J S
2009-Jun-11 19:57 UTC
[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. Isn’t 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 BIC logLik 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 0.0000 Asym.TypeMississippi -10.53045 2.208318 64 -4.76854 0.0000 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 0.0000 lrc.TypeMississippi -0.10412 0.121683 64 -0.85570 0.3954 lrc.Treatmentchilled -0.17124 0.111959 64 -1.52953 0.1311 lrc.TypeMississippi:Treatmentchilled 0.74188 0.221742 64 3.34570 0.0014 c0 50.51075 4.364727 64 11.57249 0.0000 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.TypeMississippi 0.458 -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=N3WeyHFbHLQC&pg=PA139&lpg=PA139&dq=mixed-effect+model+building+first+step&source=bl&ots=pR7PWIuKu8&sig=TLhq-k5O4ZNwkBWcyQI8VZk9Umk&hl=en&ei=1HguSrKaPJi0Nb3DnfUJ&sa=X&oi=book_result&ct=result&resnum=1#PPA376,M1 _________________________________________________________________ [[alternative HTML version deleted]]
David Winsemius
2009-Jun-11 20:15 UTC
[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. Isn?t 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 BIC logLik > 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 0.0000 > Asym.TypeMississippi -10.53045 2.208318 64 > -4.76854 0.0000 > 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 0.0000 > lrc.TypeMississippi -0.10412 0.121683 64 > -0.85570 0.3954 > lrc.Treatmentchilled -0.17124 0.111959 64 > -1.52953 0.1311 > lrc.TypeMississippi:Treatmentchilled 0.74188 0.221742 64 > 3.34570 0.0014 > c0 50.51075 4.364727 64 > 11.57249 0.0000 > 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.TypeMississippi 0.458 -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=N3WeyHFbHLQC&pg=PA139&lpg=PA139&dq=mixed-effect+model+building+first+step&source=bl&ots=pR7PWIuKu8&sig=TLhq-k5O4ZNwkBWcyQI8VZk9Umk&hl=en&ei=1HguSrKaPJi0Nb3DnfUJ&sa=X&oi=book_result&ct=result&resnum=1#PPA376,M1 > > > > _________________________________________________________________ > > > [[alternative HTML version deleted]] > > ______________________________________________ > R-help at 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