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.
"Inflection points in community-level homeless rates." Ann. Appl. Stat. 15 (2) 1037 - 1053, June 2021. https://doi.org/10.1214/20-AOAS1414