[R] multinom(): likelihood of model?

[Prof Brian Ripley]

On Mon, 16 May 2005, Brooks Miner wrote:

> Professor Ripley,
>
> Thanks very much.  You comments were very helpful.  I've got it (almost) all 
> figured out now.  My model is for discrete data (discrete response AND 
> predictors).  The issue I'm stuck on is that my saturated model does NOT 
> predict exactly; the constant is ~1874.052.
>
> Here is an example of my model with much less data, showing how the saturated 
> model does not predict exactly (constant ~ 440.6375).

Because you have an aggregated model: counts, not individual observations.

>
>
> library(nnet)
> fem.labs<- 
> factor(c("Fem1","Fem2","Fem3","Fem4","Fem5","Fem6"),levels=c("Fem1","Fem 
> 2","Fem3","Fem4","Fem5","Fem6"))
> site.labs<-factor(c("Site01","Site02","Site03","Site04"))
> dyad.labs<-factor(c("M","H","U"),levels=c("M","H","U"))
> data.table<-expand.grid(Site=site.labs, Female=fem.labs,Dyad=dyad.labs)
> data<- 
> c(20,16,21,16,13,11,15,13,27,27,30,19,24,25,29,23,24,20,25,25,24,18,26,2 
> 0,2,0,2,2,1,1,0,1,3,3,3,6,4,3,2,4,2,1,3,1,3,4,1,1,5,11,4,9,1,3,0,1,3,3,0 
> ,8,4,4,1,5,6,11,4,6,3,8,3,9)
> data.table<-structure(.Data=data.table[rep(1: 
> nrow(data.table),data),],row.names=1:length(data))
> fit.saturated.model<-multinom(Dyad~Female*Site,data=data.table)
> fit.saturated.model$deviance # Why is this NONZERO?
>
>
> Am I setting up the regression for the saturated model incorrectly??
>
> Thanks in advance. . .
>
> - Brooks
>
> ----------------------------
> Brooks Miner
> Research Scientist
> Laird Lab
> UW Biology
> 206.616.9385
> http://protist.biology.washington.edu/Lairdlab/
>
> On May 13, 2005, at 10:41 PM, Prof Brian Ripley wrote:
>
>> 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
>
>

-- 
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