Well, this is one of the many problems with sociology. There are some obvious approaches to use, such as finding crimes which are solved far beyond doubt, such as where there are many witnesses or DNA evidence, and hope this generalises to crimes which are harder to solve, such as domestic violence.

Of course, as you point out, these different kinds of violence might not generalise, as different people commit different crimes for different reasons. So I really don't know what to do about crimes that happen in private where there are no witnesses, short of putting cameras in every room of every house.