A hanging fixture outdoors does the same job it does indoors — it puts light down onto a defined space and gives that space a centre. On a covered porch or under a pergola, it is what turns a slab of decking into an outdoor room.
Height is a safety detail here
Over a walkway or an entry — at least 7 feet of clearance underneath, 8 feet where it is a main route.
Over an outdoor dining table — 30 to 36 inches above the tabletop, the same as indoors.
Over a seating area — 7 to 8 feet, high enough that nobody stands into it.
Chain or downrod?
Downrods hold the fixture rigid. That is what you want anywhere exposed to wind, since a swinging fixture will eventually work its wiring loose. Chain is adjustable and more traditional, and it is fine in a sheltered porch. Under an open pergola, take the downrod.
Rating and wind
Where it hangs
Rating
Mount
Enclosed porch ceiling
Damp
Chain or downrod
Open pergola
Wet
Downrod
Exposed patio
Wet
Downrod
Coastal exposure
Wet, marine finish
Downrod
Open bottom or enclosed?
An open-bottomed lantern throws more light down and is easier to clean. An enclosed shade keeps insects out of the fixture, which matters more than it sounds if you are eating underneath it.