I am working with a contingency table where I know that the population sizes from which the counts are derived are very different. From what I have been able to gather, an appropriate way to adjust for this is to use a logarithmic offset of my population sizes.
(1) Is it appropriate to scale the counts based on the population size, such that a new value is ((old/population size) * old).
(2) If this is fine, is it ever appropriate to multiply values by a scalar, and then possibly round, prior to performing Poisson regression? My scaled counts end up quite low in some cases (<0.1). There is signal, as I may have counts such as 0.02, 0.1, 1.1 for a given column in the matrix. Obviously, though, rounding is out of the question.
Unfortunately, I do not have access to the data that the table was populated with. If I did, then I would anticipate that a zero-inflated model might be a good fit.