[R] formula for degrees of freedom for nonlinear mixed model in nlme
Dear forum members, What is the formula to calculate denominator degrees of freedom (den df) for nonlinear mixed-effect models with covariates? My model is similar to a CO2 uptake example from Pinheiro and Bates (2000, page 376). In this CO2 dataset, there are two treatments and two types (84 observations in total), but den df for each parameter of the model is 64. Isnt it too high? Your help is greatly appreciated, Julia Summary of the CO2 example: summary(fm4CO2.nlme) Nonlinear mixed-effects model fit by maximum likelihood Model: uptake ~ SSasympOff(conc, Asym, lrc, c0) Data: CO2 AIC BIClogLik 388.4185 420.0191 -181.2092 Random effects: Formula: list(Asym ~ 1, lrc ~ 1) Level: Plant Structure: General positive-definite, Log-Cholesky parametrization StdDev Corr Asym.(Intercept) 2.349640 As.(I) lrc.(Intercept) 0.079597 -0.92 Residual 1.791962 Fixed effects: list(Asym + lrc ~ Type * Treatment, c0 ~ 1) Value Std.Error DF t-value p-value Asym.(Intercept) 41.81756 1.562426 64 26.76451 0. Asym.TypeMississippi -10.53045 2.208318 64 -4.76854 0. Asym.Treatmentchilled -2.96943 2.213172 64 -1.34171 0.1844 Asym.TypeMississippi:Treatmentchilled -10.90037 3.112220 64 -3.50244 0.0008 lrc.(Intercept)-4.55724 0.096291 64 -47.32785 0. lrc.TypeMississippi-0.10412 0.121683 64 -0.85570 0.3954 lrc.Treatmentchilled -0.17124 0.111959 64 -1.52953 0.1311 lrc.TypeMississippi:Treatmentchilled0.74188 0.221742 64 3.34570 0.0014 c0 50.51075 4.364727 64 11.57249 0. Correlation: As.(I) Asy.TM Asym.T A.TM:T lr.(I) lrc.TM Asym.TypeMississippi -0.703 Asym.Treatmentchilled -0.701 0.496 Asym.TypeMississippi:Treatmentchilled 0.497 -0.709 -0.711 lrc.(Intercept) -0.627 0.415 0.407 -0.278 lrc.TypeMississippi0.458 -0.680 -0.322 0.482 -0.535 lrc.Treatmentchilled 0.500 -0.351 -0.717 0.509 -0.594 0.445 lrc.TypeMississippi:Treatmentchilled -0.262 0.375 0.362 -0.547 0.365 -0.553 c0-0.086 0.014 0.001 0.019 0.590 -0.033 lrc.Tr l.TM:T Asym.TypeMississippi Asym.Treatmentchilled Asym.TypeMississippi:Treatmentchilled lrc.(Intercept) lrc.TypeMississippi lrc.Treatmentchilled lrc.TypeMississippi:Treatmentchilled -0.511 c0-0.057 0.140 Standardized Within-Group Residuals: Min Q1 Med Q3 Max -2.86206487 -0.49445730 -0.04217037 0.56599012 3.04061332 Number of Observations: 84 Number of Groups: 12 Link to the book: http://books.google.com/books?id=N3WeyHFbHLQCpg=PA139lpg=PA139dq=mixed-effect+model+building+first+stepsource=blots=pR7PWIuKu8sig=TLhq-k5O4ZNwkBWcyQI8VZk9Umkhl=enei=1HguSrKaPJi0Nb3DnfUJsa=Xoi=book_resultct=resultresnum=1#PPA376,M1 _ [[alternative HTML version deleted]] __ 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.
Re: [R] formula for degrees of freedom for nonlinear mixed model in nlme
The FAQ 7.35 links to this posting: https://stat.ethz.ch/pipermail/r-help/2006-May/094765.html On Jun 11, 2009, at 3:57 PM, J S wrote: Dear forum members, What is the formula to calculate denominator degrees of freedom (den df) for nonlinear mixed-effect models with covariates? My model is similar to a CO2 uptake example from Pinheiro and Bates (2000, page 376). In this CO2 dataset, there are two treatments and two types (84 observations in total), but den df for each parameter of the model is 64. Isnt it too high? Your help is greatly appreciated, Julia Summary of the CO2 example: summary(fm4CO2.nlme) Nonlinear mixed-effects model fit by maximum likelihood Model: uptake ~ SSasympOff(conc, Asym, lrc, c0) Data: CO2 AIC BIClogLik 388.4185 420.0191 -181.2092 Random effects: Formula: list(Asym ~ 1, lrc ~ 1) Level: Plant Structure: General positive-definite, Log-Cholesky parametrization StdDev Corr Asym.(Intercept) 2.349640 As.(I) lrc.(Intercept) 0.079597 -0.92 Residual 1.791962 Fixed effects: list(Asym + lrc ~ Type * Treatment, c0 ~ 1) Value Std.Error DF t- value p-value Asym.(Intercept) 41.81756 1.562426 64 26.76451 0. Asym.TypeMississippi -10.53045 2.208318 64 -4.76854 0. Asym.Treatmentchilled -2.96943 2.213172 64 -1.34171 0.1844 Asym.TypeMississippi:Treatmentchilled -10.90037 3.112220 64 -3.50244 0.0008 lrc.(Intercept)-4.55724 0.096291 64 -47.32785 0. lrc.TypeMississippi-0.10412 0.121683 64 -0.85570 0.3954 lrc.Treatmentchilled -0.17124 0.111959 64 -1.52953 0.1311 lrc.TypeMississippi:Treatmentchilled0.74188 0.221742 64 3.34570 0.0014 c0 50.51075 4.364727 64 11.57249 0. Correlation: As.(I) Asy.TM Asym.T A.TM:T lr. (I) lrc.TM Asym.TypeMississippi -0.703 Asym.Treatmentchilled -0.701 0.496 Asym.TypeMississippi:Treatmentchilled 0.497 -0.709 -0.711 lrc.(Intercept) -0.627 0.415 0.407 -0.278 lrc.TypeMississippi0.458 -0.680 -0.322 0.482 -0.535 lrc.Treatmentchilled 0.500 -0.351 -0.717 0.509 -0.594 0.445 lrc.TypeMississippi:Treatmentchilled -0.262 0.375 0.362 -0.547 0.365 -0.553 c0-0.086 0.014 0.001 0.019 0.590 -0.033 lrc.Tr l.TM:T Asym.TypeMississippi Asym.Treatmentchilled Asym.TypeMississippi:Treatmentchilled lrc.(Intercept) lrc.TypeMississippi lrc.Treatmentchilled lrc.TypeMississippi:Treatmentchilled -0.511 c0-0.057 0.140 Standardized Within-Group Residuals: Min Q1 Med Q3 Max -2.86206487 -0.49445730 -0.04217037 0.56599012 3.04061332 Number of Observations: 84 Number of Groups: 12 Link to the book: http://books.google.com/books?id=N3WeyHFbHLQCpg=PA139lpg=PA139dq=mixed-effect+model+building+first+stepsource=blots=pR7PWIuKu8sig=TLhq-k5O4ZNwkBWcyQI8VZk9Umkhl=enei=1HguSrKaPJi0Nb3DnfUJsa=Xoi=book_resultct=resultresnum=1#PPA376,M1 _ [[alternative HTML version deleted]] __ 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. David Winsemius, MD Heritage Laboratories West Hartford, CT __ 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.
Re: [R] formula for degrees of freedom for nonlinear mixed model in nlme
David Winsemius wrote: The FAQ 7.35 links to this posting: https://stat.ethz.ch/pipermail/r-help/2006-May/094765.html Actually, this is a different question from the usual why don't I get denominator df? question -- it is how are these calculated (since the poster is using nlme, not (n)lmer). The answer in this case is check Pinheiro and Bates 2000 -- I don't remember the page number exactly, looks like it's page 91 -- see Google books: http://tinyurl.com/ntygq3 If the denominator df don't agree with your intuition, you can always recompute p-values with the appropriate den df: (two-tailed) 2*pt(abs(t.score),df=dendf,lower.tail=FALSE) -- View this message in context: http://www.nabble.com/formula-for-degrees-of-freedom-for-nonlinear-mixed-model-in-nlme-tp23987913p23991255.html Sent from the R help mailing list archive at Nabble.com. __ 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.
Re: [R] formula for degrees of freedom for nonlinear mixed model in nlme
On Jun 11, 2009, at 8:47 PM, Ben Bolker wrote: David Winsemius wrote: The FAQ 7.35 links to this posting: https://stat.ethz.ch/pipermail/r-help/2006-May/094765.html Actually, this is a different question from the usual why don't I get denominator df? question -- it is how are these calculated (since the poster is using nlme, not (n)lmer). The answer in this case is check Pinheiro and Bates 2000 -- I don't remember the page number exactly, looks like it's page 91 -- see Google books: http://tinyurl.com/ntygq3 If the denominator df don't agree with your intuition, you can always recompute p-values with the appropriate den df: (two-tailed) 2*pt(abs(t.score),df=dendf,lower.tail=FALSE) Point well taken. So neither my citation nor page 91 (which also deals with LME models) are on point to the OP's question. P B say that inference regarding covariates in nlme models (which i believe was the question posed) are generally Wald statistics, and so don't really have denominator degrees of freedom, only numerators DFs. The numerator is then the observation count minus the model degrees of freedom. See 365-368 which deals with the sort of nlme model about which the OP is asking. A method for generating an anova analysis is also demonstrated on page 374. David Winsemius, MD Heritage Laboratories West Hartford, CT __ 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.
