09-11-2014 06:10 AM
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.