In ‘catch me off guard’, is the ‘off guard’ an objective complement or adjective phrase?

In ‘catch me off guard’, is the ‘off guard’ an objective complement or adjective phrase that modifies ‘me’?

My Great Uncle Algie kept trying to catch me off guard and force some magic out of me — he pushed me off the end of Blackpool pier once, I nearly drowned — but nothing happened until I was eight.

At http://media.leidenuniv.nl/legacy/console17-asada.pdf is an in-depth discussion of structures involving object complements (which structures are also said by some to involve secondary predication) . I'll just quote the introduction, which I believe gives a clear and valid classification (though the rest of the article goes on to recommend alternative analyses!):

Secondary predication is commonly classified into the two types of constructions –– depictives and resultatives –– illustrated in (1) and (2) respectively.

(1) Depictives a. John left the room angry. ‘subject-oriented’
b. John ate the fish raw. ‘object-oriented’

(2) Resultatives
John hammered the metal flat.

So the 'catch me off guard' example would be classified as 'depictive' and 'object-orient[at]ed'. 'Raw' is obviously an adjective modifying 'fish', and correspondingly, 'off guard' (or 'off my guard', equally acceptable) is what some would call a multi-word adjective , and some would label an adjectival - a string doing the job of an adjective (and some would include adjectives as a sub-set of adjectivals).

There can often be some valid soul-searching as to whether a modifier is truly modifying a nearby noun or a nearby verb (if either):

The striker shot wide. (adverb or adjective?)

He is a mere youth. (Are some youths not mere?) He is merely a youth. (Is there any significant difference in meaning from the previous version?)

It is tempting to see off guard as an adverbial. As such, it would mean ‘My Great Uncle Algie kept trying to catch me in an off guard manner’, but that clearly cannot be. It was neither the aunt nor the manner of catching that was off guard, but the nephew. It follows that off guard is an adjective which postmodifies me.

One way of dealing with this structure is to propose something called a small clause, which is effectively a structure encapsulating arguments (e.g. subject, complement) as though there was a verb, but without an actual verb present inside the "clause".

The structure crops up 'on the surface' in various cases such as:

English: They considered [[him] [tall]].

French: Il a [[les yeux] [bleus]].

It can also be argued that it is the underlying structure in various other cases, e.g.:

"Peter is tall"

"Who do they believe responsible"

can be argued to underlyingly consist of structures closer to:

[be [[Peter] [tall]] ]

[believe [[who] [responsible]] ]

(Indeed, in some languages, the verb "be" is actually not necessarily expressed, and the equivalent of "Peter tall" is actually grammatical.)

So, in your sentence, the idea would be that you have a structure such as:

They caught [him off-guard].

where "him off-guard" is in effect a type of clause that together operates as the syntactic object of the main verb.

Another possibility is to analyse "off guard" as what we might call a resultative predicate: in effect, you can argue that there's nothing particularly special about a verb that takes "precisely one object", and that "off guard" is simply one of several complements that a verb can take, just as you find in other cases such as:

Jim bet [Bob] [four pounds].

David gave [Michael] [the book].

Mary made [the cracked vase] [a feature].

I think both analyses have their merits. A problem with the latter analysis is that in many cases of what we might see as resultative predicates, the verb has the option of being unaccusative, in other words you get pairs such as:

The die turned [the material] [red].

[The material] turned [red].

whereas it makes no sense to say "He caught off-guard".

An adjective phrase and an object complement are two different levels of description, so it is possible (indeed common) for an object complement also to be an adjective phrase.

Here's a simpler example to explain what I mean:

The big man read a long book.

The big man is a noun phrase (one level of description, explaining the grammatical category of the words). It is also a subject (a different level of description, explaining the syntactical role of the phrase).

Now we need to look briefly at what an "object complement" is. We'll start with a "subject complement", because it's easier to explain. A subject complement is some kind of phrase (which may be a single word) which gives information about the subject of a particular type of verb, which we might call "existential" verbs. These are verbs like "to be", "to seem", "to look", which express something about the state of the subject:

The man is tall.
The book is long.

In these cases, tall and long are subject complements: they tell us something about the subject, rather than being objects of the verb. They are not affected by the action of the verb, but they expand on what we know about the subject. Contrast "the man buys a book", where "a book" is the object of the verb "to buy": the book is affected by the action of the verb, but gives no information about the state of the man.

An object complement is like a subject complement, but it gives extra information about the state of the object of a verb, not its subject. So instead of following one of these "existential" or state verbs, it follows the object directly, with the sense of "to be" or a similar verb implied:

They made me angry.

The structure here is subject (They), verb (made), object (me), object complement (angry). Structures which include an object complement like this often (though not always) contain verbs which express doing something physical or abstract to the object:

They called me an idiot.
They painted it red.

So, "object complement" is a structural category, explaining what a word or phrase does in a sentence.

In contrast, "adjective phrase" is more of a formal category. It explains the grammatical category of the key word in the phrase.

So in the example you give, you could argue that we have an adjective phrase ("off guard") which is performing the role of object complement in the sentence - the object being "me".

There are various arguments for and against this analysis, but the answer to the original question is, in summary, that it doesn't have to be one or the other; it could be both.