Halliday & Matthiessen (2014: 422):
There are also the type favoured in grammar tests, such as John runs faster than Jim, where the embedded element is said to be a clause with the Finite and Residue presupposed by ellipsis: ‘than Jim runs’. It appears however that these are now embedded prepositional phrases, since the normal form of a personal pronoun following than or as is oblique/absolute rather than nominative: John runs faster than me (not than I). The same applies in the nominal group when the Head is an adjective: John isn’t as tall as me.