Agreed. In addition, I think it’s important to note that, in the original implementations of the sliding algorithm, semilandmarks were slid not along the curve itself, but along tangents to the curve (= off the boundary outline). How much distortion this induces is, of course, a function of how much the semilandmarks are displaced from their original positions. However, it’s always seemed problematic to me that, after sliding, you end up with shapes that have been distorted to a greater or lesser extent. Of course, if the displacement is small the amount off distortion will (likely) be small and the results might not be all that different. Moreover, as Phillip notes, in terms of many types of analyses, linear data transformations make no difference to the outcome of an analysis. But given these facts, the point of sliding the semilandmarks at all seems questionable in many contexts. Moreover, in the case of complex boundary outline curves - in other words, the curves semilandmarks are usually called upon to quantify - since the magnitude of the slide is, to a large extent, determined by the density of the semilandmark placements, large semilandmark displacements will never occur. So, if you have a curve that is so smooth it only needs a few semilandmarks to tie down, you run the risk of generating some (presently unspecified) degree of distortion in your data by sliding the semilandmarks so long as the sliding takes place along tangents. But if your curve is complex it’s unlikely that sliding the semilandmarks will make much difference because the distance along which sliding can take place is constrained. Sliding semilandmarks is an interesting strategy in principle. But in many cases the (current) practice is fraught with problems that are rarely acknowledged. Norm MacLeod > On 6 Nov 2018, at 19:53, mitte...@univie.ac.at wrote: > > 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
I agree with Jim. However, this discussion does beg the question of what the status of landmark, semilandmark, or indeed pixel brightness configurations within multivariate spaces is? Very similar spaces have been used in the area of theoretical morphology to conduct various sorts of experiments dealing with the nature of morphological evolution, especially the development of patterns based on null models to which empirical patterns can be compared. Moreover, machine learning specialists are now using morphologies generated artificially, in ways that aren’t very different from the ways in which such visualisations can be created by morphometricians, to train their AI systems. McGhee distinguishes "theoretical morphospaces” derived from graphics equations (e.g., Raup’s coiling models) from (what he terms) the “empirical morphospaces” we deal with as morphometricians and that lie at the heart of this conversation. But are the two really that different? If so, why and in what cases? If not what does that mean for the ways in which we might use such spaces? I’ve long found this an interesting question to ponder. Any thoughts from the community? Norm MacLeod > On 15 May 2017, at 18:28, F. James Rohlf
wrote: > > What is important is not the fact that one is going +/- one standard > deviation along each axis. When shape changes are subtle one may need to go > beyond the observed range to make it more obvious to the eye what the changes > are. Exactly how far one goes away from the mean is arbitrary. It is a > visualization – not statistics. > > -- > F. James Rohlf New email: 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 > _ Professor Norman MacLeod The Natural History Museum, Cromwell Road, London, SW7 5BD (0)207 942-5204 (Office Landline) (0)785 017-1787 (Mobile) http://paleonet.org/MacLeod/ Department of Earth Sciences, University College London, Gower Street, London WC1E 6BT, UK Nanjing Institute of Geology & Palaeontology, Chinese Academy of Sciences, 39 Beijing, Donglu, Nanjing, China _ -- 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.
I can’t help you with PAST, but this reference will allow you to compute the correct statistics for a standardized major axis (often erroneously called a reduced major axis) regression. Warton, D. I., et al., 2006, Bivariate line-fitting methods for allometry: Biological Reviews, v. 81, no. 2, p. 259–291. Norm MacLeod > On 12 Mar 2016, at 14:49, Patrick Arnold
wrote: > > Dear morphometrics, > > I am frequently using PAST (paleontological statistics; what a great free > software) for the analysis of morphometric data (geometric and traditional). > Now I want to do a reduced major axis regression on bivariate data (only one > Y for each X). However, I do not found the possibility to perform a > significance test for the regression (F statistics) or for the slope and > intercept (t statistics). > It is provided for least square regression (e.g., under polynomial option) > but not for model II regression. Does anyone know a possibility to obtain > regression statistics in PAST for model II regressions? > Thanks in advance. > > Cheers > Patrick > > > -- > Patrick Arnold, M.Sc. > > wissenschaftlicher Mitarbeiter und Doktorand > Institut für Spezielle Zoologie und Evolutionsbiologie > mit Phyletischem Museum > Friedrich-Schiller-Universität Jena > Erbertstraße 1 > 07743 Jena > Germany > > Phone: +49 (0)3641 9-49165 > Fax:+49 (0)3641 9-49142 > E-mail: patrick.arn...@uni-jena.de > > -- > 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. > _ Professor Norman MacLeod Dean of Postgraduate Education and Training The Natural History Museum, Cromwell Road, London, SW7 5BD (0)207 942-5204 (Office Landline) (0)785 017-1787 (Mobile) http://www.nhm.ac.uk/hosted_sites/paleonet/MacLeod/ Department of Earth Sciences, University College London, Gower Street, London WC1E 6BT, UK Nanjing Institute of Geology & Palaeontology, Chinese Academy of Sciences, 39 Beijing, Donglu, Nanjing, China _ -- 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.