Identifying nonlinear relations among random variables: A network analytic approach

Nonlinear relations, 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 the use of network models has risen, 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 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 novel 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 and conditional mutual information. Through simulation studies and an empirical example, we show that partial distance correlations as a novel method 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.