I am having a serious issue trying to figure out why my degrees of freedom are screwy when running my proc mixed model. I have nested data for a MLM analyses, but SAS isn't providing the correct df and I'm not sure why.

I have 50 individuals with 3 or 4 time sensitive datapoints each. Measuring their physical activity per day for 4 days, I have 177 observed instances of physical activity, however SAS keeps outputting 77 df when running ddfm=bw.

I have cleaned the data and reimported, but I'm just at a loss for what to do now. I'd really appreciate any help.



1 Answer 1


Likely SAS has done nothing wrong at all. DF for mixed models isn't straightforward. See the SAS STAT manual for PROC MIXED:

It is computed by dividing the residual degrees of freedom into between-subject and within-subject portions. PROC MIXED then checks whether a fixed effect changes within any subject. If so, it assigns within-subject degrees of freedom to the effect; otherwise, it assigns the between-subject degrees of freedom to the effect (see Schluchter and Elashoff 1990). If there are multiple within-subject effects containing classification variables, the within-subject degrees of freedom are partitioned into components corresponding to the subject-by-effect interactions.

SAS will also let you specify your own DF using the DDF = option, and has many choices besides BW, each of which will give different numbers.

I have even seen it recommended (I forget in which book) that the DF for the denominator not be reported.

Update by StasK: the FAQ on the degrees of freedom for a comparable mixed model R package lmer points to a post on R-help mailing list by Douglas Bates, the author of the package, explaining the controversies surrounding these degrees of freedom.

  • 3
    $\begingroup$ Peter, I think that's Douglas Bates' (the author of R nlme package) opinion that inference on the variance parameters should not be done, and no CIs nor DFs for them should be reported. $\endgroup$
    – StasK
    Oct 16, 2012 at 20:15
  • $\begingroup$ I was assuming that the within-subject DF would be something closer to 122 (the number of observations I have at Level 2) and not 77 (what the output is giving me). I don't know the exact DF but thought it would be more aligned with this. Also, should there a particular choice for DF here instead of bw? $\endgroup$
    – Landon
    Oct 16, 2012 at 20:21
  • $\begingroup$ My not-really-expert opinion is in line with Douglas Bates very expert opinion - don't use them at all. $\endgroup$
    – Peter Flom
    Oct 16, 2012 at 21:07
  • $\begingroup$ @Landon Did you look at Andy W's comment ? You could also use fiducial inference unc.edu/~hannig/publications/CisewskiHannig2012.pdf $\endgroup$ Oct 17, 2012 at 7:59
  • 2
    $\begingroup$ Stephane, Peter, I updated Peter's answer to give references to Douglas Bates' expert opinion. I am not particularly convinced in Bates' argument myself, as I approach mixed models as a special case of maximum likelihood where, given a large enough sample size, everything will be asymptotically normal or chi-square; rather than the generalization of ANOVA and experimental designs, for which the concept of the degrees of freedom of the F-statistic is really central. But I do recognize that the small sample performance of these asymptotic $z$ or $\chi^2$ may well be terrible. $\endgroup$
    – StasK
    Oct 17, 2012 at 21:49

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