Hi, I am trying to construct a general linear model to test whether sexual selection on a male trait differs between treatment environments. Sexual selection is measured by the regression coefficient between a measure of male fitness (mating success) and the male trait value: y = Bx, where y is the mating success of an individual male, x is his value for the trait (a continuous variable), and B is the partial regression coefficient (we are actually considering multiple male traits, but we can stick with one here). The data come from an experiment involving three treatment environments, with four replicate populations nested within each treatment environment. We want to determine if selection on this trait varies among treatments, so are tempted to run the following model (in SAS proc glm):
y = treat + pop(treat) + x + treat*trait where treat is the treatment (3 levels; fixed effect), pop(treat) is population nested within treatment (random effect), x is the male's trait value, and treat*trait is the interaction term that tests for variation in selection among treatments. However, this model in effect pools all individuals among populations within each treatment(after correcting for their respective population mean) to estimate a single slope for each treatment. This is a problem because slopes likely vary among the 4 populations within each treatments. This suggests the following model: y = treat + pop(treat) + x + pop(treat)*trait + treat*trait where pop(treat)*trait is the interaction term testing for homogeneity of slopes among populations within treatments (ie, a nested ANCOVA). My questions are: 1) If the pop(treat)*trait term is significant, indicating significant variation in slopes among populations within treatments, am I justified in going on to test for a treatment effect (ie, treat*trait)? There must be some way to constuct a model to test whether slopes vary among treatments even if they vary within treatments... 2) If I am, what is the appropriate error term for the treat*trait interaction to be tested over (ie, is treat*trait tested over the MSerror or the MSpop(treat)*trait, or something else)? It seems to me that we need to be 'penalized' in some way for the presence of variation among populations within treatments, which could come about either due to the presence in the model of the pop(treat)*trait term (which sucks up variance), or because we test treat*trait over MSpop(treat)*trait instead of MSerror (whichs seems to make some sense as well). Any help would be much appreciated! Cheers, Howard ([EMAIL PROTECTED]) --------------- Howard D. Rundle Department of Zoology & Entomology University of Queensland St. Lucia, Qld. 4072 AUSTRALIA tel. + 61 7 3365 2855 fax + 61 7 3365 1655 website: http://www.uq.edu.au/~uqhrundl/ . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
