Invitation letter for a visitor visa for my niece

No need. Tell the niece to pay a visit to the consulate and apply for a visa. If she can establish nonimmigrant intent, she will be issued a visa. If she cannot, your invitation letter will not help.

It depends on the totality of the evidence presented to the Consulate along with intangibles such as the mood of the interviewing officer at the time. She should be prepared to show family/employment and other ties to her country which she has no intention of abandoning, and be prepared to answer questions about the purpose of her entry to the U.S., whom or where she will visit and where she will stay (temporarily), whether she has a definite return date (return ticket), etc.

I agree with Attorney Segal's advice. My only addition is to have her check on the local US Consulate's protocol for setting interview etc... that would be on the Consulate's website.