[R] glm questions --- saturated model

[Peter Dalgaard]

"BXC (Bendix Carstensen)" <bxc at steno.dk> writes:

> > It's important to remember that lnL is defined only up to an additive 
> > constant.  For example a Poisson model has lnL contributions -mu + 
> > y*log(mu) + constant, and the constant is arbitrary.  The 
> > differencing 
> > in the deviance calculation eliminates it.  What constant would you 
> > like to use??
> > 
> 
> I have always been und the impression that the constant chosen by glm is
> that which makes the deviance of the saturated model 0, the saturated
> model being the one with one parameter per observation in the dataset.

As David pointed out, the deviance of a saturated model is zero by
definition. However, there's nothing arbitrary about the constant in a
likelihood either since it is supposed to be a density if seen as a
function of y (well, if you *really* want to quibble, it's a density
with respect to an arbitrary measure, so you could get an arbitrary
constant in if you insist, I suppose). The point is that the constant
is *uniformative* since it depends on y only, not mu, and hence that
people tend to throw some bits of the likelihood away, and not always
the same bits.

-- 
   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