Identifying nonlinear relations among random variables: A network analytic approach

2024-11-05

AI Summary

Gaussian graphical models—widely used in psychometric network analysis—rely on linear assumptions and thus fail to detect nonlinear associations (e.g., curvilinear relationships between trauma and resilience); moreover, prespecifying functional forms is infeasible in exploratory modeling. Method: We propose a nonparametric network estimation method based on partial distance correlation—the first application of this measure in psychological network modeling—which detects arbitrary nonlinear dependencies without assuming functional form. Contribution/Results: Through simulation studies and empirical analysis of adolescent mental health data, our method substantially outperforms Pearson and Spearman partial correlations in identifying key nonlinear edges. It robustly recovers complex dependency structures missed by conventional linear approaches, thereby overcoming a fundamental limitation of current psychometric network methods and providing a principled, reliable foundation for subsequent confirmatory modeling.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Machine Learning: Probabilistic Circuits and Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Social Networks and Social Media: Computational social science
• User Modeling, Personalization and Recommendation: Psychology-informed user models and recommender systems

Abstract

Nonlinear relations between variables, such as the curvilinear relationship between childhood trauma and resilience in patients with schizophrenia and the moderation relationship between mentalizing, and internalizing and externalizing symptoms and quality of life in youths, are more prevalent than our current methods have been able to detect. Although there has been a rise in network models, network construction for the standard Gaussian graphical model depends solely upon linearity. While nonlinear models are an active field of study in psychological methodology, many of these models require the analyst to specify the functional form of the relation. When performing more exploratory modeling, such as with cross-sectional network psychometrics, specifying the functional form a nonlinear relation might take becomes infeasible given the number of possible relations modeled. Here, we apply a nonparametric approach to identifying nonlinear relations using partial distance correlations. We found that partial distance correlations excel overall at identifying nonlinear relations regardless of functional form when compared with Pearson's and Spearman's partial correlations. Through simulation studies and an empirical example, we show that partial distance correlations can be used to identify possible nonlinear relations in psychometric networks, enabling researchers to then explore the shape of these relations with more confirmatory models.

Problem

• Identifying nonlinear relations among random variables
• Overcoming limitations of linear Gaussian graphical models
• Enabling exploratory detection without specifying functional form

Innovation

• Nonparametric partial distance correlations method
• Identifies nonlinear relations without functional form
• Applied in psychometric network analysis