[R] Degrees of freedom for lm in logLik and AIC

[Ben Bolker]

Rubén Roa <rroa <at> azti.es> writes:

> 
> 
> However, shouldn't _free parameters_ only be counted for degrees of 
> freedom and for calculation of AIC?
> The sigma parameter is profiled out in a least-squares 
> linear regression, so it's not free, it's not a
> dimension of the likelihood.
> Just wondering ...
> 

  For AIC I think this distinction should only matter for the purposes
of consistency between computations in different packages/languages/contexts.
Only the differences between AIC values matter for inference.  (If you were
talking about AICc then I would tend to agree with you -- nuisance
parameters should not affect 'residual degrees of freedom'/finite-size
corrections.)