This doesn't really discuss how exactly the correlation works. I'd be interested to know if in some cases depression causes living alone instead of the other way around. I know I've isolated myself when depressed. Not having to share spaces also helps with anxiety, which often comes with depression. Also maybe there's some personality types that a both more prone to depression and more inclined to prefer solitude.

In summary I'd be interested to see a further exploration of how exactly these work together