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I've got a set of football results and I want to make a probabilty model of football scores as described in Dixon, Coles (1997, http://www.math.ku.dk/~rolf/teaching/thesis/DixonColes.pdf). They estimate the parameters based on maximum likelihood and the model assumes the variables are independent Poisson.

Now I have 2 questions:

  • How should I transform my data to input them in the model?
  • What packages in R are best for maximum likelihood estimation of this nature?
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  • $\begingroup$ Related: stats.stackexchange.com/q/11800/2970 (including an answer with a reference to Dixon and Coles). There are also some tangentially related questions; see the games tag. $\endgroup$
    – cardinal
    Commented Jul 7, 2012 at 13:29
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    $\begingroup$ Note that the Maher model (4.1) in the Dixon and Coles paper is just a straightforward GLM. It is very similar to the second model discussed in the answer here. $\endgroup$
    – cardinal
    Commented Jul 7, 2012 at 13:38
  • $\begingroup$ For American's like me it would havae been helpful in you had mentioned that you are referring to associated football/soccer and not the American game of football where points are scored in units of 2, 3 and 6. $\endgroup$
    – Michael R. Chernick
    Commented Jul 7, 2012 at 15:01

2 Answers 2

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The bivpois package, written by Karlis and Ntzoufras, uses the EM-algorithm for maximum likelihood estimation in this kind of bivariate Poisson models (and some generalisations of them). I don't think that it's on CRAN anymore, but you can find it here.

For more information, see the description of the package in Journal of Statistical Software and the related paper by Karlis and Ntzoufrasin in The Statistician (which is a continuation of the work by Dixon and Coles).

The package contains examples where you can see how to format your data. It's been a few years since I played around with it, but from what I remember it was quite easy to use.

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  • $\begingroup$ I am having some trouble with the bivpois package. I can not make it load to my R Studio. See db.tt/5XZJubGx. I am running Mac OSX Snow Leopard/R 2.11.1 Could anyone help me out? $\endgroup$
    – Peter Hopkins
    Commented Jul 8, 2012 at 19:35
  • $\begingroup$ This error message occasionally pops up when packages are intalled manually. How did you install the package, @PeterHopkins? $\endgroup$
    – MånsT
    Commented Jul 8, 2012 at 20:05
  • $\begingroup$ I downloaded the source bivpois_0.50-3.1.tar.gz from the link above. Then used the install.package() function. In R Studio it's not among avalable packages despite being listed by installed.packages(). $\endgroup$
    – Peter Hopkins
    Commented Jul 8, 2012 at 20:39
  • $\begingroup$ @PeterHopkins: Did you get any warning messages during installation? I tried install.packages("~/myfolder/bivpois_0.50-3.1.tar.gz",repos=NULL) and it succesfully installed the package in R 2.15.1 on Linux. I guess that it's possible that this is an R Studio issue - would you be willing to try to install it in "regular" R? $\endgroup$
    – MånsT
    Commented Jul 9, 2012 at 6:24
  • $\begingroup$ Ok, the regular R and Package Installer / Local Source Package / At System Level finally got me through. Thanks @MansT for the assistance. $\endgroup$
    – Peter Hopkins
    Commented Jul 9, 2012 at 17:47
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You should look at the VGAM package - it has functions to fit the Bradley-Terry model described in the linked questions in the comments.

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