Google Analytics is good, but it is not superman. It can't measure everything
that matters in your online community.
It can't tell you how many discussions are positive, or how many
super-members you have. It can't tell you how many members are creating content
and how many are merely lurking. It can't tell you which groups are inviting
friends and if those friends are engaging in the community. It can't tell you if
you're fostering relationships that matter.
For some of this stuff, you need to track it yourself. Do you need to track
every member? Of course not. You need to track enough to know what's improving
and what's not. You need a quick poll that reflects the general trends.
I'd pick one new member per day, and see how s/he is doing 1, 2 and 3 months later. Keep it simple and keep it brief.