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

Matthew L. Fidler fidler at math.utah.edu
Wed Jan 15 17:38:38 CET 2003

On Wed, 2003-01-15 at 09:18, Douglas Bates wrote:
> "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...  
> Why?  The likelihood is the product of the probability densities of
> the observations given the parameters and a probability density can be
> greater than 1.
> The belief that a likelihood must be less than 1 is a common
> misconception

True,  if the variance is small (less than one), it can have that
feature.  I forgot;  thank you for reminding me. However I still cannot
get the non-central F to return the right tail (according to my linear
model's noncentral F distribution tables....)  I thought it wasn't
working because I couldn't get it to produce the log-liklihood function
that I derived.  I forgot to divide the residual sum of squares by N,
however....  sorry.
Matthew L. Fidler
fidler at math.utah.edu

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