[R] how calculation degrees freedom

Søren Højsgaard Soren.Hojsgaard at agrsci.dk
Fri Jan 27 19:47:24 CET 2006

Degrees of freedom for mixed models is a delicate issue - except in certain orthogonal designs. 
However, I'll just point out that for lmer models, there is a simulate() function which can simulate data from a fitted model. simulate() is very fast - just like lmer(). So one way to "get around the problem" could be to evaluate the test statistic (e.g. -2 log Q) in an empirical distribution based on simulations under the model; that is to calculate a Monte Carlo p-value. It is fairly fast to and takes about 10 lines of code to program. 
Of course, Monte Carlo p-values have their problems, but the world is not perfect....
Along similar lines, I've noticed that the anova() function for lmer models now only reports the mean squares to go into the numerator but "nothing for the denominator" of an F-statistic; probably in recognition of the degree of freedom problem. It could be nice, however, if anova() produced even an approximate anova table which can be obtained from Wald tests. The anova function could then print that "these p-values are large sample ones and hence only approximate"...
Best regards


Fra: r-help-bounces at stat.math.ethz.ch på vegne af Douglas Bates
Sendt: fr 27-01-2006 17:06
Til: gabriela escati peñaloza
Cc: R-help at stat.math.ethz.ch
Emne: Re: [R] how calculation degrees freedom

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
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.

>   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 questions about S-PLUS.

> Lic. Gabriela Escati Peñaloza
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