Dean and Andrea, I wanted to follow up on what Dean wrote regarding using residuals from a pooled within-group regression, and what I think may be important discussion that follows from it. Considerable research has gone into investigating this issue, and as Dean points out, most of the time it is best to include the additional predictor (let's just use centroid size) in the model and fit it with the shape ~ group + size + group:size term. Indeed, I think we could all find 10-15 different papers (each) that discuss this issue (and a few of them pertaining to geometric morphometrics).
However, there are some common cases in geometric morphometrics that I think many of us deal with, and at least to my mind we do not have a very satisfactory guide to deal with some of them. Let's imagine a case that I think is particularly common in geometric morphometric studies, where we are examining sexual shape dimorphism, where we have sex as a categorical predictor as well as centroid size. So we might start with the model shape ~ sex + size + sex:size Geometric morphometric analyses are pretty sensitive, and at least with some systems (like fly wings) sample sizes tend to be relatively high. Frequently I have observed that the evidence is not consistent (based on Null Hypothesis Statistical Testing, NHST) with a common allometric relationship between the two sexes. Indeed since NHST (and assessment of significance) is in part a function on sample size, with large enough N, this term will be significant (even if the magnitude of effect is very small). Thus (as Dean has already clearly laid out) it may be unreasonable to use a pooled within-group regression and use the residuals (so that you can separate out allometric from non-allometric components of sexual shape dimorphism for instance). However, if you go ahead and examine the vector correlations/angle between the slopes (shape ~ size) across sexes you will observe that the vector correlation is ~1 (angle is ~0). Similarly the partial coefficient of determination (r^2) for the size:sex term is quite small relative to the partial r^2 for the marginal contributions of size and sex. Thus despite the NHST suggesting a lack of a common allometric relationship, this "deeper" examination suggests the slopes are very similar. So what do you do (again if you want to partition the allometric and non-allometric components of shape variation)? if the vector correlation is 0.99 do you decide they are effectively the same and proceed with pooled within-group regression to extract residuals? How about if the VC is 0.95? 0.9? At what point do you risk causing substantial inferential problems? Or do you alternatively not try to use a pooled within-group regression at all, and instead just predict shapes for males or females at particular centroid sizes given the full model (sex + size + sex:size), so you can get a sense of the extent of sexual shape dimorphism for comparable sizes (or whatever your goals might be). While I do not expect any hard and fast rules, I am wondering if anyone has done the relevant simulations to look at when the former (residuals from pooled within-group regression) becomes substantially problematic (in terms of magnitude of the sex:size interaction term). While I can quibble and be a pedant (who among us GMers are not!), I think the paper by Nelly, Michel and Chris is very useful (but does not get into the issue about when using residuals from pooled regression is problematic). N. A. Gidaszewski, M. Baylac, and C. P. Klingenberg, “Evolution of sexual dimorphism of wing shape in the Drosophila melanogaster subgroup.,” *BMC Evol Biol*, vol. 9, p. 110, 2009. I hope this leads to useful discussion! Cheers Ian dwor...@mcmaster.ca -- 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.
