This sort of thing is why it's best to actually know someone before you start to date (let alone inviting them to your house). It's best to find out whether you can live with someone's faults before getting emotionally entangled. It's also best to find out whether they're stark-raving bonkers before letting them know where you live.
I used to try getting to know someone before dating but found that they tended to just stick me in a box that does not include romance: "I'm sorry Simon, I just don't think of you that way."
When I started just going for it and hoping I got a lot more hits. OTOH: I have this rule that I don't have sex on the first date ... and make sure I spell it out at some point. I do get the odd "well I wouldn't anyway" indignant but mostly the reaction is positive - breaks the ice - clears up the obvious question - and some women seem to see it as a challenge.
Avoids morning-after attachment anxiety like this.