Siao Xu

Latent group structure is a standard device for modeling cross-sectional dependence in large panels, yet existing partial-correlation community methods typically assign each unit to a single group and do not distinguish the formation of conditional-dependence links from their strength. We propose a two-path mixed-membership partial-correlation network (2PMM-PCN). Mixed membership governs link formation along an extensive margin, while node-specific sociability governs link strength along an intensive margin. Although the two paths have distinct economic interpretations, their node-specific components enter the population signal only through a common scale, allowing the mixed memberships to be recovered by a single spectral procedure. We develop PartialCorr-Mixed-SCORE and establish a convergence rate for the average membership estimation error under weak dependence. In an application to U.S. state employment growth, the estimated memberships reproduce the broad group structure found in earlier studies while revealing economically meaningful overlaps that a single-group assignment cannot represent.