While you do have more sample than variables, it is too close. One prefers to have many more samples than the number of variables. Another problem is that a CVA with 144 variables will mostly involve a covariance matrix that is close to being singular. One way I like to check for problems (and is provided in NTSYSpc) is to first project the data onto the PCA axes based on the pooled within-groups covariance matrix. If the CVA suggests that the PC axes with the smallest eigenvalues are the most important for distinguishing groups then you are very likely to be in trouble. In that case, apparent large differences between some groups may be due to rounding errors in the computations. One solution is to drop PCA dimensions with small eigenvalues (of course you will then not be able to detect any real differences in those dimensions but in most studies that is not likely to be a problem). That also improves the ratio of the number of samples relative to the number of variables.
It is nice to produce a CVA type plot showing the relative distances among group means. One could just do a PCA of the group means. However, the purpose of the CVA plot is to show distances that are a function of how close the means are statistically (in the sense of how easily they can be distinguished). Distances in such a plot do not correspond to the absolute amount of shape difference as measured by Procrustes distances. The choice of distance is important. One could also do a PCOORD of a matrix of generalized distances but for visualization of shapes you will need information about the shape variables themselves. That can be done after a PCOORD analysis but using a CVA is more straight-forward. Depends of the purpose of your study. Note that if projections onto the PCA axes were used as variables then the results of the CVA will have to be back-transformed. ---------------------- F. James Rohlf New email: f.james.ro...@stonybrook.edu Distinguished Professor, Emeritus. Dept. of Ecol. & Evol. & Research Professor. Dept. of Anthropology Stony Brook University 11794-4364 WWW: http://life.bio.sunysb.edu/morph/rohlf P Please consider the environment before printing this email From: Christy Hipsley [mailto:chips...@museum.vic.gov.au] Sent: Monday, November 28, 2016 6:04 PM To: MORPHMET <morphmet@morphometrics.org> Subject: [MORPHMET] the problem with CVA... or is it? Dear Morphmet-ers, I'm seeking advice on methods for visualizing shape features that distinguish multiple groups using GM. I know CVA has fallen out of favor for a number of reasons discussed here - e.g., more variables than groups, nonisotropic variation: Mitteroecker, P., and Bookstein, F. 2011. Linear discrimination, ordination, and the visualization of selection gradients in modern morphometrics. Evol. Biol. 38:100–114. Klingenberg, C. P., and Monteiro, L. R. 2005. Distances and directions in multidimensional shape spaces: Implications for morphometric applications. Syst. Biol. 54:678–688. Although given these limitations, is it really expected to give completely false results regarding the visualization of shape changes? In my study sytem, I show that ecological groups have statistically different cranial shapes, using both Procrustes ANOVA and PGLS. Now I simply want to visualize what the main features are that distinguish them, preferably using warps or wireframes, so that those changes must be directly relateable to the original landmark coordinates. I did that using individual specimens instead of species means, so I have 161 individuals vs 144 variables (48 landmarks*3D). I also did a between-group PCA on the species means which shows the same pattern, so is it technically "wrong" to show both? Thanks for any feedback on this issue, and I would appreciate to hear any alternative methods that people might use. I use MorphoJ and Geomorph for analyses. Best, Christy -- 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 <mailto:morphmet+unsubscr...@morphometrics.org> . -- 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.
