATION. If the variation in shape >> space did not have any biological significance, almost no analysis after >> alignment would be possible. >> >> Hope somewhere in this long commentary, you found something helpful, >> >> James >> >> >> >> On Tue, May 9, 2017 at 4:56 PM, dsbriss_dmd <orthofl...@gmail.com> 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/2 >> 015/8971.5458 <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. >> >> >> >> -- >> 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. >> -- >> 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. >> > -- > 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. > > > -- > 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. > -- *************************************** M Mahendiran, Ph D Scientist - Division of Wetland Ecology Salim Ali Centre for Ornithology and Natural History (SACON) Anaikatti (PO), Coimbatore - 641108, TamilNadu, India Tel: 0422-2203100 (Ext. 122), 2203122 (Direct), Mob: 09787320901 Fax: 0422-2657088 www.sacon.in -- 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. 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