I'm trying to predict the total number of Olympic medals won by a country in the summer Olympics games. I have data from 2000 to 2012 relating to the country gdp, population, number of athletes sent, etc.
I thought I could use a generalised mixed model with a Poisson distribution. This takes into account the correlation between medal counts for different years relating to the same country.
I was wondering whether there was a way to account for the fact that there needs to be a negative correlation between the response variables since a country winning more medals means other countries winning fewer medals collectively.
I believe I cannot use a multinomial model since the count of medals is not defined at the outset like the number of events is.