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 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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