I run logistic regression models where the event rate is generally very low. In my models I get a large intercept term. What bothers me is the exceptionally high chi-square of the intercept term. How do I interpret this condition?
The intercept term is the parameter estimate when all the independent variables are 0. One way that you could get the results you describe is if 0 is not a meaningful value for the IVs. E.g. suppose one of your IVs is annual income in $. Then a 0 value is far outside the data.