# [R] Multinomial Logit with multiple groups

DJ e6p at bigfoot.com
Tue Jul 15 13:17:58 CEST 2003

```Hi,

I am inexperienced with ML and R so please be tolerant :)

I am trying to replicate the method I have seen in a paper without success.
If my understanding is correct (a big 'IF') it seems to use Multinomial
Logit on multiple groups of
various sizes, with 'nature' selecting the choice (the winner) - then uses
Maximum Likelihood to optimise the parameters to produce a model for
prediction.

I have not found any examples which use this technique. What is worse the
paper only really provides a summary of the method. So I  am stuck!

Here is an short summary extract from the paper describing the method:

**************************************************
Suppose horse h* is observed to win a race.
The multinomial logit model gives:

exp(Vh*)
Ph*=  ----------            for h* = 1,2,...,H.
H
'Sigma'exp(Vh)
h=1

N
Vh =   'Sigma' An*Zhn
n=1

where Zhn=Zhn(Xh,Yn) is the measured value of attribute n for horse h in
a race.
The 'A' values in the equation are the parameters of the stochastic
utility model that must                         be estimated from a sample
of races.

The likelihiood function can be written:

j
exp(L) = 'Product' Pjh*
j=1

where j denetes a race, h* is the horse observed to win race j, and L is
the log-likelihood function.
*********************************************

In an ideal world I would hope for the R code to solve a toy problem using
the above method.
I can provide a jpg of the paper and a dataset if required.

But really, *any* help you could give to help me get to grips with it woul
be great.

Thanks,
David

```