Comments (2)
I think it is appropriate to count both: you are still fitting a model with that number of degrees of freedom to that amount of data. The fact that those degrees of freedom turn out to be "dropped" (or, in stats language, "not identified") doesn't change the fact that you have them at your disposal to make the fit better if you can; the fact that those data points don't contribute to the final distribution doesn't mean that they couldn't have been informative in principle.
Does that make sense?
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Good enough for me!
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