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Mental illness account for a very small proportion of mass shootings in the US
(www.columbiapsychiatry.org)
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One of the key features of scientific studies is that they only go as far as the data and the experimental design can support. Because of this it is not unusual for a study to give results that may be surprising or counterintuitive, but not be able to explain why. This is especially true for complex issues. I'm not trying to dismiss your question, and I think several good ideas and observations have been made in the ensuing comments, but in the end I don't think this study which describes the correlation between two factors, can give you the answer you are looking for.