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Author ORCID Identifier
https://orcid.org/0009-0000-4739-7322
Date Available
5-1-2028
Year of Publication
2026
Document Type
Doctoral Dissertation
Degree Name
Doctor of Philosophy (PhD)
College
Arts and Sciences
Department/School/Program
Statistics
Faculty
Anna L. Smith
Faculty
Derek Young
Abstract
Statistical network models are widely used to represent relational structures in social, behavioral, and public health systems, yet tools for evaluating and comparing competing models remain limited. This dissertation develops resampling-based approaches for model criticism in network settings, with a focus on latent space models for network data and models for aggregated relational data (ARD). The proposed methods provide practical frameworks for comparing competing model structures. One component of this work studies geometry selection in latent space models, where the probability of a tie depends on distances between nodes in an unobserved latent space. Although Euclidean geometry is commonly used, hyperbolic geometry can better capture structural features such as clustering and degree heterogeneity observed in complex networks. To identify the underlying geometry, prior work has compared multidimensional scaling (MDS) stress values computed from different geometries. This dissertation develops two resampling-based approaches to better account for uncertainty in this setting. One approach extends permutation-based hypothesis testing for MDS to the network data setting by comparing observed stress differences between two candidate geometries to distributions of stress differences generated in the same way as the observed values from density-preserving permuted networks, providing a nonparametric framework for assessing whether one geometry offers a significantly better representation of the observed network. To further account for the structure of the observed network, the second approach introduces a parametric bootstrap procedure that generates networks conditional on observed geodesic distances under the Gaussian latent position model (GLPM, GLP Model) and adapts the Davidson–MacKinnon J-test to compare latent space models with different geometries. Simulation studies show that both permutation and bootstrap methods improve the ability to detect the underlying geometry compared to the raw stress difference from prior work, particularly in large and sparse network settings. A second component of the dissertation develops a general framework for comparative model criticism inspired by challenges arising in aggregated relational data (ARD). We adapt the posterior predictive null check (PPN) to compare competing models by evaluating whether predictive data generated from one model can pass diagnostics designed for another. To make this framework computationally efficient, we incorporate Pareto-smoothed importance sampling (PSIS) to approximate predictive comparisons without repeatedly refitting models. Although motivated by ARD applications, this approach is broadly applicable to a wide class of Bayesian models and supports systematic comparison across multiple candidate models. Together, these contributions establish a resampling-based perspective on model criticism for network models. Through permutation tests, parametric bootstrap procedures, and efficient predictive comparison tools, this work provides practical methods for distinguishing among competing models and for supporting more reliable model evaluation in network analysis.
Digital Object Identifier (DOI)
https://doi.org/10.13023/etd.2026.244
Archival?
Archival
Funding Information
This study was supported by pilot funds from the University of Kentucky's Substance Use Priority Research Area (SUPRA), supported by the Vice President for Research.
Recommended Citation
Wang, Jieyun, "Resampling Methods for Network Model Criticism" (2026). Theses and Dissertations--Statistics. 83.
https://uknowledge.uky.edu/statistics_etds/83
