This paper develops and provides software for a class of spatial hierarchical (multilevel) models for binary outcomes, motivated by situations where outcome dependence arises both from diffusion among lower-level units and from spatially structured unobserved group effects. The authors propose two model variants—one that treats unobserved group effects as spatially independent and another that treats them as spatially dependent—and use a Bayesian estimation approach. They evaluate performance with Monte Carlo simulations and illustrate the approach by analyzing causes of civil rights protests in the United States in the 1960s.
Bayesian estimation of spatial multilevel models Binary outcomes and lower-level diffusion Monte Carlo evaluation
Data and methods
The authors build on spatial econometrics and multilevel modeling literatures to propose two spatial hierarchical models for binary outcomes: one accounting for spatially independent unobserved group effects and a second allowing those group effects to be spatially dependent. They implement a Bayesian estimation strategy and supply software to estimate the models. Their evaluation uses Monte Carlo simulations to compare model performance when diffusion and nested structure are present or omitted.
Main findings
In simulated data, the paper reports that failing to account for diffusion and/or the nested structure can bias parameter estimates and substantive effects. The paper also includes an empirical application examining the causes of civil rights protests in the United States during the 1960s to demonstrate the models and software in practice.
- Proposes two model variants for spatial dependence at different levels of nesting.
- Uses Monte Carlo simulations to assess bias when models ignore diffusion or nesting.
