Programming the statistical procedures from SAS

Degrees of freedom involved in Wald tests for parameter estimates with NLMIXED

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Degrees of freedom involved in Wald tests for parameter estimates with NLMIXED

[ Edited ]

The degrees of freedom associated with wald tests of parameter estimates for NLMIXED is: 

#Subjects - #Random Effects Parameters; by default.

 

My question is: why the number of fixed effect parameters being estimated does not count for estimating themselves?

 

E.g. I can have a dataset with a given number of subjects and try two different models: one with fewer (simpler) and another with more fixed effect parameters (more complex), and yet the wald test df for all parameters (fixed & random) is the same in both scenarios.

 

Shouldn't I lose df as I add more fixed effect parameters?

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