Also, a category that's neglected is people who could be served by existing shelter or halfway house infrastructure but choose to avoid it: I know of people who are 'homeless by choice' as a result of facilities being either (a) too scary/chaotic or (b) too moralizing (e.g. 'dry').
There's also a good deal of youth homelessness which falls into many of these categories without cleanly matching any one of them. Sometimes kids leave households because they are 'wild', but frequently because the households are dysfunctional and couch-surfing or sleeping on the streets is perceived to be no more dangerous than being at home (or being shunted into foster care).