During English class, we have been diagramming sentences, as described at http://grammar.ccc.commnet.edu/, and have had some confusion as to whether the term "my" should be considered an adjective, possessive pronoun, or prepositional phrase. This question at ESE seems to indicate that it is meant as a prepositional phrase. In sentences such as:
In my younger and more vulnerable years my father gave me some advice that I’ve been turning over in my mind ever since. (The Great Gatsby, by F. Scott Fitzgerald)
the "my" seems to be used as a prepositional pronoun, but is diagrammed as an adjective would be.