Modeling Hierarchical Spatial Interdependence for Limited Dependent Variables

Multilevel modeling accounts for outcome dependence across lower-level units due to unobserved group effects, while spatial modeling accounts for outcome dependence across units in the same level of analysis due to diffusion. Outcome dependence can occur simultaneously due to both spatial diffusion in the lower-level units and spatial diffusion in the unobserved group effects. For example, counties are nested within states and diffusion processes might take place at both levels of analysis. Building on recent research from the spatial econometrics and multilevel modeling literature, we propose a class of spatial hierarchical models with binary outcomes. One method accounts for spatially independent, unobserved group effects and the other method accounts for spatially dependent unobserved group effects. We propose a Bayesian approach to estimate such effects while also accounting for lower-level diffusion in the outcome, and provide software to estimate these models. Our Monte Carlo results demonstrate that failing to correctly account for diffusion and/or the nested structure of data can lead to bias in both parameter estimates and substantive effects. We apply these models to analyze the causes of civil rights protests in the United States in the 1960s.