Just had a look to see if I could find out anything on the web, and there seems to be evidence both ways (isn't there always). There is a study from Finland that shows more people living alone took antidepressants during the study period than those who didn't live alone. But no way of knowing if they lived alone because of their illness, or got ill because they lived alone.
BMC Public Health | Abstract | Living alone and antidepressant medication use: a prospective study in a working-age population
Is living alone bad for your mental health? - Latest News - Best Health
Living alone shouldn't of itself lead to mental illness, but isolation can (it says somewhere...)
In the UK one in three people live alone. A lot of people choose to these days. It has advantages and disadvantages.
This is a study from the US that says no proof people living alone more likely to have pre-existing psychological conditions and no more likely to have mental illness than others (it is older, from the 1980s):
http://www.jstor.org/discover/10.230...21104729409731