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By creating a new dataset of immigration-related tweets labeled for multiple framing typologies from political communication theory, we develop supervised models to detect frames. We demonstrate how users' ideology and region impact framing choices, and how a message's framing influences audience responses. We find that the more commonly-used issue-generic frames obscure important ideological and regional patterns that are only revealed by immigration-specific frames. Furthermore, frames oriented towards human interests, culture, and politics are associated with higher user engagement. 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