On Mar 28, 2011, at 16:53 , Ben Bolker wrote: > 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.) >
You're having me confused... AIC and friends are not within my "core competences" (i.e., I know what they are about, but I don't use them intensively on a daily basis), so I may be completely off base, but AFAICS _residual_ degrees of freedom never enters in the logLik computations. Also, I don't get the point about profiling -- you're just maximizing in two steps: first over sigma then over everything else, how is that different from just maximizing? On the other hand, I suppose it might be argued that the REML variant really only makes sense as a likelihood for sigma, so should have df=1. After all, it is by definition based on a transformation which makes the mean value parameters disappear. -- Peter Dalgaard Center for Statistics, Copenhagen Business School Solbjerg Plads 3, 2000 Frederiksberg, Denmark Phone: (+45)38153501 Email: pd....@cbs.dk Priv: pda...@gmail.com ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
