If you make good and much information about yourself and with references and your profile suits good with the need of the host and the hosts profile it is possible to get an invitation.
But it is very, very much job to write an invitation so a person can get a visa for entrance. I have done it four times during the last ten years. To people outside EU and east-Europe.
The Embassies are independent and wants to know so much of the economical situation etcetera that in my opinion not is worth it. Only if you get really good contact before.
That is my experience and my advice.
The Embassy asked me an invitation with the host's signature(scan it into computer and e-mail me).
Since I have no idea what are people from totally different cultural background like, I'm wondering if this makes hosts feel troublesome.