Predicative attribute is a synonym for depictive construction.
This term has long been the primary term in grammatical descriptions, before terms such as secondary predication became widespread. It seems to go back to the 19th century, but is now old-fashioned.
Halliday (1967:62) uses simply attribute in this sense.
- Halliday, Michael Alexander Kirkwood. 1967. Intonation and grammar in British English. The Hague: Mouton.
German prädikatives Attribut