Use the Association of American Universities on first reference. AAU is acceptable on second reference and in headlines. 

The AAU was founded in 1900, and MU became a member in 1908. Member universities are committed to first-rate undergraduate education, pioneering research and outstanding graduate programs. They must meet strict standards for faculty and research funding to qualify for AAU membership. MU is the only public AAU member in Missouri.

Example: MU has been a member of the Association of American Universities since 1908.