40: Functional Liquid Association: A Framework for Context-Dependent Associations

Thomas M. Menino Convention & Exhibition Center 

Liquid association measures how the association between two variables varies with a third variable, yet its classical formulation collapses this modulation into a single scalar, potentially obscuring heterogeneous, non-monotonic, or localized effects. We introduce Functional Liquid Association (FLA), which extends liquid association to a functional representation that characterizes how association evolves across the full range of the moderating variable. Within a unified projection-based framework, FLA supports both a local velocity-centric analysis that highlights rapid changes or threshold effects in association strength, and a global mode-centric analysis that summarizes dominant regimes. To enable inference without restrictive distributional assumptions, we develop permutation-based tests for detecting overall association modulation and identifying localized regions of significant change. Simulations and applications to gene expression analyses demonstrate that FLA reveals structured, condition-specific association patterns missed by classical liquid association. These results establish FLA as a practical and interpretable framework for studying context-dependent associations

Context-dependent association

Liquid association

Nonparametric inference

Permutation testing 

International Chinese Statistical Association