My advice to you:
There are two people you need to avoid inviting. The culprit and the day's victim. If you do that, you're golden. So now's the perfect time to test out theories of who the culprit is and what pattern they're using in who they kill. Unfortunately, you have to test both at the same time, so if you're wrong, you have no idea which theory is wrong. I'm evil like that. But it's an opportunity to eliminate suspects.