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Spatial- and Spatiotemporal-Autoregressive Probit Models of Interdependent Binary Outcomes*

  • Robert J. Franzese, Jude C. Hays and Scott J. Cook


Spatial/spatiotemporal interdependence—that is, that outcomes, actions or choices of some unit-times depend on those of other unit-times—is substantively important and empirically ubiquitous in binary outcomes of interest across the social sciences. Estimating and interpreting binary-outcome models that incorporate such spatial/spatiotemporal dynamics directly is difficult and rarely attempted, however. This article explains the inferential challenges posed by spatiotemporal interdependence in binary-outcome models and recent advances in their estimation. Monte Carlo simulations compare the performance of one of these consistent and asymptotically efficient methods (maximum simulated likelihood, using recursive importance sampling) to estimation strategies naïve about (inter-) dependence. Finally, it shows how to calculate, in terms of probabilities of outcomes, the estimated spatial/spatiotemporal effects of (and response paths to) hypotheticals of substantive interest. It illustrates with an application to civil war in Sub-Saharan Africa.



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Robert J. Franzese, Jr. is a Professor of Political Science, University of Michigan, Ann Arbor, MI 48109 ( Jude C. Hays is an Associate Professor of Political Science, University of Pittsburgh, Pittsburgh, PA 15260 ( Scott J. Cook is an Assistant Professor of Political Science, Texas A&M University, College Station, TX 77840 ( Though many more provided helpful feedback at various stages of this project, we are particularly indebted to Patrick Brandt, Scott McClurg, Eric Neumayer, Thomas Plümper, Lena Schaffer, Curt Signorino, Vera Troeger and the participants of the 2013 Spatial Models of Politics conference at Texas A&M. Thanks are also in order to the reviewers and editor for their useful comments and suggestions. All remaining errors are our own. To view supplementary material for this article, please visit



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Supplementary materials

Franzese supplementary material
Web Appendices File

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Supplementary materials

Franzese supplementary material
Web Appendices File

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