# [R] how calculation degrees freedom

gabriela escati peñaloza gescati at yahoo.com.ar
Tue Jan 31 13:15:31 CET 2006

```Dear Dr. Bates,
Thank you very much for your response.

--- Douglas Bates <dmbates at gmail.com> escribió:

> On 1/27/06, gabriela escati peñaloza
> <gescati at 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
> section 2.4.2

the algorithm described in Pinheiro and Bates.

>
> 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".

However, what I don't understand (among other things)
is why my two parameters appear to be estimated at
different grouping levels (based on the DF values).
Affect this different values of DF at the estimates
parameters? The estimates fixed effects were get at
the same level of grouping?
>
> 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.
>
> >   Note: I working with Splus 6.1. for Windows
>
> Technically this email list is for questions about
> R.  There is
> another list, s-news at biostat.wustl.edu, for

> I apreciate any response.

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> >
>

Lic. Gabriela Escati Peñaloza
Biología y Manejo de Recursos Acuáticos
Centro Nacional Patagónico(CENPAT).
CONICET
Bvd. Brown s/nº.
Chubut
Argentina

Tel: 54-2965/451301/451024/451375/45401 (Int:277)
Fax: 54-29657451543

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