Can You Diagram this Sentence?

Years ago, I was editing a piece and could not for the life of me decide upon the proper grammar for a certain phrase, a colloquialism I've seen written two ways. I thought if I could diagram the sentence, I would then know how to edit it, but even with the help of The Little, Brown Handbook and CMS, I couldn't figure it out.

I ended up on the phone with a Writer's Digest editor trying to determine the proper wording for this sentence:

I better be going  OR

I'd better be going.

The editor was nice and offered a lot of advice, but she was not able to diagram the sentence, either, and asked me why I needed to. I explained my endeavor to her.

"You can't diagram that phrase," she said. "It's a colloquialism." She advised thusly: Use I better be going for informal prose, and I'd better be going for more formal prose.

I've followed her advice ever since, but it seems to me as if there's somehow an object in that phrase. It niggles at me. I better be going. Is this phrase actually shorthand, a phrase that represents a grammatically correct sentence from the old days, something like this: It is better for me to leave than to stay.

Better has to have a reason for being there. What do you think? Can you diagram this sentence?