I've researched this problem a bit, but I want to make sure I'm not stepping on a landmine somewhere. I've read that one can use a Poisson regression for rate data if an offset or exposure term is included in the equation (constrained to one). To make this happen, I could:
1) Transform crime rates into counts and make the offset term = (1/population) * 100,000 so that the coefficients describe multiplicative changes in rates per 100,00 people.
2) Transform crime rates into counts and make the offset term = population so coefficients are multiplicative changes in crimes per capita.
3) Leave crime rates in the original form and make the offset term = (1/population) * 100,000.
4) Leave crime rates in the original form and make the offset term = population.
For the moment, I'm using option 1, but I'd like to cross-check because everything else I've read is a bit murky.
Thank you.