An elliptical sentence is a sentence that leaves out implied words. For example, if I am writing about two boys, I can write “The two left school early.” The word “boys” is implied and not written.
Generally, this doesn’t cause problems. It gets tricky when using elliptical sentences making a comparison that end in pronouns. Consider these two sentences with very different meanings.
“Sue likes cake more than I.”
“Sue likes cake more than me.”
Both sentences are grammatically correct. Depending on your meaning, you will choose one or the other. Here’s how you decide.
“I” is a subject pronoun, which means that it needs a verb. The verb is not here. Given the context of the sentence, the implied action is “like cake.” “Sue likes cake more than I (like cake).” This works for other subject pronouns, too.
“Me” is an object pronoun, which means that it is the recipient of an action. The implied action here is “like.” “Sue likes cake more than (she likes) me.” This works for other object pronouns, too.
Here’s the point. When choosing the correct pronoun for this type of sentence, consider what words you are implying, and then choose a subject pronoun or object pronoun to match the implied words.