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
<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
<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
<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
<https://sites.google.com/site/alcardini/home/main>
>
> FREE Yellow BOOK on Geometric Morphometrics:
> https://tinyurl.com/2013-Yellow-Book
<https://tinyurl.com/2013-Yellow-Book>
>
> ESTIMATE YOUR GLOBAL FOOTPRINT:
>
http://www.footprintnetwork.org/en/index.php/GFN/page/calculators/
<http://www.footprintnetwork.org/en/index.php/GFN/page/calculators/>
>
> --
> MORPHMET may be accessed via its webpage at
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--
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
<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
<http://www.italian-journal-of-mammalogy.it/public/journals/3/issue_241_complete_100.pdf>
ESTIMATE YOUR GLOBAL FOOTPRINT:
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