The Annals of Applied Statistics

Dynamics of homelessness in urban America

Chris Glynn and Emily B. Fox

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The relationship between housing costs and homelessness has important implications for the way that city and county governments respond to increasing homeless populations. Though many analyses in the public policy literature have examined inter-community variation in homelessness rates to identify causal mechanisms of homelessness [J. Urban Aff. 35 (2013) 607–625; J. Urban Aff. 25 (2003) 335–356; Am. J. Publ. Health 103 (2013) S340–S347], few studies have examined time-varying homeless counts within the same community [J. Mod. Appl. Stat. Methods 15 (2016) 15]. To examine trends in homeless population counts in the 25 largest U.S. metropolitan areas, we develop a dynamic Bayesian hierarchical model for time-varying homeless count data. Particular care is given to modeling uncertainty in the homeless count generating and measurement processes, and a critical distinction is made between the counted number of homeless and the true size of the homeless population. For each metro under study, we investigate the relationship between increases in the Zillow Rent Index and increases in the homeless population. Sensitivity of inference to potential improvements in the accuracy of point-in-time counts is explored, and evidence is presented that the inferred increase in the rate of homelessness from 2011–2016 depends on prior beliefs about the accuracy of homeless counts. A main finding of the study is that the relationship between homelessness and rental costs is strongest in New York, Los Angeles, Washington, D.C., and Seattle.

Article information

Ann. Appl. Stat., Volume 13, Number 1 (2019), 573-605.

Received: November 2017
Revised: May 2018
First available in Project Euclid: 10 April 2019

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Zentralblatt MATH identifier

Homelessness housing costs missing data state-space


Glynn, Chris; Fox, Emily B. Dynamics of homelessness in urban America. Ann. Appl. Stat. 13 (2019), no. 1, 573--605. doi:10.1214/18-AOAS1200.

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Supplemental materials

  • Metro-level supporting figures. As supplementary material, we present figures for each of the 25 largest metros in the United States from 2011–2017. For each metro, we present: (a) the posterior predictive distribution for homeless counts, $C_{i,1:T}^{*}|C_{1:25,1:T}$, $N_{1:25,1:T}$, and the imputed total homeless population size, $H_{i,1:T}|C_{1:25,1:T}, H_{1:25,1:T}$; (b) the predictive distribution for the total homeless population in 2017, $H_{i,2017}| C_{1:25,1:T},N_{1:25,1:T}$; (c) the posterior distribution of increase in the total homeless population with increases in ZRI; and (d) the sensitivity of the inferred increase in the homelessness rate from 2011–2016 to different annual changes in count accuracy.