B1071
Title: Accounting for network dependencies when assessing covariate effects via graphon random effect
Authors: Nurzhan Sapargali - Ludwig Maximilian University of Munich (Germany) [presenting]
Cornelius Fritz - Pennsylvania State University (United States)
Benjamin Sischka - Ludwig Maximilian University of Munich (Germany)
Goeran Kauermann - LMU Munich (Germany)
Abstract: The primary interest in analyzing network data in many cases lies in assessing the effects of exogenous covariates on edge formation rather than understanding structural aspects of the observed network. Yet, most models for network data focus on the latter issue and most importantly impose specific structural assumptions. To formulate a generalized linear model framework that allows for straightforward incorporating and interpreting covariate effects, while also accounting for the complex dependency structure without encompassing too restrictive assumptions, graphon-structured residuals are introduced. An extension to the graphon model is developed where one can use covariate information by extending the linear predictor with a graphon and using a suitable link function. In this context, the graphon model is an appropriate modeling framework as, following the Aldous-Hoover theorem, the family of graphon models comprises the probability distribution of any infinite vertex-exchangeable networks. This characteristic makes it a flexible modeling tool without restrictive structural assumptions. The approach heeds recent calls that network dependence can lead to spurious associations if not accounted for and that one should test a substantive theory with models with adequate predictive power. In two application cases to binary and weighted networks, the need to account for dependencies and the link-prediction abilities of the model is showcased.
