Yes, it was always well known that sliding adds covariance but this is irrelevant for most studies, especially for group mean comparisons and shape regressions: the kind of studies for which GMM is most efficient, as Jim noted. If you consider the change of variance-covariance structure due to (a small amount of) sliding as an approximately linear transformation, then the sliding is also largely irrelevant for CVA, relative PCA, Mahalanobis distance and the resulting group classifications, as they are all based on the relative eigenvalues of two covariance matrices and thus unaffected by linear transformations. In other words, in the lack of a reasonable biological null model, the interpretation of a single covariance structure is very difficult, but the way in which one covariance structure deviates from another can be interpreted much easier.
Concerning your example: The point is that there is no useful model of "totally random data" (but see Bookstein 2015 Evol Biol). Complete statistical independence of shape coordinates is geometrically impossible and biologically absurd. Under which biological (null) model can two parts of a body, especially two traits on a single skeletal element such as the cranium, be complete uncorrelated? Clearly, semilandmarks are not always necessary, but making "cool pictures" can be quite important in its own right for making good biology, especially in exploratory settings. Isn't the visualization one of the primary strengths of geometric morphometrics? It is perhaps also worth noting that one can avoid a good deal of the additional covariance resulting from sliding. Sliding via minimizing bending energy introduces covariance in the position of the semilandmarks _along_ the curve/surface. In some of his analyses, Fred Bookstein just included the coordinate perpendicular to the curve/surface for the semilandmarks, thus discarding a large part of the covariance. Note also that sliding via minimizing Procrustes distance introduces only little covariance among semilandmarks because Procrustes distance is minimized independently for each semilandmark (but the homology function implied here is biologically not so appealing). Best, Philipp Am Dienstag, 6. November 2018 18:34:51 UTC+1 schrieb alcardini: > > Yes, but doesn't that also add more covariance that wasn't there in > the first place? > Neither least squares nor minimum bending energy, that we minimize for > sliding, are biological models: they will reduce variance but will do > it in ways that are totally biologically arbitrary. > > In the examples I showed sliding led to the appearance of patterns > from totally random data and that effect was much stronger than > without sliding. > I neither advocate sliding or not sliding. Semilandmarks are different > from landmarks and more is not necessarily better. There are > definitely some applications where I find them very useful but many > more where they seem to be there just to make cool pictures. > > As Mike said, we've already had this discussion. Besides different > views on what to measure and why, at that time I hadn't appreciated > the problem with p/n and the potential strength of the patterns > introduced by the covariance created by the superimposition (plus > sliding!). > > Cheers > > Andrea > > On 06/11/2018, F. James Rohlf <f.jame...@stonybrook.edu <javascript:>> > wrote: > > I agree with Philipp but I would like to add that the way I think about > the > > justification for the sliding of semilandmarks is that if one were smart > > enough to know exactly where the most meaningful locations are along > some > > curve then one should just place the points along the curve and > > computationally treat them as fixed landmarks. However, if their exact > > positions are to some extend arbitrary (usually the case) although still > > along a defined curve then sliding makes sense to me as it minimizes the > > apparent differences among specimens (the sliding minimizes your measure > of > > how much specimens differ from each other or, usually, the mean shape. > > > > > > > > _ _ _ _ _ _ _ _ _ > > > > F. James Rohlf, Distinguished Prof. Emeritus > > > > > > > > Depts. of Anthropology and of Ecology & Evolution > > > > > > > > > > > > From: mitt...@univie.ac.at <javascript:> <mitt...@univie.ac.at > <javascript:>> > > Sent: Tuesday, November 6, 2018 9:09 AM > > To: MORPHMET <morp...@morphometrics.org <javascript:>> > > Subject: [MORPHMET] Re: semilandmarks in biology > > > > > > > > I agree only in part. > > > > > > > > Whether or not semilandmarks "really are needed" may be hard to say > > beforehand. If the signal is known well enough before the study, even a > > single linear distance or distance ratio may suffice. In fact, most > > geometric morphometric studies are characterized by an oversampling of > > (anatomical) landmarks as an exploratory strategy: it allows for > unexpected > > findings (and nice visualizations). > > > > > > > > Furthermore, there is a fundamental difference between sliding > semilandmarks > > and other outline methods, including EFA. When establishing > correspondence > > of semilandmarks across individuals, the minBE sliding algorithm takes > the > > anatomical landmarks (and their stronger biological homology) into > account, > > while standard EFA and related techniques cannot easily combine point > > homology with curve or surface homology. Clearly, when point homology > > exists, it should be parameterized accordingly. If smooth curves or > surfaces > > exists, they should also be parameterized, whether or not this makes the > > analysis slightly more challenging. > > > > > > > > Anyway, different landmarks often convey different biological signals > and > > different homology criteria. For instance, Type I and Type II landmarks > > (sensu Bookstein 1991) differ fundamentally in their notion of homology. > > Whereas Type I landmarks are defined in terms of local anatomy or > histology, > > a Type II landmark is a purely geometric construct, which may or may not > > coincide with notions of anatomical/developmental homology. ANY > reasonable > > morphometric analysis must be interpreted in the light of the > correspondence > > function employed, and the some holds true for semilandmarks. For this, > of > > course, one needs to understand the basic properties of sliding > landmarks, > > much as the basic properties of Procrustes alignment, etc.. For > instance, > > both the sliding algorithm and Procrustes alignment introduce > correlations > > between shape coordinates (hence their reduced degrees of freedom). This > is > > one of the reasons why I have warned for many years and in many > publications > > about the biological interpretation of raw correlations (e.g., > summarized in > > Mitteroecker et al. 2012 Evol Biol). Interpretations in terms of > > morphological integration or modularity are even more difficult because > in > > most studies these concepts are not operationalized. They are either > > described by vague and biologically trivial narratives, or they are > > themselves defined as patterns of correlations, which is circular and > makes > > most "hypotheses" untestable. > > > > > > > > The same criticism applies to the naive interpretation of PCA scree > plots > > and derived statistics. An isotropic (circular) distribution of shape > > coordinates corresponds to no biological model or hypothesis whatsoever > > (e.g., Huttegger & Mitteroecker 2011, Bookstein & Mitteroecker 2014, and > > Bookstein 2015, all three in Evol Biol). Accordingly, a deviation from > > isometry does not itself inform about integration or modularity (in any > > reasonable biological sense). > > > > The multivariate distribution of shape coordinates, including "dominant > > directions of variation," depend on many arbitrary factors, including > the > > spacing, superimposition, and sliding of landmarks as well as on the > number > > of landmarks relative to the number of cases. But all of this applies to > > both anatomical landmarks and sliding semilandmarks. > > > > > > > > I don't understand how the fact that semilandmarks makes some of these > > issues more obvious is an argument against their use. > > > > > > > > Best, > > > > > > > > Philipp > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > Am Dienstag, 6. November 2018 13:28:55 UTC+1 schrieb alcardini: > > > > As a biologist, for me, the question about whether or not to use > > semilandmarks starts with whether I really need them and what they're > > actually measuring. > > > > On this, among others, Klingenberg, O'Higgins and Oxnard have written > some > > very important easy-to-read papers that everyone doing morphometrics > should > > consider and carefully ponder. They can be found at: > > https://preview.tinyurl.com/semilandmarks > > > > I've included there also an older criticism by O'Higgins on EFA and > related > > methods. As semilandmarks, EFA and similar methods for the analysis of > > outlines measure curves (or surfaces) where landmarks might be few or > > missing: if semilandmarks are OK because where the points map is > irrelevant, > > as long as they capture homologous curves or surfaces, the same applies > for > > EFAs and related methods; however, the opposite is also true and, if > there > > are problems with 'homology' in EFA etc., those problems are there also > > using semilandmarks as a trick to discretize curves and surfaces. > > > > Even with those problems, one could still have valid reasons to use > > semilandmarks but it should be honestly acknowledged that they are the > best > > we can do (for now at least) in very difficult cases. Most of the > studies I > > know (certainly a minority from a now huge literature) seem to only > provide > > post-hoc justification of the putative importance of semilandmarks: > there > > were few 'good landmarks'; I added semilandmarks and found something; > > therefore they work. > > > > > > > > From a mathematical point of view, I cannot say anything, as I am not a > > mathematician. On this, although not specific to semilandmarks, a > > fundamental reading for me is Bookstein, 2017, Evol Biol (also available > for > > a few days, as the other pdfs, at the link above). That paper is one of > the > > most inspiring I've ever read and it did inspire a small section of my > > recent Evol Biol paper on false positives in some of the tests of > > modularity/integration using Procrustes data. For analyses using sliding > > semilandmarks, the relevant figures are Figs 4-5, that suggest how > tricky > > things can be. If someone worries that that's specific to my example > data > > (and it could be!), the experiment is trivial to repeat on anyone's own > > semilandmark data. > > > > Taken from the data of the same paper, below you find a PCA of rodent > > hemimandibles (adults, within a species) using minBE slid semilandmarks > or > > just 9 'corresponding' landmarks. The advantage of semilandmarks, > compared > > to the 9 landmarks, is that they allow to capture a dominant direction > of > > variation (PC1 accounting for 14% of shape variance), whose positive > extreme > > (magnified 3 times) is shown with a really suggestive deformation grid > > diagram. In comparison, 9 landmarks do not suggest any dominant > direction of > > variation (each PC explaining 9-5% of variance), the scatterplot is > circular > > and the TPS shape diagram much harder to interpret. > > > > What these two PCAs have in common is that they are both analyses of > random > > noise (multivariate random normally distributed numbers added to a mean > > shape). > > > > > > > > All the best > > > > > > > > Andrea > > > > > > > > 9 LANDMARKS PLUS 22 SLID SEMILANDMARKS > > > > > > < > https://groups.google.com/a/morphometrics.org/group/morphmet/attach/dcce33d95d952/oclbeaidoponnmni.jpeg?part=0.1.1&view=1&authuser=0> > > > > > > > > 9 LANDMARKS > > > > > > < > https://groups.google.com/a/morphometrics.org/group/morphmet/attach/dcce33d95d952/pebddfgpogepigmi.jpeg?part=0.1.2&view=1&authuser=0> > > > > > > > > -- > > > > Dr. Andrea Cardini > > Researcher, Dipartimento di Scienze Chimiche e Geologiche, Università di > > Modena e Reggio Emilia, Via Campi, 103 - 41125 Modena - Italy > > tel. 0039 059 2058472 > > > > Adjunct Associate Professor, School of Anatomy, Physiology and Human > > Biology, The University of Western Australia, 35 Stirling Highway, > Crawley > > WA 6009, Australia > > > > E-mail address: alca...@gmail.com <javascript:> , andrea....@unimore.it > > <javascript:> > > WEBPAGE: https://sites.google.com/site/alcardini/home/main > > > > FREE Yellow BOOK on Geometric Morphometrics: > > https://tinyurl.com/2013-Yellow-Book > > > > ESTIMATE YOUR GLOBAL FOOTPRINT: > > http://www.footprintnetwork.org/en/index.php/GFN/page/calculators/ > > > > -- > > 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+u...@morphometrics.org <javascript:> > > <mailto:morphmet+u...@morphometrics.org <javascript:>> . > > > > -- > > 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+u...@morphometrics.org <javascript:>. > > > > > -- > > Dr. Andrea Cardini > Researcher, Dipartimento di Scienze Chimiche e Geologiche, Università > di Modena e Reggio Emilia, Via Campi, 103 - 41125 Modena - Italy > tel. 0039 059 2058472 > > Adjunct Associate Professor, School of Anatomy, Physiology and Human > Biology, The University of Western Australia, 35 Stirling Highway, > Crawley WA 6009, Australia > > E-mail address: alca...@gmail.com <javascript:>, andrea....@unimore.it > <javascript:> > WEBPAGE: https://sites.google.com/site/alcardini/home/main > > FREE Yellow BOOK on Geometric Morphometrics: > > http://www.italian-journal-of-mammalogy.it/public/journals/3/issue_241_complete_100.pdf > > > ESTIMATE YOUR GLOBAL FOOTPRINT: > http://www.footprintnetwork.org/en/index.php/GFN/page/calculators/ > -- 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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