# Degrees of freedom in my mixed model

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.

Thanks!

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.

• 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. Oct 16 '12 at 20:15
• 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? Oct 16 '12 at 20:21
• My not-really-expert opinion is in line with Douglas Bates very expert opinion - don't use them at all. Oct 16 '12 at 21:07
• @Landon Did you look at Andy W's comment ? You could also use fiducial inference unc.edu/~hannig/publications/CisewskiHannig2012.pdf Oct 17 '12 at 7:59
• 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. Oct 17 '12 at 21:49