There is research in this area. But you can just use your brain, man. Fuckin' A.
The reality is our culture is a violent one, especially compared to 30 or 50 years ago. It seems pretty obvious that if you pump millions of brains with thousands of violent images over years that you'll get an uptick in violence. And there are the societal factors which I already mentioned, which compound these influences, and you conveniently ignore. We live more and more silo'd lives with less community and extended family structure and support, often in abusive situations (drugs, alcohol, physical abuse) and so on. the weird Asperger kid no longer has an uncle, grandpa, pastor, whoever to turn him around. So he fixates on thoughts of violence and sinks to a mental state where he goes on a shooting spree.
Performing back ground checks or more screening will have a very limited impact, and you aren't going to be able to ban guns. You could potentially impact society - through introspection and incremental change.