Negative Count Variables in Data --- modeling migration I'm trying to explain migration rates in Europe with my regression using pca/pcr in glm. Of course some of the count data has to be negative in regions people move out of. This presents a problem for my regression, since I wanted to use the Poisson distribution (tip from my supervisor), which I obviously can't with the negative values in my data.
How can I work around this? Which other models could be used?
One thing i already did too, but not sure if I CAN do it: I just used the regions with positive migration ratios. But I'm sure this somehow skews my results even tho I get many significant regressors. 
 A: This is more of a modeling issue than a negative count issue.  The count of people leaving a region is just as "positive" a number as the count of people entering a region; you've simply chosen to code it as a negative number because you are thinking of it in terms of net population changes in a region instead of population flows between regions.  
If you are modeling the flow $x_{ijt}$ from region $i$ to region $j$ in time period $t$, you can easily set up the regression(s) so that $x_{ijt} \geq 0$.  In fact, setting the first index to be equal to the source region and the second to be equal to the destination region accomplishes this for you without any additional effort, as, if the flow $x_{ijt}$ is negative, the source region is actually $j$ and the destination region is actually $i$, and switching the indices reverses the sign.
If you are simply modeling the flows into and out of a region, you can construct two regressions, one for the source regions and one for the destination regions.  There are lots of reasons why people might leave a region that are of little relevance to their choice of destination and vice versa, so the two models would almost certainly have overlapping, but not identical, sets of features (independent variables.)  This would likely be an inferior model to the detailed flow model, however, as people, except in extreme circumstances, don't tend to leave a region without having somewhere substantially better to go firmly in mind; this means the decision is based on a comparison of regions rather than on one region only.  It isn't that common that "anywhere" is substantially better than where you are today, although of course there are plenty of examples of just that in human and European history.  
A: Counts cannot be negative by definition. You are not dealing with count data, so you need a model for non-count data, for example a model using a Skellam distribution (distribution for the difference between two Poisson-distributed random variables), there's even an R package for that.
