In the wake of the terrible shooting at an elementary school in Newtown, Conn., national attention has turned again to the complex links between violence, mental illness and gun control.

The gunman, Adam Lanza, 20, has been described as a loner who was intelligent and socially awkward. And while no official diagnosis has been made public, armchair diagnosticians have been quick to assert that keeping guns from getting into the hands of people with mental illness would help solve the problem of gun homicides.

Arguing against stricter gun-control measures, Representative Mike Rogers, Republican of Michigan and a former F.B.I. agent, said, “What the more realistic discussion is, ‘How do we target people with mental illness who use firearms?’ ”