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

From: Douglas Bates <>
Date: Mon 10 Jul 2006 - 02:19:41 EST

On 7/8/06, M R Robinson <> 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
> ______________________________________________
> mailing list
> PLEASE do read the posting guide!
> mailing list PLEASE do read the posting guide! Received on Mon Jul 10 02:24:12 2006

Archive maintained by Robert King, hosted by the discipline of statistics at the University of Newcastle, Australia.
Archive generated by hypermail 2.1.8, at Mon 10 Jul 2006 - 04:16:02 EST.

Mailing list information is available at Please read the posting guide before posting to the list.