Ability of geometric morphometric methods to estimate a known covariance matrix

Landmark-based morphometric methods must estimate the amounts of translatio n, rotation, and scaling (or, nuisance) parameters to remove nonshape varia tion from a set of digitized figures. Errors in estimaties of these nuisanc e variables will be reflected in the covariance structure of the coordinate s, such as the residuals from a superimposition, or any linear combination of the coordinates, such as the partial warp and standard uniform scores. A simulation experiment was used to compare the ability of the generalized r esistant fit (GRF) and a relative warp analysis (RWA) to estimate known cov ariance matrices with various correlations and variance structures. Random covariance matrices were perturbed so as to vary the magnitude of the avera ge correlation among coordinates, the number of landmarks with excessive va riance, and the magnitude of the excessive variance. The covariance structu re was applied to random figures with between 6 and 20 landmarks. The resul ts show the expected performance of GRF and RWA across a broad spectrum of conditions. The performance of both GRF and RWA depended most strongly on t he number of landmarks. RWA performance decreased slightly when one or a fe w landmarks had excessive variance. GRF performance peaked when similar to 25% of the landmarks had excessive variance. In general, both RWA and GRF p erformed better at estimating the direction of the first principal axis of the covariance matrix than the structure of the entire covariance matrix. R WA tended to outperform GRF when >similar to 75% of the coordinates had exc essive variance. When <75% of the coordinates had excessive variance, the r elative performance of RWA and GRF depended on the magnitude of the excessi ve variance; when the landmarks with excessive variance had standard deviat ions (<sigma>) greater than or equal to 4 sigma minimum, GRF regularly outp erformed RWA.