Let me start off by apologizing if my examples offend anyone.
I think it depends on the age of the minor, as well as the crime. Take this as an example; There's is a six year old and a sixteen year old. Both of them are males, and rob a convenience store at gunpoint.
I'd say there's a good chance that the six year old is just acting something out that he saw in a movie. There's a very low chance that the kid decided on his own that he's going to rob a store. Young kids are impressionable, but they're too young to be corrupted by things like drugs, and violence. Certainly not sex. I may be giving the six year old too much slack, but I honestly couldn't see what motive a six year old could have. They're more likely to steal, than rob a store.
The sixteen year old on the other hand, could have many reasons why he could be robbing this store. From a scientific standpoint, a sixteen year old should be close to exiting puberty, if they haven't already. So there's plenty of possible motives. Sex, Drugs, Status, Gambling, Debts. All probable motives for the sixteen year old.
Robbery isn't as serious as something as murder (or it's many variations), but it's the best example I can give of age leading to motive. I think if you're at the age that you can have petty motives such as the ones mentioned, then you should be responsible for your actions. The six year old, I think should have a psychological diagnosis to see if there's any underlying mental illness. As far as the sixteen year old is concerned, I believe that they should be sent to a rehabilitation program, and then a halfway house. Make them learn a lesson about the path they're taking.
However in my opinion, something such as murder isn't excusable. Assuming they were found guilty in court; If the six year old committed a murder, he definitely needs a therapist, a psych evaluation, and be put into a better home. Obviously the parents are doing a very poor job with the child if something like that happens. Whether it's poor parenting, or it's a mental disorder, obviously it was more than they could handle. The sixteen year old, psych evaluation, therapist, put them in a new home, and put them on parole for five to ten years.