[R] denominator degrees of freedom and F-values in nlme

Douglas Bates bates at stat.wisc.edu
Sun Jul 9 18:19:41 CEST 2006

On 7/8/06, M R Robinson <matthew.r.robinson at ed.ac.uk> wrote:
> Hello,
> I am struggling to understand how denominator degrees of freedom and
> subsequent significance testing based upon them works in nlme models.
> I have a data set of 736 measurements (weight), taken within 3
> different age groups, on 497 individuals who fall into two
> morphological catagories (horn types).
> My model is:  Y ~ weight + horn type / age group, random=~1|individual
> I am modeling this using glmm.PQL function with family=neg.bin
> (negative binomial distribution, estimating theta based upon a glm
> without individual as a random effect). My data set will not be
> balanced, with varying numbers of measurements taken on different
> individuals and some individuals have no weight measures just a
> morphological type.
> My output:
>               denDF    numberdf
> Intercept     495
> weight        232       1
> horn type     495       1
> horn type:age 232       4
> So my question is where do these denDF come from and how are they
> calculated? I wish to then test significane of these fixed effects and
> can get F-ratio's and P-values but are these appropriate?

The algorithm for calculating those denominator degrees of freedom is
given in Chapter 2 of Pinheiro and Bates (2000), Mixed-effects Models
in S and S-PLUS, Springer.  It was designed to reproduce the results
of the BETWEENWITHIN option in SAS PROC MIXED.  On looking at that
algorithm recently I no longer feel that it is a good way of doing the
calculation but I don't have a better alternative at present.

Also, that algorithm and the use of the F test is suggested for linear
mixed models.  I'm not sure that it would apply "out of the box" to a
generalized liner mixed model, which is what you are fitting here.
However, for practical purposes you could assume a "worst case" of 232
denominator degrees of freedom for all terms because there is so
little difference between an F statistic with 232 denominator degrees
of freedom and one with  495 denominator degrees of freedom.

> Thank-you for your time.
> Kind regards
> Matthew
> *********************************
> Matt Robinson
> Institute of Evolutionary Biology
> Room 413, Ashworth Labs,
> King's Buildings,
> University of Edinburgh
> EH9 3JT, UK
> Tel: 0131 650 5990
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