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.

翻译：变量间的非线性关系，例如精神分裂症患者童年创伤与心理韧性之间的曲线关系，以及青少年心智化能力与内化/外化症状及生活质量之间的调节关系，比我们现有方法能够检测到的更为普遍。尽管网络模型的应用日益增多，但标准高斯图模型的网络构建仅依赖于线性假设。虽然非线性模型已成为心理学方法论研究的热点领域，但多数此类模型要求分析者预先设定关系的函数形式。在进行更具探索性的建模时（如横断面网络心理测量学），考虑到需要建模的可能关系数量众多，预先设定非线性关系的具体函数形式往往不可行。本文采用非参数方法，通过偏距离相关系数来识别非线性关系。研究发现，与皮尔逊偏相关系数和斯皮尔曼偏相关系数相比，偏距离相关系数在识别各类函数形式的非线性关系方面表现出显著优势。通过模拟研究和实证案例，我们证明偏距离相关系数可用于识别心理测量网络中的潜在非线性关系，从而使研究者能够借助更具验证性的模型进一步探索这些关系的具体形态。