Modal Substitutes

I have a sentence that I am trying to label parts of speech, but having some difficulty.The sentence is:

I am allowed to ride the roller coaster

I know that 'am allowed to' is a substitute for the modal verb 'may' as in:

I may ride the roller coaster

In the second example, I have 'I' as the subject, 'may' as a modal connected to the verb 'ride', and 'the roller coaster' as a noun phrase serving as a direct object of the verb.

My question is this: How do I label the parts of the substitute 'am allowed to' to make up a modal.

I have look through phrase structure rules and cannot find a rule that says modals may be phrases made up of other parts of speech.

Any Ideas?

Calcio

I - pronoun subject
am - linking verb
allowed - predicate adjective
to ride - infinitive complement of allowed
the roller coaster - noun phrase object of ride

Alternately, depending on the analytical technique you are using, the sentence is derived by transformations of the underlying structure:

someone allow [ I ride the roller coaster ]

CJ

what is the pronoun of flowers.