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.