Skip to main content Accessibility help
×
Home

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

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

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.

Copyright

Footnotes

Hide All
*

Robert J. Franzese, Jr. is a Professor of Political Science, University of Michigan, Ann Arbor, MI 48109 (franzese@umich.edu). Jude C. Hays is an Associate Professor of Political Science, University of Pittsburgh, Pittsburgh, PA 15260 (jch61@pitt.edu). Scott J. Cook is an Assistant Professor of Political Science, Texas A&M University, College Station, TX 77840 (sjcook@tamu.edu). 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.

Footnotes

References

Hide All
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.
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):12601288.
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):2744.
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):286297.
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, 169196.
Braithwaite, Alex. 2010. ‘Resisting Infection: How State Capacity Conditions Conflict Contagion’. Journal of Peace Research 47(3):311319.
Buhaug, Halvard, and Gleditsch, Kristian S.. 2008. ‘Contagion or Confusion? Why Conflicts Cluster in Space’. International Studies Quarterly 52(2):215233.
Carter, David B., and Signorino, Curt S.. 2010. ‘Back to the Future: Modeling Time Dependence in Binary Data’. Political Analysis 18(3):271292.
Chamberlain, Gary. 1993. ‘Feedback in Panel Data Models’. Working Paper No. 1656. Cambridge, MA: Harvard Institute of Economic Research.
Cook, Scott J. 2015. ‘The Echo of Conflict: Modeling the Dependence of Civil Conflict in Space and Time’. Working Paper, Texas A&M University.
Diehl, Paul F. 1991. ‘Geography and War: A Review and Assessment of the Empirical Literature’. International Interactions 17:1127.
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, 145168.
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.
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):140164.
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, 570604. Oxford: Oxford University Press.
Franzese, Robert J., and Hays, Jude C.. 2008b. ‘Interdependence in Comparative Politics: Substance, Theory, Empirics, Substance’. Comparative Political Studies 41(4/5):742780.
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.
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.
Heckman, James J. 1978. ‘Dummy Endogenous Variables in a Simultaneous Equation System’. Econometrica 46:931959.
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):3348.
Honore, Bo E., and Kyriazidou, Ekaterini. 2000. ‘Panel Data Discrete Choice Models with Lagged Dependent Variables’. Econometrica 68(4):839874.
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.
Kathman, Jacob D. 2010. ‘Civil War Contagion and Neighborhood Interventions’. International Studies Quarterly 54:9891012.
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.
Lake, David A., and Rothchild, Donald, eds. 1998. The International Spread of Ethnic Conflict. Princeton, NJ: Princeton University Press.
LeSage, James P. 1999. Spatial Econometrics. http://www.rri.wvu.edu/WebBook/LeSage/spatial/wbook.pdf, accessed 22 May 2015.
LeSage, James P. 2000. ‘Bayesian Estimation of Limited Dependent Variable Spatial Autoregressive Models’. Geographical Analysis 32(1):1935.
LeSage, James P., and Pace, Robert K.. 2009. Introduction to Spatial Econometrics. Boca Rotan, FL: CRC Press.
McMillen, Daniel P. 1992. ‘Probit with Spatial Autocorrelation’. Journal of Regional Science 32:335348.
McMillen, Daniel P. 1995. ‘Selection Bias in Spatial Econometric Models’. Journal of Regional Science 35(3):417436.
Most, Benjamin, and Starr, Harvey. 1980. ‘Diffusion, Reinforcement, and Geopolitics and the Spread of War’. The American Political Science Review 74(4):932946.
Murdoch, James, and Sandler, Todd. 2002. ‘Economic Growth, Civil Wars, and Spatial Spillovers’. Journal of Conflict Resolution 46(1):91110.
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, 493508.
Pinkse, Joris, and Slade, Margaret E.. 1998. ‘Contracting in Space: An Application of Spatial Statistics to Discrete-Choice Models’. Journal of Econometrics 85:125154.
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.
Salehyan, Idean, and Gledistch, Kristina S.. 2006. ‘Refugees and the Spread of Civil War’. International Organization 60(2):335366.
Starr, Harvey, and Most, Benjamin A.. 1983. ‘Contagion and Border Effects on Contemporary African Conflict’. Comparative Political Studies 16(1):92117.
Vijverberg, Wim P.M. 1997. ‘Monte Carlo Evaluation of Multivariate Normal Probabilities’. Journal of Econometrics 76:281307.
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):244260.
Type Description Title
WORD
Supplementary materials

Franzese supplementary material
Web Appendices File

 Word (413 KB)
413 KB
PDF
Supplementary materials

Franzese supplementary material
Web Appendices File

 PDF (844 KB)
844 KB

Metrics

Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed