KMAN Publication Inc. (KMANPUB) Applied Family Therapy Journal (AFTJ) 3041-8798 7 Serial Number 32 2026 03 01 Uncovering Nonlinear Dynamics in Intergenerational Anxiety: Support Vector Regression of Parental Psychological Control, Child Behavioral Inhibition, and Family Climate Uncovering Nonlinear Dynamics in Intergenerational Anxiety: Support Vector Regression of Parental Psychological Control, Child Behavioral Inhibition, and Family Climate 1 11 10.61838/kman.aftj.5245 EN Journal Article 2026 01 11 <p><strong>Objective:</strong> To utilize Support Vector Regression to uncover the complex, nonlinear dynamics and threshold effects characterizing the relationship between parental psychological control, child behavioral inhibition, family climate, and the manifestation of intergenerational anxiety symptoms in children.</p> <p><strong>Methods and Materials:</strong> This study employed a cross-sectional design encompassing 482 parent-child dyads recruited from Kenya. Primary data collection instruments included the Psychological Control Scale, the Behavioral Inhibition Questionnaire, the Family Environment Scale, and the Screen for Child Anxiety Related Emotional Disorders (SCARED). To analyze the multidimensional data, a Support Vector Regression model utilizing a Radial Basis Function kernel was implemented. Model hyperparameters were optimized via 10-fold cross-validation, and individual predictor contributions were evaluated using permutation feature importance.</p> <p><strong>Findings:</strong> The Support Vector Regression model demonstrated superior predictive capability, explaining of the variance ( ) in child anxiety, significantly outperforming standard Multiple Linear Regression ( ). Permutation analysis identified child behavioral inhibition as the most critical predictor, accounting for a increase in model error when neutralized, followed closely by parental psychological control ( ), family conflict ( ), and family cohesion ( ). Furthermore, partial dependence profiles revealed a critical toxicity threshold: child anxiety spiked exponentially only when parental psychological control exceeded standard deviations above the mean, while high family conflict acted as a synergistic non-linear amplifier specifically for highly inhibited youth.</p> <p><strong>Conclusion:</strong> The intergenerational transmission of anxiety is fundamentally governed by complex, non-linear tipping points and synergistic temperamental vulnerabilities that are most accurately captured and understood through advanced machine learning models.</p> https://www.journals.kmanpub.com/index.php/aftj/article/download/5245/9524