How could any parent kill his own children?

That's been a typical reaction to the news that Aaron Schaffhausen was accused of slashing the throats of his three young daughters last week in River Falls, Wis.

But the phenomenon, called filicide, is more common than most people might want to believe, and not all parents who do it are mentally unhinged, according to one of the country's foremost experts.

"The general lay-public response is they must be crazy, but that's not always the case," said Dr. Phillip Resnick, a professor of psychiatry at Case Western Reserve University in Cleveland. Only some are psychotic, he said, meaning they have no command of what is real.

Resnick, who has for 40 years evaluated parents accused of killing their kids, conducted a seminal study on filicide in which he identified five types of the crime.

One type -- revenge against a spouse -- may best fit the scenario authorities laid out in the charges against Schaffhausen, 34, who was divorced from the girls' mother in January.

High-profile cases

But all the types are represented in high-profile cases from across the country and the Twin Cities in the past decade or so, including the 1998 stranglings of six children in St. Paul by their mother, and the laundry-tub drowning of an Eden Prairie infant by his father in 2010.

Resnick said one out of every 33 homicides in the United States is the killing of a child under 18 by their parent, or between 250 and 300 of the country's killings each year. In a 2005 study, he found filicide to be the third-leading cause of death of American children ages 5 to 14.

After spouses killing spouses, parents killing children is the most common variety of family homicide, according to a U.S. Bureau of Justice Statistics study of homicides from 1976 to 2005.

The charges against Schaffhausen allege that he killed daughters Amara, 11, Sophie, 8, and Celia, 5, on Tuesday during an unscheduled visit to the River Falls home where they lived with their mother, Jessica. She told police he called her that afternoon and said: "You can come home now because I killed the kids."

While that scenario -- especially the chilling phone call -- suggests Schaffhausen may have killed his daughters to hurt his ex-wife, other factors Resnick found in most revenge-type filicide cases have yet to be demonstrated as part of this case.

"Usually there's been either a child custody battle or infidelity, and there's so much anger by the one spouse that they use the children to get back at the other," Resnick said.

According to the couple's Jan. 9 divorce decree, Aaron Schaffhausen agreed to give his ex-wife primary physical custody of the children, and he was to have them for most of their summer breaks and on various holidays each year. They had joint legal custody, with shared responsibility for major decisions.

He agreed to take sole charge of their debts of $196,500 and pay $1,353 child support out of the $4,666 in gross income he earned monthly as a carpenter, most recently in the oil fields of western North Dakota.

There's no evidence in the decree that the couple fought over custody or other issues. In fact, neither had an attorney.

But the break-up didn't remain amicable. In March, she complained to River Falls police that he had called from Minot, N.D., and threatened to kill her. River Falls police called Minot police, asking for a "health and safety" check on him at the apartment he shared with a fellow carpenter, according to Minot police.

"Units spoke with Aaron Schaffhausen. He states he has no intention to go back to Wisconsin. Everything is fine at this time," the police report said.

Jessica Schaffhausen told police that when her ex-husband called last week, he said he was in St. Paul and wanted to see the kids. She agreed, but on the condition that he be gone by the time she got home because she "did not wish to see him," according to the complaint charging him with three counts of first-degree intentional homicide.

After the killings, Schaffhausen's employer, a St. Paul construction firm engaged in projects in North Dakota, revealed he was fired July 5 after he didn't show up for work.

Other common types

Some parents say they killed the kids for their own good, a category Resnick calls the "altruistic type."

"Often they'll intend to take their own life and take the children with them as an extended suicide, or they have the delusion the children are better off dead," Resnick said.

A St. Paul woman made such a claim when she was sentenced in 1999 for strangling all six of her children.

"I know I was wrong ... but they don't have to suffer no more," Khoua Her, 25, told the judge who sentenced her to 50 years in the Shakopee prison. She said her life as a Hmong immigrant had been full of abuse, and she wanted to spare her kids the same fate.

When parents kills infants, it's often because they never wanted the baby -- a third type of filicide -- or they fatally abuse the baby, a fourth type, Resnick said.