To be true, the vary subject looks a little bit strange. The allometry is just a non-linear relation between several variables - say, between size and shape variables. So, procrustes analysis will remove the "size factor" completely only if the above relation is not allometric but isometric. If it is actually allometric, than a portion of "size factor" will persist in gradient of a shape variable after procrustes transformations. To analyze it further, one has to apply any non-liner form of regression analysis to extract residuals (as many participants of the forum have already suggested). Besides, it is to be taken into account, as Rohlf pointed it out, that the power coefficient alpha is to be equal to 1 and the uniform component is to be included in the analysis when the one's task is to investigate just the allometric relation between shape and size.
Igor ----- Original Message ----- From: <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Sent: Saturday, March 29, 2003 12:24 AM Subject: Re: Allometry persists after procrustes? > Pablo > > Yes, allometry will persist in most data sets (i.e., if there is a > sufficient range of variation in size). > > Geometric morphometrics (landmark-based and outline-based alike) uses > a strictly geometric definition of shape. These methods apply a > scaling to remove variation of size (e.g., scaling to unit centroid > size), but this will not remove the allometric effects of size on > shape. > > This geometric scaling is the same as what's used in photography: > pictures of babies and grown-ups are scaled until they fit the > 9-by-13 cm picture format. But of course you will still be able to > tell that the baby is smaller that the grown-up because we know the > association between the shape of a person and their size. > > If you want to do an analysis, for example, distinguishing between > two groups with a substantial amount of size variation, you may still > need to apply some form of "size correction" to your shape data to > remove the allometric effects on shape variation. > > Normally, you will do the size correction by using the residuals from > a multivariate regression of shape on size. Depending on how > different the allometries within your groups are, this might be a bit > tricky. The solution will depend on your specific problem. > > I hope this helps. > > Best wishes, > Chris > > -- > ****************************************************************** > Christian Peter Klingenberg > School of Biological Sciences > University of Manchester > 3.614 Stopford Building > Oxford Road > Manchester M13 9PT > United Kingdom > > Telephone: +44 161 275 3899 > Fax: +44 161 275 3938 > E-mail: [EMAIL PROTECTED] > Web: http://www.sbs.man.ac.uk/chrisk > > Office: 3.530 Stopford Building (this is not the mailing address!) > ****************************************************************** > == > Replies will be sent to list. > For more information see http://life.bio.sunysb.edu/morph/morphmet.html. > == Replies will be sent to list. For more information see http://life.bio.sunysb.edu/morph/morphmet.html.
