Does anyone know of any (published) 2D geometric morphometric analyses that have used coordinate data that is scaled and transformed, but not rotated?
Euclidean Distance Matrix Analysis (EDMA) might work for you. It is described in a book called An Invariant Approach to Statistical Analysis of Shapes by Subhash R. Lele and J. T. Richtsmeier. You can find many papers on Dr. Richtsmeier's website that have used this method or variations of it: http://getahead.psu.edu/publications_new.asp. Both the transformation and rotation typically used for Procrustes do not need to be done and scaling is optional with EDMA.
Essentially, EDMA calculates all unique linear distances between landmarks and then compares mean form matrices for each sample using a nonparametric bootstrap approach. It can handle fairly small samples while still yielding a robust statistical results, and your data do not need to be normally distributed.
Hello John
Many thanks for this, but just to check - I want to retain the rotational variables in the analyses rather than remove them, and I've done some preliminary experimentation with this using morphologika2. But I'm not sure about the legitimacy of this approach given it effectively means I'm violating shape space, and was hoping there are other researchers out there that may have set a precedent.
Cheers, Susan
Hi Susan,
Are you subscribed to Morphomet http://www.morphometrics.org/home/morphmet? That might be a good place to find someone who has done this or might have recommendations on how to proceed.
Best,
John
In principle, it is possible to scale and translate landmark configurations (to remove variation in size and position), without rotating them. Of course, this requires an interpretable orientation of the studied objects and a common reference system.
Best,
Philipp
Most morphometric software allows you to step through your analysis and end wherever you wish. If your brave enough to venture into R try the geomorph code. Dennis Slice's Morpheus saves the rotations which you can reapply. I agree w/ Philipp, you'll need to make a strong case for not including rotation.
Susan, What data are you working with, if you don't mind me asking?
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