Hello everyone! Thank you for getting back to me about the eigenvectors. Looking at the sample the 60th vector is indeed a rounding error. I am going to work to increase my sample size before running this again.
-Seth Boren On Friday, August 12, 2022 at 8:37:00 PM UTC-5 [email protected] wrote: > Hi Seth, > > The number of meaningful PCs (i.e., those with non-zero variance) is > normally determined by the number of independent variables. In geometric > morphometrics that number is the number of landmark coordinates (k *2 for > 2D landmarks or k*3 for 3D). Procrustes superposition removes some of the > degrees of freedom from the variables, 4 for 2D landmarks (2 position or > translation, 1 size, and 1 rotation) or 7 for 3D (3 position, 1 size, and 3 > rotation). For 30 3D landmarks you would expect 30*3-7 = 83 PCs. > > However, sample size also limits degrees of freedom if n is less than > number of variables. Presuming you have 3D landmarks, your data are sample > limited. Technically you expect n-1 PCs for sample limited data, 59 in your > case. > > Zelditch et al’s text _Geometric Morphometrics for Biologists_ provides an > explanation that is not overly heavy on mathematics. Dryden & Mardia’s > _Statistical Analysis of Shape_ gives a more formal explanation. > > There are several reasons why you might have 60 instead of 59: might be > rounding error and the last eigenvalue is really 0, might be the > non-Euclidean Kendall shape space which leaves just a little more apparent > variance than the Procrustes degrees of freedom suggests if your eigen > decomposition algorithm has high precision. > > Note also that covariance between the landmarks also reduces the degrees > of freedom. If two coordinates covary completely then you have fewer > non-zero eigenvalues than expected. O’Keefe et al, 2022 discuss some of the > nuances related to covariance between landmarks( On Information Rank > Deficiency in Phenotypic Covariance Matrices. Syst Biol. 2022 Jun > 16;71(4):810-822. doi: 10.1093/sysbio/syab088) > > Best wishes, > David > > > > iPhone typing... > [email protected] > > On Aug 12, 2022, at 9:12 PM, Seth Boren <[email protected]> wrote: > > > > Hello! > My name is Seth Boren, and this is my first question I have ever asked > here! > > I am working on a morphometric analysis that involves 60 specimens with 30 > landmarks each. I have arranged the landmarks of these specimens into a > morphologika file and then ran it through a GPA then PCA using EVAN-Toolbox. > > The output file for my analysis has 60 PCs listed, with 60 eigenvalues > associated with them and the % explained variance broken up into 60 > portions. However, shouldn't there be 30 PCs instead, equaling the number > of landmarks? > > If anyone could help me understand what is happening you have my eternal > thanks. > > Thank you everyone for your time and consideration, > > -Seth Boren > > -- > 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]. > To view this discussion on the web visit > https://groups.google.com/d/msgid/morphmet2/2300f593-130a-4e6d-ac1d-dd6b5dfa2181n%40googlegroups.com > > <https://groups.google.com/d/msgid/morphmet2/2300f593-130a-4e6d-ac1d-dd6b5dfa2181n%40googlegroups.com?utm_medium=email&utm_source=footer> > . > > -- 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]. To view this discussion on the web visit https://groups.google.com/d/msgid/morphmet2/f4a6ae2b-24eb-4895-aa54-6195ec02cacdn%40googlegroups.com.
