There is no reliable mass screening test that can predict violent behavior. There is no way to administer a reliable instrument to every gun owner and purchaser.
Individual evaluations have been found to be almost useless as a mass preventive measure.
Only if a person is acting irrationally or making threats can we make some judgements.
Any system we could think of would have a tremendous false positive rate. Folks would be branded as a risk and that quickly would be used to deny them of rights and employment. Oh, John can't buy a gun - well, should he be school teacher?
Been studied quite intensively.