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Location, Location, Location: An MCMC Approach to Modeling the Spatial Context of War and Peace

  • Michael D. Ward (a1) and Kristian Skrede Gleditsch (a2)

Abstract

This article demonstrates how spatially dependent data with a categorical response variable can be addressed in a statistical model. We introduce the idea of an autologistic model where the response for one observation is dependent on the value of the response among adjacent observations. The autologistic model has likelihood function that is mathematically intractable, since the observations are conditionally dependent upon one another. We review alternative techniques for estimating this model, with special emphasis on recent advances using Markov chain Monte Carlo (MCMC) techniques. We evaluate a highly simplified autologistic model of conflict where the likelihood of war involvement for each nation is conditional on the war involvement of proximate states. We estimate this autologistic model for a single year (1988) via maximum pseudolikelihood and MCMC maximum likelihood methods. Our results indicate that the autologistic model fits the data much better than an unconditional model and that the MCMC estimates generally dominate the pseudolikelihood estimates. The autologistic model generates predicted probabilities greater than 0.5 and has relatively good predictive abilities in an out-of-sample forecast for the subsequent decade (1989 to 1998), correctly identifying not only ongoing conflicts, but also new ones.

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Anselin, Luc. 1988. Spatial Econometrics: Methods and Models. Dordrecht, The Netherlands: Kluwer.
Babst, Dean. 1964. “Electoral Governments: A Force for Peace.” Wisconsin Sociologist 1:914.
Beck, Neal, King, Gary, and Zeng, Langche. 2000. “The Problem with Quantitative Studies of Conflict: A Conjecture.” American Political Science Review 94:2136.
Besag, Julian E. 1972. “Nearest-Neighbour Systems: A Lemma with Application to Bartlett's Global Solutions.” Journal of Applied Probability 9:418.
Besag, Julian E. 1974. “Spatial Interaction and the Statistical Analysis of Lattice Systems (with Discussion).” Journal of the Royal Statistical Society, Series B, Methodological 36:192225.
Besag, Julian E. 1975. “Statistical Analysis of Non-lattice Data.” Statistician 24:179.
Besag, Julian E. 1977. “Efficiency of Pseudolikelihood Estimation for Simple Gaussian Fields.” Biometrika 64:616.
Besag, Julian E., and Moran, Patrick A. P. 1975. “On the Estimation and Testing of Spatial Interaction in Gaussian Lattice Processes.” Biometrika 62:555.
Easterly, William, and Levine, Ross. 1999. “Troubles with the Neighbours: Africa's Problem, Africa's Opportunity.” Journal of African Economies 7:120142.
Gelman, Andrew, Carlin, John B., Stern, Hal S., and Rubin, David B. 1995. Bayesian Data Analysis. London: Chapman & Hall.
Geman, Stuart, and Geman, Donald. 1984. “Stochastic Relaxation, Gibbs Distributions and the Bayesian Restoration of Images.” IEEE Transactions on Pattern Analysis and Machine Intelligence 6:721741.
Geyer, Charles J., and Thompson, Elizabeth A. 1992. “Constrained Monte Carlo Maximum Likelihood for Dependent Data (with Discussion).” Journal of the Royal Statistical Society, Series B, Methodological 54:657699.
Gleditsch, Kristian S. 2002. All International Politics Is Local: The Diffusion of Conflict, Integration, and Democratization. Ann Arbor: University of Michigan Press.
Gleditsch, Kristian S., and Ward, Michael D. 2000. “War and Peace in Space and Time: The Role of Democratization.” International Studies Quarterly 44:129.
Gleditsch, Kristian S., and Ward, Michael D. 2001. “Measuring Space: A Minimum Distance Database and Applications to International Studies.” Journal of Peace Research 38:749768.
Gotway, Carol, and Stroup, Walter. 1997. “A Generalized Linear Model Approach to Spatial Data Analysis and Prediction.” Journal of Agricultural, Biological, and Environmental Statistics 2:157178.
Gumpertz, Marcia L., Graham, Jonathan M., and Ristaino, Jean B. 1997. “Autologistic Model of Spatial Pattern of Phytophthora Epidemic in Bell Pepper: Effects of Soil Variables on Disease Presence.” Journal of Agricultural, Biological, and Environmental Statistics 2:131156.
Gumpertz, Marcia L., Wu, Chi-tsung, and Pye, John M. 1999. “Logistic Regression for Southern Pine Beetle Outbreaks with Spatial and Temporal Autocorrelation.” Technical Report 2513. Raleigh: Institute of Statistics, North Carolina State University.
Gurr Ted, Robert, and Moore, Will H. 1997. “Ethnopolitical Rebellion: A Cross-Sectional Analysis of the 1980s with Risk Assessments for the 1990s.” American Journal of Political Science 41:10791103.
Harary, Frank, Norman, Robert Z., and Cartright, Dorwin. 1965. Structural Models: An Introduction to the Theory of Directed Graphs. New York: Wiley.
Hegre, Håvard, Ellingsen, Scott Gates, Tanja, and Petter Gleditsch, Nils. 2001. “Toward a Democratic Civil Peace? Democracy, Political Change, and Civil War, 1816-1992.” American Political Science Review 95:3348.
Hoeting, Jennifer A., Leecaster, Molly, and Bowden, David. 2000. “An Improved Model for Spatially Correlated Binary Responses.” Journal of Agricultural, Biological and Environmental Statistics 5:102114.
Huffer, Fred W., and Wu, Hulin. 1998. “Markov Chain Monte Carlo for Autologistic Regression Models with Application to the Distribution of Plant Species.” Biometrics 54:509524.
Jackman, Simon. 2000. “Estimation and Inference Via Bayesian Simulation: An Introduction to Markov Chain Monte Carlo.” American Journal of Political Science 44:369398.
King, Gary, and Zeng, Langche. 2001. “Improving Forecasts of State Failure.” World Politics 53:623658.
Lopez-Vazo, Enrique, Vayá, Ester, Mora, Antonio J., and Suriñach, Jordi. 1999. “Regional Economic Dynamics and Convergence in the European Union.” Annals of Regional Science 33:343370.
Most, Benjamin A., and Starr, Harvey. 1989. Inquiry, Logic, and International Politics. Columbia: University of South Carolina Press.
Murdoch, James C., Sandler, Todd, and Sargent, Keith. 1997. “A Tale of Two Collectives: Sulfur versus Nitrogen Oxides Emission Reduction in Europe.” Economica 64:281301.
O'Loughlin, John, Ward, Michael D., Lofdahl, Corey L., Cohen, Jordin S., Brown, David S., Reilly, David, Gleditsch, Kristian S., and Shin, Michael. 1998. “The Diffusion of Democracy, 1946-1994.” Annals of the Association of American Geographers 88:545574.
Ripley, Brian D. 1988. Statistical Inference for Spatial Processes. Cambridge: Cambridge University Press.
Rummel, Rudolph J. 1983. “Libertarianism and International Violence.” Journal of Conflict Resolution 27:2771.
Rummel, Rudolph J. 1984. “Libertarianism, Violence within States, and the Polarity Principle.” Comparative Politics 16:443463.
Rummel, Rudolph J. 1985. “Libertarian Propositions on Violence within and between Nations.” Journal of Conflict Resolution 29:419455.
Schrodt, Philip A. 2000. “Forecasting Conflict in the Balkans Using Hidden Markov Models.” Presented at the Annual Meetings of the American Political Science Association, Washington, DC.
Schrodt, Philip A., and Mintz, Alex. 1988. “A Conditional Probability Analysis of Regional Interactions in the Middle East.” American Journal of Political Science 32:217230.
Shin, Michael E., and Ward, Michael D. 1999. “Lost in Space: Political Geography and the Defense-Growth Trade-off.” Journal of Conflict Resolution 43:793816.
Signorino, Curtis. 1999. “Strategic Interaction and the Statistical Analysis of International Conflict.” American Political Science Review 92:279298.
Singer, J. David, and Small, Melvin. 1994. Correlates of War Project: International and Civil War Data, 1816-1992 (ICPSR 9905). Ann Arbor, MI: Interuniversity Consortium for Political and Social Research.
Strauss, Davis, and Ikeda, Michael. 1990. “Pseudolikelihood Estimation for Social Networks.” Journal of the American Statistical Association 85:204212.
Wallensteen, Peter, and Sollenberg, Margareta. 1999. “Armed Conflict, 1989-98.” Journal of Peace Research 36:593606.
Ward, Michael D. 1988. “Cargo Cult Social Science and Eight Fallacies of Comparative Political Research.” International Studies Notes 13:7577.
Ward, Michael D., and Gleditsch, Kristian S. 1998. “Democratizing for Peace.” American Political Science Review 92:5161.
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