Thomas,
The Procrustes Motion Analysis approach of Adams and Cerney (2007: J.
Biomechanics) could be used for examining patterns in your
data. Essentially, you do GPA on the set of 3D coordinates, and
re-associate the shape data with the time component. At each time
step, you have a multivariate shape, and the sequence of these forms
a growth trajectory through shape space. The attributes of these
growth trajectories (their size, shape, and orientation) can then be
statistically compared to one another for an assessment of growth
trajectory similarity.
Another option you should explore is the size-shape space approach of
Mitteroecker, Gunz, Bookstein and colleagues (2004: J. Hum Evol; and
2005: Evol. & Devel.). Their approach generates a data space
combining the shape data and logCSize (see papers for mathematical
details), where allometric trajectories can then be examined.
Assessment of allometry path similarity is certainly relevant to
growth studies, so this approach also seems appropriate for your data.
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 09:53 AM 5/2/2007, you wrote:
>This question refers to the proper way to analyze 4-Dimensional data
>sets using geometric morphometrics.
>
>The data that I am talking about are a series of 3D data measured from
>two different groups at regular time intervals - essentially changing
>shapes during growth. The question I would like to address is if the
>same types of changes in shape over time occur in both groups. In terms
>of a simple bivariate analysis each group can be characterized by
>shape/time and the analysis would compare the shape/time slopes between
>the two groups. The complication is that "shape" is multivariate
>landmark data and that there is no reason to believe that shape change
>would have a quasi-linear relationship with time.
>
>So, my question is how to approach these data. Do I conduct a Procrustes
>analysis of the entire data set including the time, essentially a
>superimposition of 4D data, and compare groups with these numbers -
>treating the time value as just another dimension (XYZT coordinates)?
>Or, do I conduct a Procrustes superimposition of the 3D landmark data
>first and then re-associate them with their time values? Or, is there a
>third way to go? The problem here is similar to the setup described by
>Dean and Cerney in their Journal of Biomechanics (2007) article,
>although I am not entirely certain that their solution applies to this
>case. Maybe it does, but right now, it's a little confusing.
>
>I am not sure which way is correct, and I would appreciate the advice of
>the group. Either way I go, I see this analysis as a MANOVA with
>repeated measures of shape using time as the independent variate. I
>would like to be able to set this up as a resampling analysis, but I
>can't think how I would do that with a repeated measures design. Again,
>any help would be appreciated.
>
>On an aside, I submitted the 4D data as an NT-SYS file to Morpheus, and
>it plotted the data just fine. I'm not sure what the plot means (a 2D
>summary of a 4D data set), but I thought it was interesting that the
>program still did something. Morphologika went the more expected route
>and refused to accept 4D data.
>
>
>Thomas M. Greiner, Ph.D.
>Assistant Professor of Anatomy
>Dept. of Health Professions
>University of Wisconsin - La Crosse
>1725 State Street
>La Crosse, WI 54601 USA
>Phone: (608) 785-8476
>Fax: (608) 785-8460
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