By research, I mean that I signed out of my account and tried to comment on my own page. Here's what I found...
Go to the bottom of the post.
It should say 0 comments (unless I actually have comments)
THIS IS A LINK, CLICK IT
This is the next page shown. Type in your comment.
Then click the drop-down menu.
Sign in with whatever account you'd like.
For example: if you have a gmail account, click Google Account.
Okay, now if you don't have any of those accounts, there are two options:
1) Save a step, and comment on Facebook
2) Make a blog account with blogspot.com
If none of this helps.. I apologize. =\