June 2021 Inflection points in community-level homeless rates
Chris Glynn, Thomas H. Byrne, Dennis P. Culhane
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Ann. Appl. Stat. 15(2): 1037-1053 (June 2021). DOI: 10.1214/20-AOAS1414


Statistical models of community-level homeless rates typically assume a linear relationship to covariates. This linear model assumption precludes the possibility of inflection points in homeless rates—thresholds in quantifiable metrics of a community that, once breached, are associated with large increases in homelessness. In this paper we identify points of structural change in the relationship between homeless rates and community-level measures of housing affordability and extreme poverty. We utilize the Ewens–Pitman attraction (EPA) distribution to develop a Bayesian nonparametric regression model in which clusters of communities with similar covariates share common patterns of variation in homeless rates. A main finding of the study is that the expected homeless rate in a community begins to quickly increase once median rental costs exceed 30% of median income, providing a statistical link between homelessness and the U.S. government’s definition of a housing cost burden. Our analysis also identifies clusters of communities that exhibit distinct geographic patterns and yields insight into the homelessness and housing affordability crisis unfolding on both coasts of the United States.


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Chris Glynn. Thomas H. Byrne. Dennis P. Culhane. "Inflection points in community-level homeless rates." Ann. Appl. Stat. 15 (2) 1037 - 1053, June 2021. https://doi.org/10.1214/20-AOAS1414


Received: 1 March 2020; Revised: 1 September 2020; Published: June 2021
First available in Project Euclid: 12 July 2021

MathSciNet: MR4298954
zbMATH: 1477.62378
Digital Object Identifier: 10.1214/20-AOAS1414

Keywords: Bayesian hierarchical model , Ewens–Pitman attraction , Homelessness , housing affordability , random partition model

Rights: Copyright © 2021 Institute of Mathematical Statistics


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Vol.15 • No. 2 • June 2021
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