[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
A linear-in-parameters specification leads to:
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
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