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.

  • $\begingroup$ I wouldn't worry about this issue, which will have a minor effect, until other potentially much greater issues are addressed. In particular, (a) the count of medals is such a crude indicator of success and (b) it's so unlikely you will find much of a relationship with anything except number of athletes sent, that you should invest your initial efforts in establishing whether you can detect anything of interest in your data. $\endgroup$ – whuber Jul 15 at 20:17

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