Dear Mike, Many thanks for the reply!
When the procD.allometry function performs HOS test with multiple group labels given, does it compute the regression vectors for each group, and then tests whether the coefficients of these vectors were equal, using some multivariate statistical test? If so, is there an option that outputs the regression vectors? Given the high frequency of the latter being discussed in the primary GM literature, it seems important to be able to extract this result from the function. Finally, on the interpretation side - If group variation is significant, but not logCS, then under the model shape~size+group, does this imply that shape variation is mainly explained by variation in species, and allometry is absent? Regards, T.F. On Thursday, December 8, 2016 at 6:08:17 PM UTC+8, Mike Collyer wrote: > > Dear Tsung, > > The procD.allometry function performs two basic processes when groups are > provided. First, it does a homogeneity of slopes (HOS) test. This test > ascertains whether two or more groups have parallel or unique slopes (the > latter meaning at least one groups’s slope is different than the others). > The HOS test constructs two linear models: shape ~ size + group and shape > ~ size + group + size:group, and performs an analysis of variance to > determine if the size:group interaction significantly reduces the residual > error produced. (Note: log(size) is a possible and default choice in this > analysis.) > > After this test, procD.allometry then provides an analysis of variance on > each term in the resulting model from the HOS test. > > Regarding your question, if the HOS test reveals there is significant > heterogeneity in slopes, the coefficients returned allow one to find the > unique linear equations, by group, which would be found from separate runs > on procD.allometry, one group at a time. If the HOS test reveals that > there is not significant heterogeneity in slopes, the coefficients > constrain the slopes for different groups to be the same (parallel). > > Finally, and I think more to your point, the projected regression scores > are found by using for a (in the Xa calculation you note) the coefficients > that represent a common or individual slope from the linear model produced. > The matrix of coefficients, B, is arranged as first row = intercept, > second row = common slope, next rows (if applicable) are coefficients for > the group factor (essentially change the intercept, by group), and finally, > the last rows are the coefficients for the size:group interaction (if > applicable), which change the common slope to match each group’s unique > slope. Irrespective of the complexity of this B matrix, a is found as the > second row. If you run procD.allometry group by group, it is the same as > (1) asserting that group slopes are unique and (2) changing a to match not > the common slope, but the summation of the common slope and the > group-specific slope adjustment. One could do that, but would lose the > ability to compare the groups in the same plot, as each group would be > projected on a different axis. > > Hope that helps. > > Mike > > > On Dec 8, 2016, at 3:37 AM, Tsung Fei Khang <[email protected] > <javascript:>> wrote: > > Hi all, > > I would like to use procD.allometry to study allometry in two species. > > I understand that the function returns the regression score for each > specimen as Reg.proj, and that the calculation is obtained as: > s = Xa, where X is the nxp matrix of Procrustes shape variables, and a is > the px1 vector of regression coefficients normalized to 1. I am able to > verify this computation from first principles when all samples are presumed > to come from the same species. > > However, what happens when we are interested in more than 1 species (say > 2)? I could run procD.allometry by including the species labels via > f2=~gps, where gps gives the species labels. Is there just 1 regression > vector (which feels weird, since this should be species-specific), or 2? If > so, how can I recover both vectors? What is the difference of including > f2=~gps using all data, compared to if we make two separate runs of > procD.allometry, one for samples from species 1, and another for samples > from species 2? > > Thanks for any help. > > Rgds, > > TF > > > > > > > " PENAFIAN: E-mel ini dan apa-apa fail yang dikepilkan bersamanya > ("Mesej") adalah ditujukan hanya untuk kegunaan penerima(-penerima) yang > termaklum di atas dan mungkin mengandungi maklumat sulit. 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