I'd like to respond to your question because it comes up so often. As noted by Carmelo in the other posting, a large number of variables relative to the number of cases can lead to statistical problems. But often it does not.
In all analyses that treat each variable separately - including the computation of mean shapes and shape regressions - the number of variables does NOT matter! Also in principal component analysis (PCA) and between-group PCA there is NO restriction on the number of variables. However, the distribution of landmarks across the organism can influence the results. E.g., if one part - say the face - is covered only by a few anatomical landmarks, and another part - e.g., the neurocranium - by many semilandmarks, the latter one will dominate PCA results. But this holds true for all kinds of landmarks and variables, not only for semilandmarks. Analyses that involve the inversion of a covariance matrix - such as multiple regression, CVA, relative eigenanalysis, reduced rank regression, and parametric multivariate tests - require a clear excess of cases over variables. In any truly multivariate setting (such as geometric morphometrics), these analyses - if unavoidable - should ALWAYS be preceded by some sort of variable reduction and/or factor analysis. Again, this is not specific to semilandmarks. Partial least squares (PLS) is somewhat in-between these to groups. As shown in Bookstein's 2016 paper, the singular values (maximal covariances) in PLS can be strongly inflated if the number of variables is large compared to the number of cases. The singular vectors, however, are more stable. Essentially, the number of semilandmarks should be determined based on the anatomical details to be captured. More semilandmarks are not "harmful," perhaps just a waste of time. Best, Philipp Mitteroecker Am Montag, 5. November 2018 18:52:57 UTC+1 schrieb Diego Ardón: > > Good day everybody, I actually have twoI'd like to respond to your > question because it comes up so often. > > As noted by Carmelo in the other posting, a large number of variables > relative to the number of cases can lead to statistical problems. But often > it does not. > > In all analyses that treat each variable separately - including the > computation of mean shapes and shape regressions - the number of variables > does NOT matter! Also in principal component analysis (PCA) and > between-group PCA there is NO restriction on the number of variables. > However, the distribution of landmarks across the organism can influence > the results. E.g., if one part - say the face - is covered only by a few > anatomical landmarks, and another part - e.g., the neurocranium - by many > semilandmarks, the latter one will dominate PCA results. But this holds > true for all kinds of landmarks and variables, not only for semilandmarks. > > Analyses that involve the inversion of a covariance matrix - such as > multiple regression, CVA, relative eigenanalysis, reduced rank regression, > and parametric multivariate tests - require a clear excess of cases over > variables. In any truly multivariate setting (such as geometric > morphometrics), these analyses - if unavoidable - should ALWAYS be preceded > by some sort of variable reduction and/or factor analysis. Again, this is > not specific to semilandmarks. > > Partial least squares (PLS) is somewhat in-between these to groups. As > shown in Bookstein's 2016 paper, the singular values (maximal covariances) > in PLS can be strongly inflated if the number of variables is large > compared to the number of cases. The singular vectors, however, are more > stable. > > Essentially, the number of semilandmarks should be determined based on the > anatomical details to be captured. More semilandmarks are not "harmful", > perhaps just a waste of time. > > Best, > > Philipp Mitteroecker > > > > > > questions here regarding semi-landmarks: > > So, I was adviced to use semi-landmarks, I placed them with MakeFan8, > saved the files as images and then used TpsDig to place all landmarks, > however I didn't make any distinctions between landmarks and > semi-landmarks. What unsettles me is (1) that I've recently comed across > the term "sliding semi-landmarks", which leads me to believe semi-landmarks > should behave in a particular way. > > The second thing that unsettles me is whether "more semi-landmarks" means > a better analysis. I can understand that most people wouldn't use 65 > landmarks+semilandmarks because it's a painstaking job to digitize them, > however, in my recent reads I've comed across concepts like a "Variables to > specimen ratio", which one paper suggested specimens should be 5 times the > number of variables. I do have a a data set of nearly 400 specimens, but it > does come short if indeed I should have 65*2*5 specimens! > > Please, I'll appreciate some feedback :) > -- 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 morphmet+unsubscr...@morphometrics.org.
