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# How to maximise a likelihood function in the form of a Multinomial Logit Model

Hi There,

I hope you can help me. I have a problem which can best be explained by the following:

I randomly select 50 to 60 mice (from a population of 1000) and race them across the room. Each mouse is marked by a number between 1 to 1000. I record the race winner's ID and its weight. I repeat this race for each minute, for 100 000 minutes; and the results are compiled to form my data.

I would like now to assess the explanatory power of weight to the probability of winning and towards this end I would like to estimate a coefficient (Beta) that will maximise a likelihood function in the form of:

L = sum_operator(from t=1 to T) log[   exp(V*) / sum_operator(from j=1 to J)[exp(V)]   ],

where V represents a linear regression model (V = Beta*Weight), V* represents the winner,  t represent minutes and j represents the number of mice for the particular race.

Is there a set of SAS code that can do this? Other then brute-force, I'm hoping there's an elegant code to solve the above problem.

Thanks

Joe

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