Though preceding work in computational argument quality (AQ) mostly focuses on assessing overall AQ, researchers agree that writers would benefit from feedback targeting individual dimensions of argumentation theory. However, a large-scale theory-based corpus and corresponding computational models are missing. We fill this gap by conducting an extensive analysis covering three diverse domains of online argumentative writing and presenting GAQCorpus: the first large-scale English multi-domain (community Q&A forums, debate forums, review forums) corpus annotated with theory-based AQ scores. We then propose the first computational approaches to theory-based assessment, which can serve as strong baselines for future work. We demonstrate the feasibility of large-scale AQ annotation, show that exploiting relations between dimensions yields performance improvements, and explore the synergies between theory-based prediction and practical AQ assessment.