Dear morphometricians,
many thanks to all those who either in emails directly to me or to
morphmet contributed to this discussion.
It was very interesting and instructive.
I have a lot of sympathy for Ian's point about what to do when one uses
an ANCOVA to test slopes and finds that it is significant but the
difference in the fit of the a model with separate lines compared to one
with parallel is tiny. I had at least a few times when that happened to me.
With short trajectories (say, static allometry in mammal crania), I'd be
very cautious. In my experience, when trajectories are short, one needs
very but really very large samples to trust the estimates. With longer
trajectories and much more allometric variance (as often in ontogenetic
allometry), besides checking the angles, if one really wants to try a
'size-correction' despite all the issues raised by Dean, Joe et al., I
would possibly also explore the sensitivity of the 'correction' to
different choices of size value used for the correction: if the
divergence of the trajectories is really small (despite significance), I
would expect results to be robust to the use of the smallest, largest or
average size in the samples.
Again, thanks a lot for your feedback.
Cheers
Andrea
On 24/03/2016 16:12, Ian Dworkin wrote:
Dean and Andrea,
I wanted to follow up on what Dean wrote regarding using residuals
from a pooled within-group regression, and what I think may be important
discussion that follows from it. Considerable research has gone into
investigating this issue, and as Dean points out, most of the time it is
best to include the additional predictor (let's just use centroid size)
in the model and fit it with the shape ~ group + size + group:size
term. Indeed, I think we could all find 10-15 different papers (each)
that discuss this issue (and a few of them pertaining to geometric
morphometrics).
However, there are some common cases in geometric morphometrics that I
think many of us deal with, and at least to my mind we do not have a
very satisfactory guide to deal with some of them. Let's imagine a case
that I think is particularly common in geometric morphometric studies,
where we are examining sexual shape dimorphism, where we have sex as a
categorical predictor as well as centroid size.
So we might start with the model
shape ~ sex + size + sex:size
Geometric morphometric analyses are pretty sensitive, and at least with
some systems (like fly wings) sample sizes tend to be relatively high.
Frequently I have observed that the evidence is not consistent (based on
Null Hypothesis Statistical Testing, NHST) with a common allometric
relationship between the two sexes. Indeed since NHST (and assessment of
significance) is in part a function on sample size, with large enough N,
this term will be significant (even if the magnitude of effect is very
small).
Thus (as Dean has already clearly laid out) it may be unreasonable to
use a pooled within-group regression and use the residuals (so that you
can separate out allometric from non-allometric components of sexual
shape dimorphism for instance).
However, if you go ahead and examine the vector correlations/angle
between the slopes (shape ~ size) across sexes you will observe that the
vector correlation is ~1 (angle is ~0). Similarly the partial
coefficient of determination (r^2) for the size:sex term is quite small
relative to the partial r^2 for the marginal contributions of size and
sex. Thus despite the NHST suggesting a lack of a common allometric
relationship, this "deeper" examination suggests the slopes are very
similar.
So what do you do (again if you want to partition the allometric and
non-allometric components of shape variation)? if the vector correlation
is 0.99 do you decide they are effectively the same and proceed with
pooled within-group regression to extract residuals? How about if the VC
is 0.95? 0.9? At what point do you risk causing substantial inferential
problems?
Or do you alternatively not try to use a pooled within-group regression
at all, and instead just predict shapes for males or females at
particular centroid sizes given the full model (sex + size + sex:size),
so you can get a sense of the extent of sexual shape dimorphism for
comparable sizes (or whatever your goals might be).
While I do not expect any hard and fast rules, I am wondering if anyone
has done the relevant simulations to look at when the former (residuals
from pooled within-group regression) becomes substantially problematic
(in terms of magnitude of the sex:size interaction term).
While I can quibble and be a pedant (who among us GMers are not!), I
think the paper by Nelly, Michel and Chris is very useful (but does not
get into the issue about when using residuals from pooled regression is
problematic).
N. A. Gidaszewski, M. Baylac, and C. P. Klingenberg, “Evolution of
sexual dimorphism of wing shape in the Drosophila melanogaster
subgroup.,” /BMC Evol Biol/, vol. 9, p. 110,
