maximisation of a multinomial logit likelihood function

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This project is a re-post. NOTE: solution must be written in SAS Hi There, I hope someone can help me with this . 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 Any other approach that robustly forecasts the probability of a win would be acceptable, in addition to the above.

Mathematics

SAS

Statistics

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@d2imatrix

Hi, We went through your requirement. We have developed logistic regression based models using 'proc logistic' in SAS. If we understand correctly you always choose a set of 50 or 60 mice and one among them come out as winner (lets say dependent variable winner=1 and rest all are 0). This way you construct 100,000 sets (random sampling with replacement from 1000 mice) of runs. So in your compiled data you will have 100,000 'one' and almost 100,000x49 (or59 at times) 'zeros'. Using this data and weight as independent variable we can construct a logistic model to check whether probability of winning is being explained by weight or not. At this point we know that 'proc catmod' is used for multi-nomial logistic regression. We need a day to study the design which you are tying to construct. Will you be able to give us a day for that? Kindly let us know if there's any other information you would like to share. Regards, Pal

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@simulnetcode1221

Hi, dear. You have posted very interesting project. I have interested in your project. I think i can do it. because I have experience in such project. regards.

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@nanakwaliz26

I am dedicated to provide my clients with quality products.i have again much experience in this field. I hope my proposal will taken into consideration. Yours Faithfully Qwamy cute

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@rausri4u

Hi, I have very good experience in multivariate data analysis using SAS and am also having the entire SAS environment set up. If possible just share with me some basic info about the project and i will definitely give you a very good output for the project. So if you give me an opportunity to serve i will prove out be very much fruitful. You can send me an sms any time.

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@shushmak87

I have expertise in statistics and SAS, which is the key requirement the this project. I can complete this project with accuracy. Please send me message to carry forward. Thanks

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