Exploring datasets from http://next.nomics.world, I'm finding no link between gender equality and population density adjusted loneliness. But, removing outliers with excessive loneliness for their population densities (MT, CZ), I'm getting a moderate correlation (.4) between gender inequality index and male loneliness (male to female loneliness ratio among 24 to 34 year olds), so my model might explain male loneliness in particular. Haven't looked into the other factors I've conjectured.