To what extent, the researchers asked middle-age adults, do your parents ignore suggestions or advice that would make their lives easier or safer?

Ignore instructions from their doctors?

Insist on doing things their own way, even if that makes their own or others’ lives more difficult, inconvenient or unsafe?

That’s how several studies directed by Allison Heid, a gerontologist consulting at Penn State and Rowan University, measured adult children’s perceptions of stubbornness among their aging parents.

It proved a widespread complaint.

In an initial study of 189 adult children and their parents, Heid and her colleagues found that 77% of children (average age: 55) reported stubborn behavior by their parents, at least sometimes.

But two-thirds of the parents (average age: 80) described themselves as stubborn, too.

In a later study the researchers asked 192 middle-age children to keep a seven-day diary of parental interactions. Of those who had contact with their parents that week, 31% reported “insistent” behaviors and 17% reported “risky” behaviors; 11% said they encountered both.

“The stories are endless,” said Heid, whose interest in the subject was sparked by a grandmother determined to shovel snow, despite her children’s protests, into her 80s.

Lori Kayne, a geriatric social worker in Bridgewater, N.J., can tell such stories. Her late father, whose poor balance had caused multiple falls but no serious injuries, resisted her pleas to use his walker. “We had a lot of screaming matches,” she recalled — but she never prevailed.

Then last year her father fell and fractured several vertebrae. “He was in terrible agony for months,” Kayne said — but at least he was finally relying on the walker. She figured that at 87 he’d grown more reasonable.

Nope. “As soon as he started to feel better, he refused the walker, even though he knew what could happen,” Kayne said, sighing.

The more polite social science term for such skirmishes: mismatched goals. “If the goal is not shared — the older adult wants to walk to the grocery store himself, and the child says, ‘I don’t think it’s a good idea’ — that’s when conflict can arise,” Heid explained.

Such clashes, and related reports of stubbornness, increase when the parent and child live together, she found. Perceived stubbornness also rises when a parent’s disability increases.

“When a child steps in, most commonly there’s a safety issue,” Heid said. “The parent may not share those feelings about their capabilities.”

These familiar, probably universal safety-versus- autonomy debates have led some critics to object that adult children overemphasize the former, when what matters more to their parents is maintaining independence and pursuing what they find meaningful.

Reasoning with someone who seems impervious to it sounds, well, challenging. “It’s a really hard thing, this mismatch between what we need and what we want and what’s good for us,” said Marci Gleason, a social psychologist at the University of Texas at Austin.

Social scientists have learned that older adults who provide support have increased well-being and better health. Receiving help, on the other hand, is associated with negative mood.

After decades of helping their children, older people understandably balk at becoming dependent on them. “Even if intellectually they accept it, actually receiving help is difficult,” Gleason said. “It can signal that you’re not needed, and people want to feel needed.”

She suggests trying to equalize power in the relationship, allowing the parent to also provide support, even by just listening empathetically to a child’s account of her tough week. “It could be beneficial for the relationship to not have it all be one-sided,” Gleason said.

She’s also a fan of incremental progress, a negotiation that leads to a more reciprocal exchange.

As proof of concept, meet the Abrams family.

Carl Abrams, a 90-year-old retired Air Force colonel, lives in Williamstown, N.J., with his wife, Joan, 88. He cheerfully agrees that, yes, he’s plenty stubborn. “He gets very angry and oppositional,” said his older daughter Tamar Abrams, 63, who visits twice monthly from Falls Church, Va.

In 2016 the family was worried about his driving. Carl Abrams had knocked several side mirrors off his Buick, sometimes wandered out of his lane, once fell asleep at the wheel and sideswiped a truck. It was time to relinquish the keys, the family said.

After extended wrangling, Abrams agreed to a retest by the state motor vehicle agency, a gambit that backfired. “We were convinced he would fail, but he aced it,” said his daughter.

Months passed; his wife began refusing to ride with him. The family negotiated a series of escalating restrictions: First, Abrams agreed not to drive at night. Then, to drive only to familiar places. Finally, to stay within 5 miles of home.

“Sometimes he would blow up,” Tamar Abrams said. “But if you gave him some time and then returned to the discussion, he’d be OK.”

Now Carl Abrams relies on a bright red, battery- powered scooter. “An excellent compromise,” he said. “If it wasn’t for the scooter, I’d go crazy in the house.”

Twice weekly he cruises 2 miles to have lunch at Applebee’s, where the servers all know his name, and picks up a few groceries on his way home.

“If he didn’t have to cross a major intersection, it would be a lovely ritual,” Tamar Abrams said. Nobody (except Carl Abrams) feels good about his navigating across six lanes on his scooter, even at a traffic light.

But she understands. “You’re holding on for dear life to who you think you are,” she said. So, “we hold our breath and let him do it.”