# Re: [R] how calculation degrees freedom

From: Douglas Bates <dmbates_at_gmail.com>
Date: Sat 28 Jan 2006 - 03:06:00 EST

On 1/27/06, gabriela escati peñaloza <gescati@yahoo.com.ar> wrote:
> Hi, I' m having a hard time understanding the computation of degrees of freedom

So do I and I'm one of the authors of the package :-)

> when runing nlme() on the following model:
>
> > formula(my data.gd)
> dLt ~ Lt | ID
>
> TasavB<- function(Lt, Linf, K) (K*(Linf-Lt))
>
> my model.nlme <- nlme (dLt ~ TasavB(Lt, Linf, K),
> data = my data.gd,
> fixed = list(Linf ~ 1, K ~ 1),
> start = list(fixed = c(70, 0.4)),
> na.action= na.include, naPattern = ~!is.na(dLt))
>
> > summary(my model.nlme)
> Nonlinear mixed-effects model fit by maximum likelihood
> Model: dLt ~ TasavB(Lt, Linf, K)
> Data: my data.gd
> AIC BIC logLik
> 13015.63 13051.57 -6501.814
> Random effects:
> Formula: list(Linf ~ 1 , K ~ 1 )
> Level: ID
> Structure: General positive-definite
> StdDev Corr
> Linf 7.3625291 Linf
> K 0.0845886 -0.656
> Residual 1.6967358
> Fixed effects: list(Linf + K ~ 1)
> Value Std.Error DF t-value p-value
> Linf 69.32748 0.4187314 402 165.5655 <.0001
> K 0.31424 0.0047690 2549 65.8917 <.0001
> Standardized Within-Group Residuals:
> Min Q1 Med Q3 Max
> -3.98674 -0.5338083 -0.02783649 0.5261591 4.750609
> Number of Observations: 2952
> Number of Groups: 403
> >
>
> Why are the DF of Linf and K different? I would apreciate if you could point me to a reference

The algorithm is described in Pinheiro and Bates (2000) "Mixed-effects Models in S and S-PLUS" published by Springer. See section 2.4.2

I would point out that there is effectively no difference between a t-distribution with 402 df and a t-distribution with 2549 df so the actual number of degrees of freedom is irrelevant in this case. All you need to know is that it is "large".

I will defer to any of the "degrees of freedom police" who post to this list to give you an explanation of why there should be different degrees of freedom. I have been studying mixed-effects models for nearly 15 years and I still don't understand.

Technically this email list is for questions about R. There is another list, s-news@biostat.wustl.edu, for questions about S-PLUS.

>
>
> Lic. Gabriela Escati Peñaloza
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