Andrea, I like to think of semilandmark sliding as iteratively finding fitted (predicted) values for the generalized linear model fit described by Gunz et al. (2005) (equation 4), and updating coordinates by these values until there is no more meaningful change (with regard to an acceptable criterion). If Bending energy is not used, the bending energy matrix is replaced by an identity matrix (i.e., independence), which produces the minimized Procrustes distance version of the sliding algorithm. (This is is the same as ordinary least squares being a simplification of generalized least squares by using an identity matrix for the covariance matrix in GLS estimation of parameters.) Calculating the bending energy matrix requires using the reference configuration. The hat matrix calculated in the process is typically post-multiplied by the target coordinates centered by the reference configuration. Changing the reference should, therefore, change the solution. Also, let’s not forget that with surface points, if we follow the Gunz et al. (2005) recommendation, 5 nearest neighbors are used to estimate the principal components for defining a tangent plane. One could use more nearest neighbors, which would change the tangent planes. One could also choose to project points after sliding back onto the surface (by finding the nearest neighbor) or not. One could choose to recursively update the reference configuration as the Procrustes average in each iteration, or use a constant reference. One could also choose different convergence criteria, depending on how precise the finished product should be. This is all to say that there are several - perhaps arbitrary - choices that can be made that will affect the results.
Whether these nuances have an appreciable empirical effect, I’m not sure. I doubt that shape distances would change “remarkably” (depending on one’s definition of remarkable), but I think one cannot expect that subsampling will produce the same Procrustes residuals that would be found from using one inclusive sample. As you have indicated, the same thing happens with GPA performed on “fixed” landmarks. The extent to which surface semilandmarks would be similar or more susceptible to change is hard to argue without considering whether bending energy is used, how many nearest neighbors are used, the relative density of surface points, etc. This is probably a question to answer empirically with specific data. (Get Procrustes residuals from the full data, do it again with subsetted data, and maybe do a two-block PLS analysis between two sets of matching specimens to see if there is any appreciable change.) I would be curious to know what others think. I have been thinking about this topic a lot, especially after dealing with the programming in geomorph. I’m sure there are other perspectives. Mike Michael Collyer Associate Professor Biostatistics Department of Biology Western Kentucky University 1906 College Heights Blvd. #11080 Bowling Green, KY 42101-1080 Phone: 270-745-8765; Fax: 270-745-6856 Email: [email protected]<mailto:[email protected]> On Feb 18, 2016, at 11:03 AM, andrea cardini <[email protected]<mailto:[email protected]>> wrote: Mike, does this mean that, in general, the position of the semilandmarks is strongly sample dependent, which would mean that also the shape distances might change remarkably despite the fact one has the same number of points on exactly the same surface? Say that I have two samples, A and B. I first (1) superimpose (and slide) within A. Then I do the same with both A and B together (2). Could I get appreciable differences between A1 and A2 just because of the sliding? All Procrustes shape distances depend on the sample composition. However, in my experience, differences between A1 and A2 tend to be negligible with 'standard' landmarks. Is this different with semilandmarks? Are there sensitivity analyses that explore the issue (if it's an issue)? Thanks in advance. Cheers Andrea At 17:06 18/02/2016, Collyer, Michael wrote: Contrary to your logic, subsetting your sample could have an effect. Your mean configuration would change in each of the subsamples, from the mean of your original sample, thus changing the reference configuration used in the separate GPAs performed. The reference configuration has a prominent role in the sliding of landmarks. Dr. Andrea Cardini Researcher, Dipartimento di Scienze Chimiche e Geologiche, Università di Modena e Reggio Emilia, Via Campi, 103 - 41125 Modena - Italy tel. 0039 059 2058472 Adjunct Associate Professor, Centre for Forensic Science , The University of Western Australia, 35 Stirling Highway, Crawley WA 6009, Australia E-mail address: [email protected]<mailto:[email protected]>, [email protected]<mailto:[email protected]> WEBPAGE: https://sites.google.com/site/alcardini/home/main FREE Yellow BOOK on Geometric Morphometrics: http://www.italian-journal-of-mammalogy.it/issue/view/405 or full volume at: http://www.italian-journal-of-mammalogy.it/public/journals/3/issue_241_complete_100.pdf Editorial board for: Zoomorphology: http://www.springer.com/life+sciences/animal+sciences/journal/435 Journal of Zoological Systematics and Evolutionary Research: http://www.wiley.com/bw/journal.asp?ref=0947-5745&site=1 Hystrix, the Italian Journal of Mammalogy: http://www.italian-journal-of-mammalogy.it/ -- MORPHMET may be accessed via its webpage at http://www.morphometrics.org --- You received this message because you are subscribed to the Google Groups "MORPHMET" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected].
