R help - May 2005 - multinom(): likelihood of model?

Hi all,

I'm working on a multinomial (or "polytomous") logistic regression
using R and have made great progress using multinom() from the nnet 
library.  My response variable has three categories, and there are two 
different possible predictors.  I'd like to use the likelihoods of 
certain models (ie, saturated, fitteds, and null) to calculate 
Nagelkerke R-squared values for various fitted models.

My question today is simple: once I have fitted a model using 
multinom(), how do I find the likelihood (or log likelihood) of my 
fitted model?  I understand that this value must be part of the 
$deviance or $AIC components of the fitted model, but my understanding 
is too limited at this point for me to know how to calculate the 
likelihood of my fitted model from either of these outputs.

Thanks in advance to any assistance offered.  I'd be happy to provide 
an example of my data and multinom() entries if that would help.

Gratefully,

- Brooks
----------------------------
Brooks Miner
Research Scientist
Laird Lab
UW Biology
206.616.9385
http://protist.biology.washington.edu/Lairdlab/

By definition, the deviance is minus twice the maximized log-likelihood 
plus a const.  In any of these models for discrete data, the saturated 
model predicts exactly, so the const is zero.

There are worked examples in MASS4, the book multinom() supports.

On Fri, 13 May 2005, Brooks Miner wrote:
> Hi all,
>
> I'm working on a multinomial (or "polytomous") logistic
regression using R
> and have made great progress using multinom() from the nnet library.  My 
> response variable has three categories, and there are two different
possible
> predictors.  I'd like to use the likelihoods of certain models (ie, 
> saturated, fitteds, and null) to calculate Nagelkerke R-squared values for 
> various fitted models.
>
> My question today is simple: once I have fitted a model using multinom(),
how
> do I find the likelihood (or log likelihood) of my fitted model?  I 
> understand that this value must be part of the $deviance or $AIC components
> of the fitted model, but my understanding is too limited at this point for
me
> to know how to calculate the likelihood of my fitted model from either of 
> these outputs.
>
> Thanks in advance to any assistance offered.  I'd be happy to provide
an
> example of my data and multinom() entries if that would help.
>
> Gratefully,
>
> - Brooks
> ----------------------------
> Brooks Miner
> Research Scientist
> Laird Lab
> UW Biology
> 206.616.9385
> http://protist.biology.washington.edu/Lairdlab/
>
> ______________________________________________
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> PLEASE do read the posting guide!
http://www.R-project.org/posting-guide.html
>
-- 
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