Twitter had initiated granting of datasets some time back (now closed)[0] on the merits of a short proposal. The number of groups who eventually got access to the data were very few[1]. I hope in the future they increase the number of grants.

[0] https://blog.twitter.com/2014/introducing-twitter-data-grant...

[1] https://blog.twitter.com/2014/twitter-datagrants-selections