CID Models on Real-world Social Networks and Goodness of Fit Measurements

TL;DR

This paper introduces a new goodness of fit measure called stratified-sampling cross-validation (SCV) for evaluating CID models on real-world social networks, addressing limitations of traditional metrics.

Contribution

The paper proposes the SCV metric for assessing network model fit, specifically tailored for CID models, and demonstrates its effectiveness on real social network data.

Findings

SCV effectively evaluates CID models on social networks

Different models are suitable for different network structures

Patterns of model fit are generalized across networks

Abstract

Assessing the model fit quality of statistical models for network data is an ongoing and under-examined topic in statistical network analysis. Traditional metrics for evaluating model fit on tabular data such as the Bayesian Information Criterion are not suitable for models specialized for network data. We propose a novel self-developed goodness of fit (GOF) measure, the `stratified-sampling cross-validation' (SCV) metric, that uses a procedure similar to traditional cross-validation via stratified-sampling to select dyads in the network's adjacency matrix to be removed. SCV is capable of intuitively expressing different models' ability to predict on missing dyads. Using SCV on real-world social networks, we identify the appropriate statistical models for different network structures and generalize such patterns. In particular, we focus on conditionally independent dyad (CID) models such as the Erdos Renyi model, the stochastic block model, the sender-receiver model, and the latent space model.