Monte Carlo goodness-of-fit tests for degree corrected and related stochastic blockmodels
Abstract
We construct Bayesian and frequentist finite-sample goodness-of-fit tests for three different variants of the stochastic blockmodel for network data. Since all of the stochastic blockmodel variants are log-linear in form when block assignments are known, the tests for the latent block model versions combine a block membership estimator with the algebraic statistics machinery for testing goodness-of-fit in log-linear models. We describe Markov bases and marginal polytopes of the variants of the stochastic blockmodel and discuss how both facilitate the development of goodness-of-fit tests and understanding of model behaviour. The general testing methodology developed here extends to any finite mixture of log-linear models on discrete data, and as such is the first application of the algebraic statistics machinery for latent-variable models.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Sep 15, 2023
- Source ID
- 10.1093/jrsssb/qkad084
Entities
People
- Bowei Yan
- Dane Wilburne
- Debdeep Pati
- Liam Solus
- Mateja Raič
- Nikita Alexeev
- Robert Williams
- Sonja Petrović
- Vishesh Karwa
Organizations
- Air Force Office of Scientific Research
- Illinois Institute of Technology
- MITRE Corporation
- National Science Foundation
- Office of Naval Research
- Rose–Hulman Institute of Technology
- Royal Institute of Technology
- Simons Foundation
- Temple University
- Texas A&M University
- The Citadel
- United States Department of Energy
- University of Illinois at Chicago