A structural analysis of U.S. homelessness through Markov random fields: Identifying predictors and potential causal links through permutation tests

Many researchers who study homelessness argue that traditional frameworks are often too narrow, failing to account for groups outside the reach of social services. Despite historic calls to broaden the scope of sampling to encompass structural forces, only recent advancements have enabled the development of a robust framework for accurate measurement and analysis. This study utilizes Markov random fields (MRFs) to explore the influences of key structural indicators on homelessness from 2007 to 2024. By employing partial correlations, we investigate the interplay among geographic locations at the state-level among the following variables: the job market, median rent, eviction rates, occupancy rates, median income, the construction of new homes, the cost of one-bedroom units, funding from Housing and Urban Development (HUD), and policies under democrat or republican elections (by state). Our findings reveal that rent, income, and the availability of single-bedroom units are the foremost predictors of homelessness rates, underscoring the significance of housing affordability and availability as central determinants. The analysis also distinguishes variation in conditional dependence patterns between states governed by different political parties, even as they change, spotlighting substantial differences in the partial association rates across partisan lines. The results emphasize the need for policy reforms targeted at increasing housing affordability over more long-term strategies, such as the construction of new homes, and suggest that political contexts distinctly shape the effectiveness of structural interventions. These insights offer a valuable framework for policymakers aiming to address the root causes of homelessness through targeted structural reforms. An exploratory lag-1 directed temporal network reveals that the HUD↔homelessness feedback cycle is empirically present especially in Republican-led states; we report this as suggestive (cluster-permutation p = 0.12) and as a hypothesis for future panel-VAR work. We frame the conditional-dependence structure as descriptive rather than causal, state the assumptions a causal reading would require, and provide four supplementary specifications — cluster bootstrap, two-way state-and-year fixed-effects residualisation, nonparanormal transformation, and Fast Causal Inference — that probe each assumption.