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

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

“The stories are endless,” said Dr. 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,” Ms. 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,” Ms. Kayne said, sighing.