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You didn't mention the nationality of your niece. She can apply for a visit visa but it will be difficult to convince the visa officer that she will leave the country before her visa ends, keeping in mind she is 18 and has recently finished school. But if you are willing to sponsor her complete stay then its worth a try to apply on her behalf. Guess you will need to show your bank statements, payslips etc that you can afford to keep her for the whole duration of her stay.
Just follow a visitor visa route and make sure you follow the checklist, simple.