At the NYPD we used to break down hostage takers into four broad categories:
Professional criminals who found themselves trapped after trying to escape from a crime.
Emotionally disturbed individuals—a catchall category for everyone from a paranoid schizophrenic to a severely depressed person.
People involved in domestic incidents, possibly the most unpredictable of all. These incidents involve people who know each other and in many cases are married or living together.
Terrorists—groups driven by distorted beliefs, be they political, religious, or ethnic. The common perception is that the police or government does not negotiate with a terrorist, but that’s not necessarily true.