There's no matrix. My wife got invited after 10+ stays and at least 40+ nights. However, I got invited after only 3 stays with 10 nights (then again, I'm very generous with the managers and staff, so maybe they put in a good word? Or is it I book suites and my wife's company only allowed bookings in non-suites? Who knows....) Anyway, here are the elite perks besides the standard F of MO:

1) $100 food/beverage credit for 1-2 nights stays, $200 credit for 3 nights or more.
2) Managers and staff will line up to meet you at entrance (should you use their transportation), then one (or a few) of them will personally escort you to the room for check-in.
3) High chance of upgrade to suites (F of MO you get mostly "view" upgrades).
4) If you have anything you wanted to do in your residential city, tell them, and usually they'll come through (if your request is reasonable) vs simply being F of MO member (this is based on personal experience. I always plan ahead on my personal entertainment requests to hotel I'm going to, and I found out as F of MO they sometimes just dismissed my request, but as Elite member it always come through. For example, asking for a private tour at Presidential Palace so I don't feel rush, or a hard to book restaurant in Taipei, you have to pay extra of course).