Hierarchical Bayesian Adaptive Lasso Methods on Exponential Random Graph Models

Abstract

Abstract The analysis of network data has become an increasingly prominent and demanding field across multiple research fields including data science, health, and social sciences, requiring the development of robust models and efficient computational methods. One well-established and widely employed modeling approach for network data is the Exponential Random Graph Model (ERGM). Despite its popularity, there is a recognized necessity for further advancements to enhance its flexibility and variable selection capabilities. To address this need, we propose a novel hierarchical Bayesian adaptive lasso model (BALERGM), which builds upon the foundations of the ERGM. The BALERGM leverages the strengths of the ERGM and incorporates the flexible adaptive lasso technique, thereby facilitating effective variable selection and tackling the inherent challenges posed by high-dimensional network data. The model improvements have been assessed through the analysis of simulated data, as well as two authentic datasets. These datasets encompassed friendship networks and a respondent-driven sampling dataset on active and healthy lifestyle awareness programs.