Thomas,
The model you described is MANCOVA, with groups, size, and group*size
interaction as the main model effects. When the interaction term of a
MANCOVA is significant, asking the question of group difference via the
main effect is no longer useful, because the allometric relationships
are not concordant among the groups themselves. Further, you cannot
simply adjust the shape data for each group separately, as you are then
comparing residual shape based on different allometric relationships for
each group. Instead, it is preferable to alter the way you think about
your question so that it more closely aligns with the biological
patterns that you observe in your data.
When the interaction term is significant, this effectively shifts the
group difference question away from 'pure' shape differences, and
instead to determining HOW the allometric trajectories themselves
differ. It turns out that there are several ways that the interaction
term could be found significant; all of which are biologically
interesting. First, the slopes could differ among groups. This is
equivalent to having allometric trajectories pointing in different
directions in shape space. However, it may be the case that the amount
of shape change associated with size may differ among groups. This is
equivalent to the magnitude of shape change being different among
groups, which will also exhibit a significant interaction term. Of
course, both of these may be occurring in your data set. Finally, the
shape of the allometric trajectories could also differ, but you would
not identify that unless you are using non-linear allometric procedures.
To determine which of these aspects of allometric shape change differ in
your data set requires tests of both magnitude and direction. The
analytical procedure is described in:
Collyer & Adams. 2007. Analysis of two-state multivariate phenotypic
change in ecological studies. /Ecology./ 88:683-692.
The paper describes the scenario for 2 categorical factors, but the
approach for a continuous covariate is identical. For extensions and
related topics see also:
Adams, and Collyer. 2007. Analysis of character divergence along
environmental gradients and other covariates. Evolution.61:510-515.
Adams, and Cerney. 2007. Quantifying biomechanical motion using
Procrustes motion analysis. Journal of Biomechanics. 40:437-444.
Hope this helps.
Dean
Dean C. Adams
Associate Professor
Department of Ecology, Evolution, and Organismal Biology, and
Department of Statistics
253 Bessey Hall
Iowa State University
Ames, IA 50011
tel: (515) 294-3834
fax: (515) 294-1337
web: http://www.public.iastate.edu/~dcadams
At 03:01 PM 8/23/2007, you wrote:
> Dear morphometricians,
>
> I work on the Origin of Orcadian voles using a GPA analysis on first
> lower molar (M1) Landmarks.
> I use TPS series and NTSYS-pc to perform the analyses.
> Voles' M1 display huge differences in their centroid size which has,
> according to the multivariate regression, highly significant effect over
> shape variance.
> I would like to remove this allometric component. Is it possible to
> perfom a standardization with TPSregr?
>
> Thank you very much in advance for any kind of help
>
> Thomas
>
> --
> Dr Thomas Cucchi
> Postdoctoral Research Associate
> Durham University
> Department of Archaeology
> South road
> Durham
> DH1 3LE
>
> Tel:
> 00 44 (0) 191 33 41162
>
> e-mail:
> [EMAIL PROTECTED]
>
> --
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> For more information visit http://www.morphometrics.org
> <http://www.morphometrics.org/>
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