[R] Bug or Feature? LogLik.nls and non-central F distribution.

Peter Dalgaard BSA p.dalgaard at biostat.ku.dk
Wed Jan 15 17:26:02 CET 2003

"Matthew L. Fidler" <fidler at math.utah.edu> writes:

> > logLik(short.alif.fit);
> `log Lik.' 6.307024 (df=1)
> My problem with this number is that exp(logLik) > 1.  If the error
> structure is independent, identically distributed normal (which I
> assumed was the case), then the Likelihood function should only give a
> number from 0 to 1...  

Whatever gave you that idea? Likelihoods can easily be larger than 1
for the same reasons that densitites can. Besides, there is often a
multiplicative factor removed from the calculation when it depends on
data only.

> I am running R 1.6.1.  Perhaps this is due to
> some strange assumption of non-independent normals???  Maybe something
> else???  I assumed that the Likelihood function should be
> -n/2*log(2*pi)-n/2*log(d)-n/2
> Where d=MLE (biased) estimator of the variance

But that's unbounded as d goes to zero and log(d) becomes negative!

   O__  ---- Peter Dalgaard             Blegdamsvej 3  
  c/ /'_ --- Dept. of Biostatistics     2200 Cph. N   
 (*) \(*) -- University of Copenhagen   Denmark      Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)             FAX: (+45) 35327907

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