Halliday & Matthiessen (2014: 606):
Reference creates cohesion by creating links between referents – elements at the level of meaning; but there is also a resource operating at the level of wording, either a clause or some smaller item. This takes two forms, substitution and ellipsis; but we shall refer to it simply as ellipsis, since substitution can be interpreted as a systemic variant. Ellipsis makes it possible to leave out parts of a structure when they can be presumed from what has gone before. Ellipsis indicates continuity, allowing speaker and addressee to focus on what is contrastive… . Unlike reference, ellipsis is usually confined to closely contiguous passages, and is particularly characteristic of question + answer or similar ‘adjacency pairs’ in dialogue.
Here again Matthiessen misrepresents Halliday's model of reference by infusing it with Martin's (1992) misunderstandings of it as participant identification. Reference is a relation between reference item and referent, not between referents. Any relations between referents will be those of lexical cohesion; cf Halliday's (1985: 295-6; 1994: 316) original wording: