summary lme (intercept) and new question (df in lme)

["Bernd Puschner" <bernd.puschner@bkh-guenzburg.de>]

dear s-plus users,

thanks to douglas bates, bert gunter, and manuela huso for answering my
question about the meaning of the intercept's p-value in lme. the answer is:
The p-value is for the (marginal) test of the Intercept = 0 versus Intercept
!= 0.

I have another question pertaining to lme (to which I couldn't find answers
in pinheiro/bates: "mixed effects..."): when computed a lme-model (of change
in time of the criterion variable) with two predictors, one continuous, the
other factorial (3 categories):

model.lme <- lme(data = iip.in, random = ~in.therm | code, fixed = oqsd ~
(x1 + as.factor(thern)) * in.therm, na.action = na.omit),

the fixed effects part of the output looks like this

> summary(model.lme)
...
Fixed effects: oqsd ~ (x1 + as.factor(thern)) * in.therm
                              Value Std.Error  DF   t-value p-value
              (Intercept)  40.90453 0.7882101 932  51.89547  <.0001
                       x1  -0.07581 0.2215110 532  -0.34226  0.7323
        as.factor(thern)1  -1.04852 0.8783406 532  -1.19375  0.2331
        as.factor(thern)2   0.09866 0.4917715 532   0.20062  0.8411
                 in.therm  -0.38881 0.0450593 932  -8.62895  <.0001
              x1:in.therm  -0.00077 0.0133241 932  -0.05813  0.9537
as.factor(thern)1in.therm   0.05369 0.0457854 932   1.17262  0.2412
as.factor(thern)2in.therm  -0.01635 0.0306450 932  -0.53351  0.5938

 ...
Number of Observations: 1472
Number of Groups: 536

How exactly does S-Plus calculate the degrees of freedom?

Thanks for any ideas.

Bernd