Count Data? Which Regression Analysis to Use?

[jrb173]

I'm in a bit of a pinch here. I am working on my undergrad capstone project, examining the relationship between income inequality and violent crime in U.S. counties.

Here is my dilemma:

I believe my dependent variable (number of violent crimes) to be count data, correct? It is a simple count of how many times a violent crime occured in county X. I have been advised that this is not the case, however, I have a strong feeling that I am correct on this. A number of previous studies on the subject have utilized either a poisson regression or a negative binomial regression model while exploring essentially the same topic.

I am referencing Morgan Kelly (2000) inequality and crime as my guide through this paper. I feel as though negative binomial regression is the way to go, however I have been advised to use a tobit model. Any suggestions?

[alexchien · Accepted solution]

Tobit models (censored Normal regression) are typically used for censored data. For data such as count of crimes, it is usually left censored (i.e. under reporting). SAS doesn't directly support censored Poisson regression at this point (It will be available in the future from SAS/ETS COUNTREG procedure). However, you can use PROC MODEL (SAS/ETS) to fit whatever model you like as long as you know the form of the likelihood, or PROC MCMC (SAS/STAT) for Bayesian censored Poisson regression. Tobit model should work well if the counts are not too small (something like > 5). You can use either PROC QLIM(SAS/ETS) or PROC LIFEREG(SAS/STAT) to fit Tobit models.

alex