Disentangling network dependence among multiple variables

TL;DR

This paper compares and adapts two methods for disentangling shared network dependence in multivariate data, highlighting their assumptions, effectiveness, and sensitivity to assumption violations for valid statistical inference.

Contribution

It introduces adaptations of pre-whitening methods for network data and analyzes their assumptions and limitations in reducing spurious associations.

Findings

Both methods effectively reduce spurious associations when assumptions hold

Sensitivity to assumption violations can lead to residual bias

Explicit modeling of dependence levels improves inference accuracy

Abstract

When two variables depend on the same or similar underlying network, their shared network dependence structure can lead to spurious associations. While statistical associations between two variables sampled from interconnected subjects are a common inferential goal across various fields, little research has focused on how to disentangle shared dependence for valid statistical inference. We revisit two different approaches from distinct fields that may address shared network dependence: the pre-whitening approach, commonly used in time series analysis to remove the shared temporal dependence, and the network autocorrelation model, widely used in network analysis often to examine or account for autocorrelation of the outcome variable. We demonstrate how each approach implicitly entails assumptions about how a variable of interest propagates among nodes via network ties given the network structure. We further propose adaptations of existing pre-whitening methods to the network setting by explicitly reflecting underlying assumptions about "level of interaction" that induce network dependence, while accounting for its unique complexities. Our simulation studies demonstrate the effectiveness of the two approaches in reducing spurious associations due to shared network dependence when their respective assumptions hold. However, the results also show the sensitivity to assumption violations, underscoring the importance of correctly specifying the shared dependence structure based on available network information and prior knowledge about the interactions driving dependence.