[R] log likelihood and deviance

Prof Brian Ripley ripley at stats.ox.ac.uk
Fri Jul 28 15:39:13 CEST 2000

> Date: Fri, 28 Jul 2000 09:10:34 -0400 (EDT)
> From: Ben Bolker <ben at zoo.ufl.edu>

>   The deviance is typically defined as -2*(log likelihood).

Sorry, that is a common misconception and misuse.  For a GLM it has a
precise technical meaning, in the original papers and in McCullagh &
Nelder.  The *scaled* deviance (qualifier normally incorrectly omitted)
is the difference in 2*(log likelihood) between a saturated model and
the actual model.  So although log likelhoods are by definition 
defined only up to an additive constant (which depends on the base
measure for the densities but there is a standard choice),
deviances are as well-defined as `saturated model' is.

> However, glm output may not be giving you the absolute log-likelihood --
> in these applications it's often easier to drop various multiplicative
> constants that appear in the likelihood, which become additive constants
> in the log-likelihood or deviance, which don't affect any of the
> statistical conclusions of the analysis.

They do in so far as the residual (scaled) deviance is concerned!

> On Fri, 28 Jul 2000, Alvine Bissery wrote:
> > I'm fitting glm models and the summary gives the deviance of the model .
> > 
> > I would like to obtain the log likelihood
> > How can I do ?

Via the AIC.  Since R's AIC is (assuming the scale is known) is

  -2 * (log-likelihood)  + 2 * #linear parameters,

you can work backwards.

Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272860 (secr)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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