Did you know that geomorph is not just for landmark-based geometric morphometric (shape) data?
We are committed to providing statistical tools for multivariate AND multidimensional morphometric data.
As laid out in the recent series of papers on Phylogenetic Comparative Methods for high-dimensional data (Adams 2014a, Adams 2014b, Adams 2014c, Adams & Felice 2014), harnessing the R-mode – Q-mode equivalency as first shown by Gower (1966) has allowed us to overcome the issue of greater variables (p) than specimens (n).
Certainly geometric morphometrics has been doing this for many years, using the Procrustes ANOVA (Goodall 1991) which is a distance-based (Q-mode) approach. The distance-based PGLS has a substantially better type I error than previously implemented approaches (Adams & Collyer 2015).
The issue, in short is that when you have p greater than or very close to n, there will be problems; your test will lose power or worse it simply will not work. The solution is to use the functions below that are designed for multivariate datasets (e.g. sets of linear measurements*) as well as multidimensional shape data (from landmark coordinates).
Procrustes ANOVA and pairwise tests for morphometric data, using complex linear models
Comparing rates of morphological evolution on phylogenies
Compare modular signal to alternative subsets
Morphological disparity for one or more groups of specimens
Quantify morphological integration between two modules of morphometric data
Pairwise comparisons of slopes of morphometric data
Pairwise group comparisons of morphometric data
Quantify phylogenetic morphological integration between two sets of variables
Assessing phylogenetic signal in morphometric data
Procrustes ANOVA/regression for morphometric data
Phylogenetic ANOVA/regression for morphometric data
Quantify and compare shape change trajectories
Two-block partial least squares analysis for two sets of morphometric data (or with non-morphometric data)
In all functions, the input would be a n x p matrix, that is specimens in rows and measurements in columns.
* Linear measurements may require correction for size. See Mosimann (1970; and Mosimann & James 1979).
- Adams, D. C. 2014a. A generalized K statistic for estimating phylogenetic signal from shape and other high-dimensional multivariate data. Systematic Biology 63: 685-697.
- —. 2014b. Quantifying and comparing phylogenetic evolutionary rates for shape and other high-dimensional phenotypic data. Systematic Biology 63: 166-177.
- —. 2014c. A method for assessing phylogenetic least squares models for shape and other high-dimensional multivariate data. Evolution 68: 2675-2688.
- Adams, D. C., and R. Felice. 2014. Assessing phylogenetic morphological integration and trait covariation in morphometric data using evolutionary covariance matrices. PloS ONE 9:e94335.
- Adams, D.C. & Collyer, M.L., 2015. Permutation tests for phylogenetic comparative analyses of high-dimensional shape data: what you shuffle matters. Evolution, 69: 823–829.
- Goodall, C. R. 1991. Procrustes methods in the statistical analysis of shape. J. R. Stat. Soc. B 53: 285–339.
- Gower, J.C., 1966. Some Distance Properties of Latent Root and Vector Methods Used in Multivariate Analysis. Biometrika, 53: 325-338.
- Mosimann, J.E., 1970. Size Allometry: Size and Shape Variables with Characterizations of the Lognormal and Generalized Gamma Distributions. Journal of the American Statistical Association, 65: 930–945.
- Mosimann, J.E. & James, F.C., 1979. New Statistical Methods for Allometry with Application to Florida Red-Winged Blackbirds. Evolution, 33: 444–459.