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
>
>
>
>
>     ------------------------------------------------------------------------
>
>     ______________________________________________
>     R-help@r-project.org <mailto:R-help@r-project.org> mailing list
>     https://stat.ethz.ch/mailman/listinfo/r-help
>     PLEASE do read the posting guide
>     http://www.R-project.org/posting-guide.html
>     and provide commented, minimal, self-contained, reproducible code.
>

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