Jun: Short answer: There is no such thing as df for a nonlinear model (whether or not mixed effects).
Longer answer: df is the dimension of the null space when the data are projected on the linear subspace of the model matrix of a **linear model ** . So, strictly speaking, no linear model, no df. HOWEVER... nonlinear models are usually (always??) fit by successive linear approximations, and approximate df are obtained from these approximating subspaces. However, the problem with this is that there is no guarantee that the relevant residual distributions are sufficiently chisq with the approximate df to give reasonable answers. In fact, lots of people much smarter than I have spent lots of time trying to figure out what sorts of approximations one should use to get trustworthy results. The thing is, in nonlinear models, it can DEPEND on the exact form of the model -- indeed, that's what distinguishes nonlinear models from linear ones! So this turns out to be really hard and afaik these smart people don't agree on what should be done. To see what one of the smartest people have to say about this, search the archives for Doug Bates's comments on this w.r.t. lmer (he won't compute such distributions nor provide P values because he doesn't know how to do it reliably. Doug -- please correct me if I have it wrong). A stock way to extricate oneself from this dilemma is: bootstrap! Unfortunately, this is also probably too facile: for one thing, with a nondiagonal covariance matrix (as in mixed effects models), how do you resample to preserve the covariance structure? I believe this is an area of active research in the time series literature, for example. For another, this may be too computationally demanding to be practicable due to convergence issues. Bottom line: there may be no good way to do what you want. Note to experts: Please view this post as an invitation to correct my errors and provide authoritative info. Cheers to all, Bert Bert Gunter Genentech Nonclinical Biostatistics -----Original Message----- From: r-help-boun...@r-project.org [mailto:r-help-boun...@r-project.org] On Behalf Of Jun Shen Sent: Monday, July 12, 2010 12:34 PM To: R-help Subject: [R] What is the degrees of freedom in an nlme model Dear all, I want to do a F test, which involves calculation of the degrees of freedom for the residuals. Now say, I have a nlme object "mod.nlme". I have two questions 1.How do I extract the degrees of freedom? 2.How is this degrees of freedom calculated in an nlme model? Thanks. Jun Shen Some sample code and data ================================================================= mod.nlme<-nlme(RESP~E0+(Emax-E0)*CP**gamma/(EC50**gamma+CP**gamma),data=Data , fixed=E0+Emax+gamma+EC50~1, random=list(pdDiag(EC50+E0+gamma~1)), groups=~ID, start=list(fixed=c(E0=1,Emax=100,gamma=1,b=50)) ) The "Data" object structure(list(ID = c(1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L), CP = c(1, 2, 3, 4.5, 5, 7.5, 11.25, 12, 18, 30, 45, 60, 90, 120, 150, 200, 1, 2, 3, 4.5, 5, 7.5, 11.25, 12, 18, 30, 45, 60, 90, 120, 150, 200, 1, 2, 3, 4.5, 5, 7.5, 11.25, 12, 18, 30, 45, 60, 90, 120, 150, 200, 1, 2, 3, 4.5, 5, 7.5, 11.25, 12, 18, 30, 45, 60, 90, 120, 150, 200, 1, 2, 3, 4.5, 5, 7.5, 11.25, 12, 18, 30, 45, 60, 90, 120, 150, 200, 1, 2, 3, 4.5, 5, 7.5, 11.25, 12, 18, 30, 45, 60, 90, 120, 150, 200, 1, 2, 3, 4.5, 5, 7.5, 11.25, 12, 18, 30, 45, 60, 90, 120, 150, 200, 1, 2, 3, 4.5, 5, 7.5, 11.25, 12, 18, 30, 45, 60, 90), RESP = c(3.19, 2.52, 2.89, 3.28, 3.82, 7.15, 11.2, 16.25, 30.32, 55.25, 73.56, 82.07, 89.08, 95.86, 97.97, 99.03, 3.49, 4.4, 3.54, 4.99, 3.81, 10.12, 21.59, 24.93, 40.18, 61.01, 78.65, 88.81, 93.1, 94.61, 98.83, 97.86, 0.42, 0, 2.58, 5.67, 3.64, 8.01, 12.75, 13.27, 24.65, 46.1, 65.16, 77.74, 87.99, 94.4, 96.05, 100.4, 2.43, 0, 6.32, 5.59, 8.48, 12.32, 26.4, 28.36, 43.38, 69.56, 82.53, 91.36, 95.37, 98.36, 98.66, 98.8, 5.16, 2, 5.65, 3.48, 5.78, 5.5, 11.55, 8.53, 18.02, 38.11, 58.93, 70.93, 85.62, 89.53, 96.19, 96.19, 2.76, 2.99, 3.75, 3.02, 5.44, 3.08, 8.31, 10.85, 13.79, 32.06, 50.22, 63.7, 81.34, 89.59, 93.06, 92.47, 3.32, 1.14, 2.43, 2.75, 3.02, 5.4, 8.49, 7.91, 15.17, 35.01, 53.91, 68.51, 83.12, 86.85, 92.17, 95.72, 3.58, 0.02, 3.69, 4.34, 6.32, 5.15, 9.7, 11.39, 23.38, 42.9, 61.91, 71.82, 87.83)), .Names = c("ID", "CP", "RESP"), class = "data.frame", row.names = c(NA, -125L)) ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
