A1394
Title: Linear regression with probabilistic networks for network-linked data
Authors: Jingnan Zhang - University of Science and Technology of China (China) [presenting]
Abstract: Network-linked data, consisting of a network together with unit-level covariates and responses, have attracted increasing attention because they combine relational information with attributes of individual units. Existing regression methods for such data either impose an autoregressive neighborhood-average form for peer effects while treating the observed adjacency matrix as exact, or introduce a flexible network-cohesion component without explicitly modeling peer-response dependence. In this paper, we propose a probabilistic regression framework for network-linked data that incorporates network information through the edge-probability matrix rather than the observed adjacency matrix. The proposed model uses connection probabilities to weight peer responses and uses latent positions to capture network cohesion, thereby accounting for network randomness while preserving peer effects. We develop a two-step algorithm that first estimates the latent network structure and then plugs the estimated probability matrix and latent positions into the regression likelihood. We establish consistency of the estimated probability matrix and latent positions, and further prove consistency and debiased asymptotic normality for the regression parameter estimators. The theoretical findings are supported by extensive simulation studies and an application to a S\~ao Paulo seller competition network-linked dataset.
