[R] formula for degrees of freedom for nonlinear mixed model in nlme

[David Winsemius]

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
>
>
>
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David Winsemius, MD
Heritage Laboratories
West Hartford, CT