# [R] Log-likelihood function

Doxastic connect.chris at gmail.com
Wed May 2 10:46:21 CEST 2007

```You're right.  I do need to learn more.  I never learned null/residual
deviance.  I know the deviance is equivalent to an anova decompostion.  But
I've never dealt with it seperated like this.

I understand deviance as the difference between two model's log-likelihood
difference between them and the most complex.  I want to compare two models
that are not the most complex.  That is why I wanted the log-likelihood.

I am using the poisson distribution because my response is count data, so
the link is the log.  If the deviance in R is computed by comparing the
fitted model against the most saturated (which would make sense).  Then yes,
I can use that.  I just picked the log-likelihood because I'm comparing two
models.  And that's the best way.  But, it's equivalent if R compares the
fitted to the most complex.

I assumed the deviance print out tested the fitted model against the least
complex.  This tests whether the current model parameters can be dropped
(that's what I thought the null deviance meant).  I'm not sure what the
residaul deviance means though.

My main concern is why the likelihood functions differed between SAS and R.
If anyone has encountered this or understands why, I would appreciate some
help.

Prof Brian Ripley wrote:
>
> I think you need to learn about deviances, which R does print.
>
> Log-likelihoods are only defined up to additive constants.  In this case
> the conventional constant differs if you view this as a Poisson or as a
> product-multinomial log-linear model, and R gives you the log-likelihood
> for a Poisson log-linear model (assuming you specified family=poisson).
> However, deviances and differences in log-likelihoods do not depend on
> which.
>
> More details and worked examples can be found in MASS (the book, see the
> FAQ), including other ways to fit log-linear models in R.
>
>
> On Tue, 1 May 2007, someone ashamed of his real name wrote:
>
>> I've computed a loglinear model on a categorical dataset.  I would like
>> to
>> test whether an interaction can be dropped by comparing the
>> log-likelihoods
>> from two models(the model with the interaction vs. the model without).
>> Since R does not immediately print the log-likelihood when I use the
>> "glm"
>> function, I used SAS initially.  After searching for an extracting
>> function,
>> I found one in R.  But, the log-likelihood given by SAS is different from
>> the one given by R.  I'm not sure if the "logLik" function in R is giving
>> me
>> something I don't want.  Or if I'm misinterpreting the SAS output.  Can
>> anyone help?
>>
>
> --
> 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 272866 (PA)
> Oxford OX1 3TG, UK                Fax:  +44 1865 272595
>
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