Hello all, Projection of multidimensional shape vector onto another vector is a commonly used technique in GM. Klingenberg used this approach to calculate shape score (The pace of morphological change: historical transformation of skull shape in St Bernard dogs). Likewise, Philipp Gunz used this technique to obtain cranial globularity score that quantifies each specimen's position along the vector representing cranial shape differences between modern and archaic specimens (Neandertal Introgression Sheds Light on Modern Human Endocranial Globularity). Higher globularity score may indicate more modern/archaic cranial shape, depending on the direction of comparison. For both shape score and globularity score, each specimen is given one single value.
In a recent paper by Zaidi et al. (Facial masculinity does not appear to be a conditiondependent male ornament and does not reflect MHC heterozygosity in humans), human facial masculinity is likewise calculated by projecting shape data onto a vector that quantifies differences in consensus facial shape between famales and males (calc_masc_03262018.R file from https://github.com/Arslan-Zaidi/Facial_masculinity_MHC). However, Zaidi performed shape vector projection in a different way. I illustrate Gunz's and Zaidi's method as below: [image: Snipaste_2020-05-08_16-18-04.png] In words, Gunz collapsed all coordinates of all landmarks into a single multidimensional vector for projection. In contrast, Zaidi performed the projection landmark-wise to obtained one score for each landmark and averaged the scores across all landmarks to obtain an overall score for each specimen. *But the problem is the globscore by Gunz and M_overall score by Zaidi are not numerically identical when the same dataset is analyzed.* Gunz's approach is consistent with how shape score was calculated by tradition. In geomorpho package in R, shape score is calculated through RRPP:::center(as.matrix(Y)) %*% B %*% ((t(B) %*% B) ^ -0.5), where Y contains shape data with n (number of specimens) rows and p*k columns (p landmarks in k dimensions). This is in line with Gunz's approach. The fascinating aspect of Zaidi's approach is that each landmark is given one score, which facilitates visualization (e.g., Fig 2B allows for color maps to be overlayed onto facial morphs, which allows for statitical assessment and visualization of the effect of covariates on facial masculinity for each landmark. Following Gunz's approach, this is not possible because each specimen is given only one single score). The question is how should we perceive Zaidi's approach to calculating score for each landmark, is it truely reasonable in GM? In addition, if we do follow Zaidi to estimate shape/globularity/masculinity score for each landmark in our dataset, should we just average scores over landmarks to obtain the overall score or should we still stick to Gunz's approach when calculating overall score? Kieran -- 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/morphmet2/712f8480-a9bb-4f25-a332-8aae6722681a%40googlegroups.com.
