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Evaluating Aggregated Relational Data Models with Simple Diagnostics

Ian Laga, Benjamin Vogel, Jieyun Wang, Anna Smith, Owen Ward

TL;DR

This work presents a fast, reproducible diagnostic workflow for Aggregated Relational Data ARD/NSUM analyses that assesses covariate structure, residual correlation, and distributional assumptions using point estimates such as $MLE$ or $MAP$. By applying a sequence of diagnostics—covariate residual plots, a Tracy–Widom test for group correlation, and rootograms with dispersion metrics—the framework guides model refinement and helps practitioners choose among Poisson, Negative Binomial, and correlated extensions. Through the Ukraine ARD and simulation studies, the authors show how the approach identifies common misfits, reveals strong group correlation, and justifies more expressive models like correlated or degree-correlated ARD variants. The methods are implemented in the networkscaleuprlang R package, enabling rapid, transparent model evaluation before final inference, with practical impact for reliable population size and network inference from ARD data.

Abstract

Aggregated Relational Data (ARD) contain summary information about individual social networks and are widely used to estimate social network characteristics and the size of populations of interest. Although a variety of ARD estimators exist, practitioners currently lack guidance on how to evaluate whether a selected model adequately fits the data. We introduce a diagnostic framework for ARD models that provides a systematic, reproducible process for assessing covariate structure, distributional assumptions, and correlation. The diagnostics are based on point estimates, using either maximum likelihood or maximum a posteriori optimization, which allows quick evaluation without requiring repeated Bayesian model fitting. Through simulation studies and applications to large ARD datasets, we show that the proposed workflow identifies common sources of model misfit and helps researchers select an appropriate model that adequately explains the data.

Evaluating Aggregated Relational Data Models with Simple Diagnostics

TL;DR

This work presents a fast, reproducible diagnostic workflow for Aggregated Relational Data ARD/NSUM analyses that assesses covariate structure, residual correlation, and distributional assumptions using point estimates such as or . By applying a sequence of diagnostics—covariate residual plots, a Tracy–Widom test for group correlation, and rootograms with dispersion metrics—the framework guides model refinement and helps practitioners choose among Poisson, Negative Binomial, and correlated extensions. Through the Ukraine ARD and simulation studies, the authors show how the approach identifies common misfits, reveals strong group correlation, and justifies more expressive models like correlated or degree-correlated ARD variants. The methods are implemented in the networkscaleuprlang R package, enabling rapid, transparent model evaluation before final inference, with practical impact for reliable population size and network inference from ARD data.

Abstract

Aggregated Relational Data (ARD) contain summary information about individual social networks and are widely used to estimate social network characteristics and the size of populations of interest. Although a variety of ARD estimators exist, practitioners currently lack guidance on how to evaluate whether a selected model adequately fits the data. We introduce a diagnostic framework for ARD models that provides a systematic, reproducible process for assessing covariate structure, distributional assumptions, and correlation. The diagnostics are based on point estimates, using either maximum likelihood or maximum a posteriori optimization, which allows quick evaluation without requiring repeated Bayesian model fitting. Through simulation studies and applications to large ARD datasets, we show that the proposed workflow identifies common sources of model misfit and helps researchers select an appropriate model that adequately explains the data.
Paper Structure (25 sections, 14 equations, 33 figures, 1 table)

This paper contains 25 sections, 14 equations, 33 figures, 1 table.

Table of Contents

  1. Introduction
  2. Aggregated Relational Data
  3. ARD Models
  4. Working Example
  5. Diagnostic Structure
  6. Diagnostic Tools
  7. Covariates
  8. Application to Ukraine ARD.
  9. Correlation structure
  10. Application to Ukraine ARD.
  11. Distributional Tests
  12. Rootogram
  13. Application to Ukraine ARD.
  14. Overdispersion test
  15. Application to Ukraine ARD.
  16. ...and 10 more sections

Figures (33)

  • Figure 1: Proposed diagnostic structure for ARD models. A maximum of three null models are fit, and all diagnostics depend on these null models.
  • Figure 1: (Simulation 1) Covariate selection diagnostics
  • Figure 2: Local covariate plots for the Ukraine ARD.
  • Figure 2: (Simulation 1) Group correlation diagnostics
  • Figure 3: Global covariate plots for the Ukraine ARD.
  • ...and 28 more figures