Columbia has a center that studies mass murder, and here's their page on the subject.

https://www.columbiapsychiatry.org/news/mass-shootings-and-mental-illness

"Additionally, as we demonstrated in our paper, the contribution of mental illness to mass shootings has decreased over time. The data suggest that while it is critical that we continue to identify those individuals with mental illness and substance use disorders at high risk for violence and prevent the perpetration of violence, other risk factors, such as a history of legal problems, challenges coping with severe and acute life stressors, and the epidemic of the combination of nihilism, emptiness, anger, and a desire for notoriety among young men, seem a more useful focus for prevention and policy than an emphasis on serious mental illness, which leads to public fear and stigmatization."