On 03-Nov-10 21:06:53, Jourdan Gold wrote: > Hello, from a search of the archives and functions, I am looking for > information on creating random correlated counts from a multivariate > Poisson distribution. I can not seem to find a function that does this. > Perhaps, it has not yet been created. Has anyone created an R package > that does this. > > thanks, > Jourdan Gold
One of the problems with such a question is that your target is not well defined. For example, it is easy to set up correlated Possion variates in much the same elementary way as you can for (say) Normal variates. Let U, V, W be independent Poisson random variables with means mu.U, mu.V, mu.W. Then (because of the independence) X = (U+V), Y = (U+W) and Z = (U+Z) all have Poisson distributions (with means equal to the sums of the respective means for U, V, W). However, they are now correlated. The variances for X and Y are (mu.U+mu.V), (mu.U+mu.W) respectively. The expectation of their product is Exp((U+V)*(U+W)) = Exp(U^2) + Exp(U*W) + Exp(V*U) + Exp(V*W) = Var(U) + Exp(U)^2 + mu.U*mu.W + mu.V*mu.U + mu.V*mu.W = mu.U + mu.U^2 + .... while the product of their expectations is this expression without the initial mu.U, so Cov(X,Y) = mu.U and then their correlation is mu.U/sqrt((mu.U+mu.V)*(mu.U+mu.W). Thus you could set up X and Y in this way with chosen positive correlations (though you can't get negative correlations ion this sort of way and still have Poisson-distributed X and Y). As another example, you could have the distribution of Y conditional on the outcome of X, e.g. X is Poisson with mean mu.X, and, given that X=x, Y is Poisson with mean x. Then both are still Poisson and have positive correlations. On the other hand, given X=x, you could make Y Poisson with mean 1/(1+x). Then both are still Poisson but this time are negatively correlated: the larger X=x, the smaller Y is likely to be. (Working out the marginal mean of Y might be a nasty little exercise ... ). These two methods (and there are many others possible) will lead to different forms for the joint distribution of (X,Y). So "correlated counts from a multivariate Poisson distribution" does not lead to a definite target! So it would be useful if you could specify precisely what you want that phrase to mean. Ted. -------------------------------------------------------------------- E-Mail: (Ted Harding) <ted.hard...@wlandres.net> Fax-to-email: +44 (0)870 094 0861 Date: 03-Nov-10 Time: 22:44:56 ------------------------------ XFMail ------------------------------ ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
