Gernot Huber asked -- > 1. Why do you have to force a linear regression through the origin > when using phylogenetically independent contrasts (PICs)?
Because their expectations are zero. A contrast could be either X1 - X2 or X2 - X1, for one thing. The expectations of X1 and X2 are identical so their difference (in either direction) has expectation zero. > 2. If you suspect an inverse linear relationship, would you transform > one axis so you could still force the regression through the origin? > If so, what's the best transformation? The machinery assumes a bivariate normal distribution. So if, say, Y = a(1/X) + b, wouldn't that mean you were assuming that Y and 1/X were distributed as bivariate normal? If so, the distribution of X looks wierd when (1/X) gets near zero. But at least in that case If so, you could do that transformation (1/X) at the beginning. Or are you assuming that Y and X are bivariate normal and then Y = a(1/X) + b? That is dicier since X could in principle get down to zero and then there is a loud explosion on the Y scale. Assuming (ln X, ln Y) is bivariate normal seems safer, especially if the characters have natural limits at zero. Then the regression might just be a simple linear one. Joe ---- Joe Felsenstein j...@gs.washington.edu Department of Genome Sciences and Department of Biology, University of Washington, Box 355065, Seattle, WA 98195-5065 USA _______________________________________________ R-sig-phylo mailing list R-sig-phylo@r-project.org https://stat.ethz.ch/mailman/listinfo/r-sig-phylo
