What sentence part is "visitors" in "I'm not allowed visitors"?

Solution 1:

Yes, I think you are on the right lines.

But the way I would describe it is to say that visitors is part of an object clause - which is to have visitors.

The verb allowed attracts similar object clauses with all kinds of things, the infinitive part to have being elided in all cases. E.g. I'm not allowed sugar/days off work/reading material etc.

Of course allowed takes many other infinitives as well, but which are not necessarily elided e.g. I'm not allowed to see my friends. Equally it works in the positive I'm allowed to go on outings.

This is the simple explanation, but if you are looking for the Advanced Level one, then see @StoneyB, below.

Solution 2:

1. I'm not allowed visitors.

is a passive version of

2. [Somebody] does not allow me visitors.

In both, visitors is the thematic Patient and syntactic Direct Object. I/me is the thematic Beneficiary in both; in 1. it is cast as the syntactic Subject, and in 2. it is cast as the syntactic Direct Object.

Compare:

A1. Photography is not allowed.
A2. [Somebody] does not allow photography.

B1. I am given a raise.
B2. [Somebody] gives me a raise.