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In Dixon, Coles (1997), they have used the maximum likelihood estimation for the two modified independent Poisson models in (4.3) to model the scores in soccer.

I am trying to use R in order to "reproduce" the alpha and beta as well as the home effect parameters (pg. 274, Table 4) without using any packages (using the usual independent Poisson models are fine too). I have tried using bivpois package but I am not sure on how to modify its parameters.

I would greatly appreciate it if anyone can help me with the R code to model the data - Scores from the home and away team for Season 2012/13 in English Premier League. So, basically i need help in coding of equation 4.3 or 4.5 using the optim function in R.

Density for poisson distribution (Only 1 independent Poisson model)

poiprob = function (x) {
 (((alpha*beta*home)^x)*exp(-(alpha*beta*home))/(factorial(x)))  
}    
as.matrix(poiprob(x=mydata$HS[1]))

Normal Poisson Likelihood Function

ll.poisson <- function(par, y) {
(alpha*beta*home) <- exp(par)
out <- sum(y * log((alpha*beta*home))) - length(y) * (alpha*beta*home)
return(out)
}

Optimisation to find the appropriate estimates for alpha and beta.

opt <- optim(par = 2, fn = ll.poisson, method = "BFGS", control = list(fnscale = -1),
y = mydata$HS)$par
mle <- exp(opt)

I encountered error in finding the estimates for the 3 parameters, alpha, beta and home effect. Can anyone advise me a way to improve the codes?

Data is in the form,

    HS  AS           Home             Away 
1    2  1           Arsenal       Aston Villa
2    1  2           Arsenal           Chelsea
3    0  0           Arsenal           Everton 
                .
                .
                .
378  2  2    Wigan Athletic Tottenham Hotspur 
379  1  2    Wigan Athletic   West Bromwich …  
380  2  1    Wigan Athletic   West Ham United
Hann
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  • Hello, as a general rule of thumb, questions on StackOverflow should show some work and effort. Specifically, requests for code should definitely have some indication of attempts and specifically what you need help with. Please feel free to edit your question and indicate where you are having difficulties – Ricardo Saporta Oct 10 '13 at 04:56
  • [This](http://stackoverflow.com/help/on-topic), [this](http://meta.stackoverflow.com/help/how-to-ask) and [this](http://stackoverflow.com/questions/5963269/how-to-make-a-great-r-reproducible-example/5963610#5963610) may serve as guide-lines for your question. – Henrik Oct 10 '13 at 09:03

0 Answers0