Africa is home to the largest species of rat in the world, the African Pouched Rat. In the USA some people keep these gigantic rats as pets! I think they would eat straight through the walls of a typical wooden Japanese house in about 5 minutes, so I hope there aren't any here!
The Giant Japanese Pouched Rat is an even rarer species. Like the African variety it is 2 foot long, but unlike the African variety, it has two heads. Here is a picture of one that the little human photographed just this week. Pretty scary huh?
Incidentally, Africa is also home to the world's smallest mouse , the African Pygmy Mouse. This is probably a better pet for a Japanese household. They are incredibly small, clean and don't smell, so suitable for Japanese tidy-living in a small space. However, they are also quite fragile and not fond of people in the same way we rats are, so it is probably more like looking after a decoration than a pet. They are also said to be more seriously noctural, whereas we rats can be woken up at most times of day and will play. Since the quarantine laws changed in Japan in Sept. 2005, it seems to be difficult to find these pygmy mice in pet shops, although I wouldn't have thought it would be so hard to breed them here.