[R] Multilevel model with lme(): Weird degrees of freedom (group level df > # of groups)

[Bertolt Meyer]

Hello everyone,

I am trying to regress applicants' performance in an assessment center  
(AC) on their gender (individual level) and the size of the AC (group  
level) with a multi-level model:

model.0 <- lme(performance ~ ACsize + gender, random = ~1 | ACNumber,  
method = "ML", control = list(opt = "optim"))

I have 1047 applicants in 118 ACs:

 > length(performance)
[1] 1047

 > length(levels(as.factor(ACNumber)))
[1] 118

There are five AC sizes and gender has two levels (coded as -1 for  
female and 1 for male):

 > length(levels(as.factor(ACsize)))
[1] 5

 > length(levels(as.factor(gender)))
[1] 2

However, when I examine the model summary, the predictor on the  
individual level (gender) and the predictor on group level (ACsize)  
have the same degrees of freedom:

 > summary(model.0)
Linear mixed-effects model fit by maximum likelihood
[...]

Random effects:
  Formula: ~1 | ACNumber
         (Intercept)  Residual
StdDev:   0.1650112 0.8146622

Fixed effects: performance ~ ACsize + gender
                  Value  Std.Error  DF   t-value p-value
(Intercept)  3.0927051 0.24573622 927 12.585467  0.0000
ACsize      -0.0568915 0.02782755 927 -2.044431  0.0412
gender       0.1679830 0.02780940 927  6.040510  0.0000
[...]

Number of Observations: 1047
Number of Groups: 118

How is it possible that the group-level predictor has a df > than the  
number of groups? I am a little at a loss here and would appreciate it  
if someone could explain this to me... What am I missing?

Regards,
Bertolt

-- 
Dr. Bertolt Meyer
Senior research and teaching associate
Social Psychology, Institute of Psychology, University of Zurich
Binzmuehlestrasse 14, Box 15
CH-8050 Zurich
Switzerland

bmeyer at sozpsy.uzh.ch
tel:   +41446357282
fax:   +41446357279
mob:   +41788966111