Mark,
The paper published by Bentor is part of a published collection. I don't
know if it is available online. (I can, if you like, scan the relevant
2-3 pages and email them to you.)
Computer Based Horse Race Handicapping and Wagering Systems: A Report
William Bentor
Thanks!
-Noah
On 8/25/09 5:25 PM, markleeds@verizon.net wrote:> Hi Noah: Do you have a referene or the paper to the horse racing paper
> that you referred
> to previously ? I can't help you with below because I haven't
mastered
> the difference yet
> between the multinomial logit and the conditional logit. Chuck's
> reference didn't help me much
> with that so if you know of others, please let me know. Thanks.
>
>
> Mark
>
>
> On Aug 25, 2009, *Noah Silverman* <noah@smartmediacorp.com> wrote:
>
> Hello
>
> I believe that I'm getting very close in my modeling application.
>
> I've come across a challenge that I am unable to solve and would
> really
> appreciate the group's opinion.
>
> I've been using the val.prob function from the Design library
(Thanks
> Frank!!) to both evaluate and visualize my model.
>
> From the scores and graph, it appears as my model is very accurate in
> predicting probabilities correctly. Please see attachment
"graph1.pdf"
>
> Since I'm scoring horse races, I assume that I need to
"normalize"
> the
> predicted probabilities by race. (Described in Bentor.)
> I am calculating a conditional logit manually since there is a bug in
> the Survival library for this function.
>
> A val.prob function applied to my conditional logit score shows an
> interesting result. The line is almost perfectly parallel to the
> "ideal" mark on the graph, but is offset by a significant
amount. My
> first thought is that this indicates an error in my calculation
> somewhere. Please see attachment "graph2.pdf"
>
> Below is the two step process that I used for the conditional logit.
> --------------------------------------------------
> 1) First a standard logistic regression is calculated on two
> variables:
> model <- lrm(label ~ val1 + val2, data = traindata )
>
> This gives me the following results:
> Coef S.E. Wald Z P
> Intercept 1.8065 0.05137 35.16 0
> val1 0.8105 0.02567 31.57 0
> val2 0.5218 0.04308 12.11 0
>
> 2) I then calculate a conditional logit:
>
> testdata$log_int <- exp( model$coefficients[2] * model$val1 +
> model$coefficients[3] * model$val2)
> for(race in testdata$races){
> testlogdata$c_prob[testdata$code== race] <-
> testdata$log_int[testdata$race== race] /
> sum(testdata$log_int[testlogdata$race == race])
> }
> ---------------------------------------------------
>
> Do you have any idea why this might be happening? Did I miss
> something
> in my calculation?
>
> Additionally, please notice the "Logistic Calibration" line
on
> graph1.
> It appears almost perfect. My thought is that whatever transformation
> the val.prob is doing to my predictions is helping. How would I
> store/access those values?
>
> Once I can finalize the prediction of probabilities, then I can
> focus on
> the application to a betting model. Having a high level of confidence
> in my models predictions is obviously the first step.
>
> I really appreciate it.
>
> Thanks!
>
> -Noah
>
>
>
>
>
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>
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