I'm trying to estimate a fractional outcome through weighted logistic regression. One of my IVs is continuous and cannot be negative. And about 45% of the values are 0. Most of the zeros are related to another IV which is binary and contains the status of the observation (active vs inactive - 70/30). In other words, 98% of the observations that are Inactive have a 0. The distribution on the Active side is 21% (zeroes) and there is a positive correlation between higher values of this IV and the response. My sample size is very large.
How do I approach modeling this situation? Specifically, what extra care is required to handle the large concentration of 0s?