# A two-stage working model strategy for network analysis under Hierarchical Exponential Random Graph Models

## TL;DR

This paper introduces a two-stage modeling approach combining Latent Space Models and ERGMs to better capture complex dependency structures in social networks, improving fit and scalability.

## Contribution

It proposes a novel two-stage strategy that leverages LSM for clustering and ERGM for dependency modeling, addressing scalability issues in network analysis.

## Key findings

- Enhanced model fit for complex network dependencies
- Improved scalability in network estimation
- Effective combination of LSM and ERGM methods

## Abstract

Social networks as a representation of relational data, often possess multiple types of dependency structures at the same time. There could be clustering (beyond homophily) at a macro level as well as transitivity (a friend's friend is more likely to be also a friend) at a micro level. Motivated by \cite{schweinberger2015local} which constructed a family of Exponential Random Graph Models (ERGM) with local dependence assumption, we argue that this kind of hierarchical models has potential to better fit real networks. To tackle the non-scalable estimation problem, the cost paid for modeling power, we propose a two-stage working model strategy that first utilize Latent Space Models (LSM) for their strength on clustering, and then further tune ERGM to archive goodness of fit.