I am trying to fit the number of crimes in a city with some enviromental variables (aka my features). I'm using a Poisson/Negative Binomial model since I have count data. The problems are:
- selecting the features which REALLY fit (I have sometimes big collinearity)
- select the smallest subset of significative features (p-values)
- understand the relative importance between them to fit the number of crimes
Possible solutions to the problems:
- Variance inflation factor (VIF). Is it ok? Sometimes interactions could be ignored. I mean: what if I have to test whenever two variabiles are important, but collinear? (e.g. population density and employment density)
- Stepwise (backward/foward/with Cross-Validation) steps to reduce the AIC. However, this does not mean that the resulting variables are significative (p-values). Should I care at all about the features' p-values?
- Standardize the input data, then looking at the Beta coefficient to see the importance of them. Is it really the best way?
Should I use something else? Keep in mind that my primary goal is not the $R^2$. I want to see and to be able to explain how some variables could explain the crime.