The college student who killed six people before shooting himself in Isla Vista, Calif., in May 2014 saw multiple therapists; they disagreed whether he had emotional problems or high-functioning autism. The Sandy Hook shooter, who killed 26 people in an elementary school in Newtown, Conn. in 2012, had seen numerous psychiatrists and psychologists for years before his mass murder, including therapists at Yale’s renowned Child Study Center. After details of the young man’s childhood and home life emerged, some experts saw evidence of early psychosis or obsessive compulsive tendencies. But the only official diagnosis Adam Lanza, the shooter, had received was Asperger’s syndrome, a mild form of autism that by itself does not dispose people to violent acts.

Dr. Michael Stone, a New York forensic psychiatrist who created a database of about 200 mass murderers, including spree and serial killers, has determined that about half had no clear evidence of mental illness before their crimes. About a quarter showed signs of depression and psychopathy — that is, hopelessness combined with a lack of remorse.

The spree killers in particular are odd types: moody, unpredictable, inhabiting an internal world that is not easily put into any category, Dr. Stone said.