CHICAGO >> President Donald Trump called the Texas church shootings gunman “deranged,” the New York bike path attacker “a very sick and deranged person,” and the Las Vegas massacre shooter “a sick, demented man.”

It’s a common reaction to mass violence — who in their right mind would commit these senseless crimes? The truth is more nuanced.

Even if it is eventually determined that one of them had been diagnosed with depression, bipolar disorder or some other psychiatric illness, experts say that alone isn’t a risk factor for violence.

“Most people with mental illness are not violent” and only 3 to 5 percent of violent acts “can be attributed to individuals living with a serious mental illness,” the U.S. Department of Health and Human Service website says.

Jeffrey Swanson, a Duke University psychiatry professor, says traits that are much more strongly linked with violence are “being young and male and having a history of childhood maltreatment, substance abuse and exposure to violence.” So is a history of committing violent acts, he said.

In a study a few years ago, Swanson found that about 1.5 percent of Americans with impulsive anger that doesn’t necessarily amount to mental illness “are carrying around guns with them.” With expansion of concealed carry laws, those numbers or probably higher today, Swanson said.

“That’s a bigger problem than besmirching 10 million people with serious mental illness in this country,” Swanson said.

After Sunday’s attack at a rural Texas church, Trump said that, based on preliminary reports, the shooter was “a very deranged individual.” He said it was “a mental health problem at the highest level” but offered no details at a press conference during a visit to Tokyo. White House officials declined to elaborate Monday when asked about Trump’s mental health reference.

Texas officials have not mentioned mental illness in describing the 26-year-old suspect, Devin Kelley. On Monday, they said the shooting was connected to a “domestic situation” in the family. He had previously been accused of domestic abuse and animal cruelty.

Kelley was found dead when his car when it crashed; authorities say he may have fatally shot himself.

Antonio Puente, president of the American Psychological Association, said Kelley’s past behaviors were “red flags.” Calling the shootings a ‘“mental health problem’ distracts our nation’s leaders from developing policies and legislation that would focus on preventing gun violence through a scientific, public health approach,” Puente said.

In New York City, extremist beliefs are thought to be behind the bike path rampage last week. Suspect Sayfullo Saipov, 29, has been charged with terrorism offenses. In the case of the Las Vegas shooter, Stephen Paddock, Stanford University scientists are studying his brain for damage or signs of disease that might be a clue to the violence. An autopsy showed no abnormalities. Authorities have not said whether the 64-year-old Paddock had a diagnosed disease.

Dr. Debra Pinals, a University of Michigan forensic psychiatrist who works with people who are mentally ill and accused of crimes, said committing mass violence “is clearly outside of normal behavior” but that doesn’t mean perpetrators all have mental illness “or are driven to these actions due to mental illness.”

The few who do have mental health problems are often grappling with other challenges, said Pinals, director of the university’s program in psychiatry, law and ethics.