Hi all, My colleague and I were working through some examples in the Pinheiro and Bates book, and ran into a bit of a puzzle. When we try fitting a simple intercept-only model to the default Orthodont dataset that includes a correlation structure, the residuals of the model no longer add up to 0 - rather, they diverge from zero quite a bit. This divergence seems to be much larger than we would expect simply from finite computational error. I'm sure that the answer is that I'm missing something fundamental about what the correlation structure is doing to the model residuals, but after quite a bit of Googling, I'm none the wiser. Can anyone suggest a source that I could read (or an answer) that could explain this behaviour? Many thanks, Adam Clark ### example code require(nlme) data(Orthodont) ## 1. fit mixed model mod_lme = lme(distance ~ 1, Orthodont, random = ~1|Subject) resid_lme = Orthodont$distance-predict(mod_lme, level = 0) # raw residuals sum(resid_lme) # ~0 # normalised residuals sum(residuals(mod_lme, type = "n")) # ~0 ## 2. fit mixed model with correlation structure mod_lme2 = lme(distance ~ 1, Orthodont, random = ~1|Subject, correlation = corSymm(form = ~1|Subject)) resid_lme2 = Orthodont$distance-predict(mod_lme2, level = 0) # raw residuals sum(resid_lme2) # -11.9! # normalised residuals sum(residuals(mod_lme2, type = "n")) # 17.8!
Adam Thomas Clark Asst. Professor Karl-Franzens-Universit?t Graz Institut f?r Biologie www.adamclarktheecologist.com [[alternative HTML version deleted]]