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

Published online by Cambridge University Press:  07 September 2015

Robert J. Franzese Jr. ,
Jude C. Hays  and
Scott J. Cook
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Abstract

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.

Type
Original Articles
Information
Political Science Research and Methods , Volume 4 , Issue 1 , January 2016 , pp. 151 - 173
Copyright
© The European Political Science Association 2015 

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Footnotes

*

Robert J. Franzese, Jr. is a Professor of Political Science, University of Michigan, Ann Arbor, MI 48109 ([email protected]). Jude C. Hays is an Associate Professor of Political Science, University of Pittsburgh, Pittsburgh, PA 15260 ([email protected]). Scott J. Cook is an Assistant Professor of Political Science, Texas A&M University, College Station, TX 77840 ([email protected]). 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 http://dx.doi.org/10.1017/psrm.2015.14.

References

Beck, Nathaniel, Epstein, David, Jackman, Simon, and O’Halloran, Sharyn. 2001. ‘Alternative Models of Dynamics in Binary Time-Series–Cross-Section Models: The Example of State Failure’. 2001 Annual Meeting of the Society for Political Methodology, Emory University, Atlanta, GA.Google Scholar
Beck, Nathaniel, Katz, Johnathan, and Tucker, Richard. 1998. ‘Taking Time Seriously: Time-Series–Cross-Section Analysis with a Binary Dependent Variables’. American Journal of Political Science 42(4):1260–1288.Google Scholar
Beck, Nathaniel, Gleditsch, Kristian S., and Beardsley, Kyle. 2006. ‘Space is More than Geography: Using Spatial Econometrics in the Study of Political Economy’. International Studies Quarterly 50(1):27–44.Google Scholar
Beron, Kurt J., Murdoch, James C., and Vijverberg, Wim P.M.. 2003. ‘Why Cooperate? Public Goods, Economic Power, and the Montreal Protocol’. Review of Economics and Statistics 85(2):286–297.CrossRefGoogle Scholar
Beron, Kurt J., and Vijverberg, Wim P.M.. 2004. ‘Probit in a Spatial Context: A Monte Carlo Analysis’. In Luc Anselin, Raymond Florax and Sergio J. Rey (eds), Advances in Spatial Econometrics: Methodology, Tools and Applications. Berlin: Springer-Verlag, 169–196.Google Scholar
Braithwaite, Alex. 2010. ‘Resisting Infection: How State Capacity Conditions Conflict Contagion’. Journal of Peace Research 47(3):311–319.Google Scholar
Buhaug, Halvard, and Gleditsch, Kristian S.. 2008. ‘Contagion or Confusion? Why Conflicts Cluster in Space’. International Studies Quarterly 52(2):215–233.Google Scholar
Carter, David B., and Signorino, Curt S.. 2010. ‘Back to the Future: Modeling Time Dependence in Binary Data’. Political Analysis 18(3):271–292.Google Scholar
Chamberlain, Gary. 1993. ‘Feedback in Panel Data Models’. Working Paper No. 1656. Cambridge, MA: Harvard Institute of Economic Research.Google Scholar
Cook, Scott J. 2015. ‘The Echo of Conflict: Modeling the Dependence of Civil Conflict in Space and Time’. Working Paper, Texas A&M University.Google Scholar
Diehl, Paul F. 1991. ‘Geography and War: A Review and Assessment of the Empirical Literature’. International Interactions 17:11–27.Google Scholar
Fleming, Mark M. 2004. ‘Techniques for Estimating Spatially Dependent Discrete-Choice Models’. In Luc Anselin, Raymond Florax and Sergio J. Rey (eds), Advances in Spatial Econometrics: Methodology, Tools and Applications. Berlin: Springer-Verlag, 145–168.Google Scholar
Franzese, Robert J., and Hays, Jude C.. 2004. ‘Empirical Modeling Strategies for Spatial Interdependence: Omitted-Variable Vs. Simultaneity Biases’. Presented at the 2004 Summer Meeting of the Society for Political Methodology, Stanford University, Stanford, CA. Available at http://www.umich.edu/~franzese/FranzeseHays.PolMeth.2004.pdf.Google Scholar
Franzese, Robert J., and Hays, Jude C.. 2007. ‘Spatial-Econometric Models of Cross-Sectional Interdependence in Political-Science Panel & Time-Series-Cross-Section Data’. Political Analysis 15(2):140–164.Google Scholar
Franzese, Robert J., and Hays, Jude C.. 2008a. ‘Empirical Models of Spatial Interdependence’. In J. Box-Steffensmeier, H. Brady and D. Collier (eds), Oxford Handbook of Political Methodology, 570–604. Oxford: Oxford University Press.Google Scholar
Franzese, Robert J., and Hays, Jude C.. 2008b. ‘Interdependence in Comparative Politics: Substance, Theory, Empirics, Substance’. Comparative Political Studies 41(4/5):742–780.Google Scholar
Franzese, Robert J., Hays, Jude C., and Cook, Scott J.. 2012. ‘Spatial-, Temporal-, and Spatiotemporal-Autoregressive Probit Models of Interdependent Binary Outcomes: Estimation and Interpretation’. Presented at the 2012 Annual European Political Science Association, Berlin.Google Scholar
Hays, Jude C. 2009. ‘Bucking the System: Using Simulation Methods to Estimate and Analyze Systems of Equations with Qualitative and Limited Dependent Variables’. Presented at the 2009 Annual St. Louis Area Methods Meeting (SLAMM), Washington University in St. Louis.Google Scholar
Heckman, James J. 1978. ‘Dummy Endogenous Variables in a Simultaneous Equation System’. Econometrica 46:931–959.Google Scholar
Hegre, Havard, Ellingsen, Tanja, Gates, Scott, and Gleditsch, Nils Petter. 2001. ‘Towards a Democratic Civil Peace? Democracy, Political Change, and Civil War, 1816-1992’. American Political Science Review 95(1):33–48.Google Scholar
Honore, Bo E., and Kyriazidou, Ekaterini. 2000. ‘Panel Data Discrete Choice Models with Lagged Dependent Variables’. Econometrica 68(4):839–874.Google Scholar
Jackman, Simon. 2000. ‘In and Out of War and Peace: Transitional Models of International Conflict’. Working paper. Stanford, CA: Stanford University. Available at http://jackman.stanford.edu/papers/inandout.pdf.Google Scholar
Kathman, Jacob D. 2010. ‘Civil War Contagion and Neighborhood Interventions’. International Studies Quarterly 54:989–1012.Google Scholar
Klier, Thomas, and McMillen, Daniel P.. 2005. ‘Clustering of Auto Supplier Plants in the US: GMM Spatial Logit for Large Samples’. Working Paper Series No. WP-O5-18, Federal Reserve Bank of Chicago.Google Scholar
Lake, David A., and Rothchild, Donald, eds. 1998. The International Spread of Ethnic Conflict. Princeton, NJ: Princeton University Press.Google Scholar
LeSage, James P. 1999. Spatial Econometrics. http://www.rri.wvu.edu/WebBook/LeSage/spatial/wbook.pdf, accessed 22 May 2015.Google Scholar
LeSage, James P. 2000. ‘Bayesian Estimation of Limited Dependent Variable Spatial Autoregressive Models’. Geographical Analysis 32(1):19–35.Google Scholar
LeSage, James P., and Pace, Robert K.. 2009. Introduction to Spatial Econometrics. Boca Rotan, FL: CRC Press.Google Scholar
McMillen, Daniel P. 1992. ‘Probit with Spatial Autocorrelation’. Journal of Regional Science 32:335–348.Google Scholar
McMillen, Daniel P. 1995. ‘Selection Bias in Spatial Econometric Models’. Journal of Regional Science 35(3):417–436.Google Scholar
Most, Benjamin, and Starr, Harvey. 1980. ‘Diffusion, Reinforcement, and Geopolitics and the Spread of War’. The American Political Science Review 74(4):932–946.Google Scholar
Murdoch, James, and Sandler, Todd. 2002. ‘Economic Growth, Civil Wars, and Spatial Spillovers’. Journal of Conflict Resolution 46(1):91–110.Google Scholar
O’Loughlin, John, and Raleigh, Clionadh. 2008. ‘Spatial Analysis of Civil War Violence’. In Kevin R. Cox, Murray M. Low and Jennifer Robinson (eds), The Sage Handbook of Political Geography. Thousand Oaks, CA: Sage, 493–508.Google Scholar
Pinkse, Joris, and Slade, Margaret E.. 1998. ‘Contracting in Space: An Application of Spatial Statistics to Discrete-Choice Models’. Journal of Econometrics 85:125–154.Google Scholar
Raleigh, Clionadh. 2004. ‘Neighbours and Neighbourhoods: Understanding the Role of Context in Civil War’. Presented at the 5th Pan-European International Relations Conference. The Hague, The Netherlands, 9–11 September.Google Scholar
Salehyan, Idean, and Gledistch, Kristina S.. 2006. ‘Refugees and the Spread of Civil War’. International Organization 60(2):335–366.Google Scholar
Starr, Harvey, and Most, Benjamin A.. 1983. ‘Contagion and Border Effects on Contemporary African Conflict’. Comparative Political Studies 16(1):92–117.Google Scholar
Vijverberg, Wim P.M. 1997. ‘Monte Carlo Evaluation of Multivariate Normal Probabilities’. Journal of Econometrics 76:281–307.Google Scholar
Ward, Michael, and Gledistch, Kristian S.. 2002. ‘Location, Location, Location: An MCMC Approach to Modeling the Spatial Context of War and Peace’. Political Analysis 10(3):244–260.Google Scholar
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