They don’t actually have data on gun ownership. They’re estimating it with the percentage of suicides committed with guns, which correlates with actual gun ownership decently but far from perfectly, and may be picking up other factors as well. There have been numerous attempts in recent years to develop a better proxy.

While the study includes data from 1998 to 2015 and deploys a blizzard of complicated statistical techniques, it’s essentially cross-sectional in nature — i.e., the authors’ claim is that “states with more permissive gun laws and greater gun ownership have higher rates of mass shootings,” rather than that,

within

states,

trends

in gun laws or gun ownership correlate with

trends

in shootings. The latter would be a far stronger finding because it would suggest that a given state, with its given attributes, has more or less violence depending on the gun laws/ownership at the time.