Measuring Spatial Mismatch Between Homelessness and Homeless Resources With a Theil Index and Statistical Inference

Brent D. Mast
U.S. Department of Housing and Urban Development

SpAM
SpAM (Spatial Analysis and Methods) presents short articles on the use of spatial statistical techniques for housing or urban development research. Through this department of Cityscape, the Office of Policy Development and Research introduces readers to the use of emerging spatial data analysis methods or techniques for measuring geographic relationships in research data. Researchers increasingly use these new techniques to enhance their understanding of urban patterns but often do not have access to short demonstration articles for applied guidance. If you have an idea for an article of no more than 3,000 words presenting an applied spatial data analysis method or technique, please send a one-paragraph abstract to rwilson@umbc.edu for review.

In this article, I employ a Theil (1972) index to measure the spatial mismatch of beds available to shelter the homeless and homeless populations across Continuum of Care regions. I demonstrate a method for statistical inference using the Theil index based on asymptotic results, focusing mainly on testing for across-state differences. Estimates reveal large differences across states in the spatial mismatch between homeless resources and homeless populations. Simulations indicated that state inferences are better for states that have a relatively larger estimated spatial mismatch and relatively larger total count of beds available to shelter the homeless.