Modelling for soccer scores 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.
 A: The paper you are reading is implicitly using $\alpha_i$ and $\beta_i$ to refer to the attack and defense parameters as described by Maher (1982).
The main difference is that Maher uses four parameters for each team (home attack, home defense, away attack and away defense) while Dixon and Coles use attack and defense parameters and another parameter to represent home advantage.
A: The MLE for the Poisson distribution is simply:
$ \lambda_{MLE}= \frac{1}{n} \sum_{i=1}^n k_i$ 
.. as far as reproducing their alterations to the Poisson distribution (a quick look tells me it has become both time-dependent and bivariate), I doubt anyone will do that for you. You're way better off using tools that actually make sense. 
A: You don't need bivariate Poisson. You can define your own function, and then use a generic optimization script like optim.
A: You are feel free to refer to bivpois R package. My previous project applied diagonal bivariate poison. as you can refer to https://github.com/scibrokes/odds-modelling-and-testing-inefficiency-of-sports-bookmakers.
