Do I actually need to fully upgrade a spirit's house to get them to cross over?

[e11]

Or is it just a general mood-improver?

[rmsgrey]

Some spirits will generate specific quests to get specific upgrades to their house. Those upgrades are needed to complete their quests. Other spirits won't ever give you a quest for a specific upgrade, and that upgrade isn't needed for them to reach the end of their quest chain.

The optional upgrades are optional, but will have an impact on mood.

[Livia]

In most cases, no, as rmsgrey already said. The purpose of doing the upgrades for those that don't is it is usually required to get the Happy Dance achievement.

That said, I like to make them all happy - that's really the overall point in the game - caring for the spirits.