Spatial, Temporal, and Spatiotemporal Autoregressive Probit Models of Binary Outcomes: Estimation, Interpretation, and Presentation

Abstract

Spatial/Spatiotemporal interdependence - i.e., that the outcomes, actions, or choices of some unit-times depend on those of others - is substantively and theoretically ubiquitous and central in binary outcomes of interest across the social sciences. However, most empirical applications omit spatial interdependence and, at best, treat temporal dependence as nuisance to be “kludged”; indeed, even theoretical and substantive discussion usually ignores (inter)dependence. Moreover, in the few contexts where spatial interdependence has been acknowledged or emphasized, such as in the social-network and policy-diffusion literatures, empirical models either do not fully reflect the simultaneity of the outcomes across units, or they do not recognize the endogeneity of the spatial lags which are used (appropriately) to model the interdependence. This paper notes and explains some of the severe challenges posed by spatiotemporal interdependence in binary-outcome models and then follows recent spatial-econometric advances to suggest two simulation-based approaches for surmounting the computational intensiveness of these models: classical recursive-importance-sampling (RIS) or Bayesian Markov-chain Monte-Carlo (MCMC). Serial autocorrelation in binary outcomes raises essentially the same challenges, so these strategies offer effective approach to temporal dependence as well. We provide Monte-Carlo comparisons of the performance of these alternative estimators for spatial probit, including comparisons to estimation-strategies blind to or naïve about (inter)dependence - i.e., omitting spatial lags or including them but treating them as exogenous regressors in standard probit estimation - and then we show how to apply related simulation methods to calculate estimated spatial effects of hypothetical shocks in terms of outcomes or probabilities of outcomes (with associated confidence/credibility regions) rather than only in parameter-estimate or latent-variable terms as in all prior spatial-probit applications. We illustrate with applications to U.S. states’ adoptions of legislative term-limits and to great-power decisions to enter World War I.

Keywords: Spatial Dependence, Temporal Dependence, Autocorrelation, Binary Outcomes, Probit

JEL Classification: C15, C21, C22, C23, C25