Objects <p>The Circumplex model has been a subject of controversy. Our study aims to validate its curvilinear hypothesis by examining the relationship between family function and psychological distress in informal caregivers of people with dementia (PwD). If a curvilinear relationship is identified, it will provide empirical support for the Circumplex model. Conversely, if a linear relationship is found, the threshold effect can be further clarified, thereby offering a foundation for personalized psychological intervention strategies for caregivers at the family level.</p> Methods <p>We recruited a total of 267 elderly PwD and their informal caregivers as research subjects. Using a self-designed questionnaire, the Kessler Psychological Distress Scale, and the Family Adaptation and Cohesion Evaluation Scales to detect curvilinear or linear relationships, perform smooth curve fitting, and conduct threshold effect analysis.</p> Results <p>Between-group differences were significant across the three family types (<i>P</i> = 0.001), as were within-group differences among the four family function types (<i>P</i> = 0.000, <i>P</i> = 0.000). A negative correlation was observed between family function and psychological distress. When the family score was ≤ 140, the psychological distress score decreased as the family function score increased (<i>P</i> &lt; 0.001). However, when the family function score was &gt; 140, the level of psychological distress remained unchanged (<i>P</i> = 0.552).</p> Conclusion <p>The better the family function of caregivers, the less likely adverse psychological conditions are to occur. A family function score of 140 can serve as a node for assigning tiered, individualized interventions.</p>