I am having trouble attaching the 'proud' to the 'am'. 'Am' is a verb and 'proud' is an adjective for the noun 'I', so should come as an adjunct for 'I', but here it would have to somehow come from the verb? After that, attaching the preposition 'of' and 'my students' is fine.
The copula complement is usually the constituent-structural complement of the VP headed by the copula.– WavesWashSandsJun 1, 2017 at 10:50
It's not an adjunct. The AdjP "proud of my students" is a subjective predicative complement of the verb "be" in its ascriptive sense. It ascribes the property of being proud ... to the referent of "I".– BillJJun 3, 2017 at 6:59
Which theory/model of syntax are you working with? Saying x-bar is not specific enough.– curiousdannii ♦Jun 3, 2017 at 22:21
(Disclaimer: I am not a specialist in Syntax)
According to the X-bar Theory, Adjectives, as any other lexical category, undergo three different levels of projection. They can have Complements (which are sisters to the head), Specifiers (or Subjects, i.e. sisters to Adj′) and Adjuncts (sisters to AdjP). Semantically speaking, the complement of an adjective is usually a Prepositional Phrase that is necessarily required for completing the meaning of the adjective. Thus, if you say proud, you have to mention the reason of the pride, which constitutes the complement of this adjective. Syntactically, proud of my students is a constituent made of an adjectival head and a prepositional complement selected by the head:
For the internal structure of the PP the usual analysis applies.