# Maximum Likelihood

#### austwins17

HORSE RACING MODEL

I'm trying to estimate the β coefficients in the following equation using maximum likelihood procedures: where βk is a coefficient which measures the relative contribution of information xij (k) to horse i's chance of winning race j.

I've attached an excel spreadsheet with some mock data. I'd like to know the formula to determine the value for β by maximizing the log likelihood function.

P.S. - I know the spreadsheet only contains one variable and data for two races, which is nowhere near enough to derive a meaningful result, but it's okay. I just need the formula.

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#### chiro

MHF Helper
Hey austwins17.

Like I said in my other response, you will need to use an iterative algorithm to get the estimates. Look up expectation maximization, exponential family distributions and generalized linear models to get the actual formulas.

You can use R to do the computations and R is free and open source. glm() will do it for you - you just need to pass it the right parameters. Once you get the family of distributions then you can supply the data to the R function.

Look up multinomial and related GLM's in R. I looked it up and there is apparently a library glmnet() that will do it for you:

http://web.stanford.edu/~hastie/glmnet/glmnet_alpha.html