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A Bayesian Poisson Vector Autoregression Model

Published online by Cambridge University Press:  04 January 2017

Patrick T. Brandt  and
Todd Sandler
Patrick T. Brandt*
Affiliation:
School of Economic, Political, and Policy Sciences, The University of Texas at Dallas, 800 W. Campbell Road, GR 31, Richardson, TX 75080
Todd Sandler
Affiliation:
School of Economic, Political, and Policy Sciences, The University of Texas at Dallas, 800 W. Campbell Road, GR 31, Richardson, TX 75080. email: [email protected]
*
e-mail: [email protected] (corresponding author)
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Abstract

Multivariate count models are rare in political science despite the presence of many count time series. This article develops a new Bayesian Poisson vector autoregression model that can characterize endogenous dynamic counts with no restrictions on the contemporaneous correlations. Impulse responses, decomposition of the forecast errors, and dynamic multiplier methods for the effects of exogenous covariate shocks are illustrated for the model. Two full illustrations of the model, its interpretations, and results are presented. The first example is a dynamic model that reanalyzes the patterns and predictors of superpower rivalry events. The second example applies the model to analyze the dynamics of transnational terrorist targeting decisions between 1968 and 2008. The latter example's results have direct implications for contemporary policy about terrorists' targeting that are both novel and innovative in the study of terrorism.

Type
Research Article
Information
Political Analysis , Volume 20 , Issue 3 , Summer 2012 , pp. 292 - 315
Copyright
Copyright © The Author 2012. Published by Oxford University Press on behalf of the Society for Political Methodology 

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Footnotes

Authors' note: We are grateful to Janet Box-Steffensmeier, Walter Enders, John Freeman, Jeff Gill, Sara Mitchell, Xun Pang, Vera Troeger, and three anonymous reviewers for their comments. Supplementary materials for this article are available on the Political Analysis Web site.

References

Aitchison, J., and Ho, C. H. 1989. The multivariate Poisson-log normal distribution. Biometrika 76: 643–53.CrossRefGoogle Scholar
Alexander, Y., and Pluchinsky, D. A. 1992. Europe's Red Terrorists: The Fighting Communist Organizations. London: Frank Cass.Google Scholar
Azar, S. 1982. The Codebook of the Conflict and Peace Data Bank (COPDAB). College Park, MD: Center for International Development.Google Scholar
Brandt, P. T., Colaresi, M. P., and Freeman, J. R. 2008. The dynamics of reciprocity, accountability, and credibility. Journal of Conflict Resolution 52: 343–74.Google Scholar
Brandt, P. T., and Freeman, J. R. 2006. Advances in Bayesian time-series modeling and the study of politics: Theory testing, forecasting, and policy analysis. Political Analysis 14: 1–36.Google Scholar
Brandt, P. T., and Sandler, T. 2009. Hostage taking: Understanding terrorism event dynamics. Journal of Policy Modeling 31: 758–78.Google Scholar
Brandt, P. T., and Sandler, T. 2010. What do transnational terrorists target? Has it changed? Are we safer? Journal of Conflict Resolution 54: 214–36.Google Scholar
Brandt, P. T., and Williams, J. T. 2001. A linear Poisson autoregressive model: The Poisson AR(p) model. Political Analysis 9: 164–84.Google Scholar
Brandt, P. T., and Williams, J. T. 2007. Multiple Time-series Models. Thousand Oaks, CA: Sage.Google Scholar
Brandt, P. T., Williams, J. T., Fordham, B. O., and Pollins, B. 2000. Dynamic modeling for persistent event count time series. American Journal of Political Science 44: 823–43.Google Scholar
Chen, A. H., and Siems, T. F. 2004. The effects of terrorism on global capital markets. European Journal of Political Economy 20: 249–66.CrossRefGoogle Scholar
Chib, S., and Winkelmann, R. 2001. Markov chain Monte Carlo analysis of correlated count data. Journal of Business & Economic Statistics 19: 428–35.Google Scholar
Congdon, P. 2005. Bayesian Models for Categorical Data. Chichester, UK: John Wiley & Sons.Google Scholar
Congdon, P. 2007. Bayesian modeling strategies for spatially varying regression coefficients: A multivariate perspective for multiple outcomes. Computational Statistics & Data Analysis 51: 2586–601.CrossRefGoogle Scholar
Deb, P., and Trivedi, P. K. 1997. Demand for medical care by the elderly: A finite mixture approach. Journal of Applied Econometrics 12: 313–36.Google Scholar
El-Basyouny, K., and Sayed, T. 2009. Collision prediction models using multivariate Poisson-lognormal regression. Accident Analysis and Prevention 41: 820–28.Google Scholar
Enders, W., and Sandler, T. 1993. The effectiveness of anti-terrorism policies: A vector-autoregression-intervention analysis. American Political Science Review 87: 829–44.Google Scholar
Enders, W., and Sandler, T. 2005. After 9/11: Is it all different now? Journal of Conflict Resolution 49: 259–77.Google Scholar
Enders, W., and Sandler, T. 2006a. Distribution of transnational terrorism among countries by income classes and geography after 9/11. International Studies Quarterly 50: 367–93.Google Scholar
Enders, W., and Sandler, T. 2006b. The Political Economy of Terrorism. Cambridge: Cambridge University Press.Google Scholar
Grunwald, G. K., Hyndman, R. J., Tedesco, L., and Tweedie, R. L. 2000. Non-Gaussian conditional linear AR(1) models. Australian and New Zealand Journal of Statistics 42: 479–95.CrossRefGoogle Scholar
Hamilton, J. 1994. Time-series Analysis. Princeton, NJ: Princeton University Press.Google Scholar
Hanson, M. A., and Schmidt, M. B. 2011. The impact of coalition offensive operations on the Iraqi insurgency. Applied Economics 43: 2251–65.Google Scholar
Heinen, A., and Rengifo, E. 2007. Multivariate autoregressive modeling of time-series count data using copulas. Journal of Empirical Finance 14: 564–83.Google Scholar
Hoffman, B. 2006. Inside Terrorism: Revised and Expanded. New York: Columbia University Press.Google Scholar
Karlis, D., and Meligkotsidou, L. 2005. Multivariate Poisson regression with covariance structure. Statistics and Computing 15: 255–65.CrossRefGoogle Scholar
King, G. 1988. Statistical models for political science event counts: Bias in conventional procedures and evidence for the exponential Poisson regression model. American Journal of Political Science 32: 838–63.Google Scholar
King, G. 1989a. A seemingly unrelated Poisson regression model. Sociological Methods & Research 17: 235–55.Google Scholar
King, G. 1989b. Unifying Political Methodology: The Likelihood Theory of Statistical Inference. Princeton, NJ: Princeton University.Google Scholar
Lütkepohl, H. 2005. New Introduction to Multiple Time-series Analysis. Berlin: Springer.Google Scholar
Ma, J. 2006. Bayesian Multivariate Poisson-Lognormal Regression for crash prediction on rural two-lane highways. PhD diss., University of Texas, Austin, TX.Google Scholar
McGinnis, M. D., and Williams, J. T. 1989. Change and stability in superpower rivalry. American Political Science Review 83: 1101–23.Google Scholar
Mickolus, E. F., Sandler, T., Murdock, J. M., and Flemming, P. 2009. International Terrorism: Attributes of Terrorist Events, 1968-2008 (ITERATE). Dunn Loring, VA: Vinyard Software.Google Scholar
Munkin, M. K., and Trivedi, P. K. 1999. Simulated maximum likelihood estimation of multivariate mixed-Poisson regression models, with applications. Econometrics Journal 2: 29–48.Google Scholar
Ord, K., Fernandes, C., and Harvey, A. C. 1993. Time-series models for multivariate series of count data. In Developments in time-series analysis in honor of Maurice B. Priestley, ed. Rao, T. S., 295–309. London: Chapman & Hall.Google Scholar
Park, J. H. 2010. Structural changes in the U.S. president's uses of force abroad. American Journal of Political Science 54: 766–82.Google Scholar
Plummer, M. 2008. Penalized loss functions for Bayesian model comparison. Biostatistics 9: 523.Google Scholar
Sims, C. A., Waggoner, D. F., and Zha, T. A. 2008. Methods for inference in large multiple-equation Markov-switching models. Journal of Econometrics 146: 255–74.Google Scholar
Sims, C. A., and Zha, T. A. 1998. Bayesian methods for dynamic multivariate models. International Economic Review 39: 949–68.Google Scholar
Sims, C. A., and Zha, T. A. 1999. Error bands for impulse responses. Econometrica 67: 1113–56.Google Scholar
Spiegelhalter, D., Best, N., Carlin, B., and Van Der Linde, A. 2002. Bayesian measures of model complexity and fit (with discussion). Journal of the Royal Statistical Society: Series B (Statistical Methodology) 64: 583–639.Google Scholar
Williams, J. T., and McGinnis, M. D. 1988. Sophisticated reaction in the U.S.-Soviet arms race: Evidence of rational expectations. American Journal of Political Science 32: 968–95.Google Scholar
Williams, J. T., and McGinnis, M. D. 1992. The dimension of superpower rivalry: A dynamic factor analysis. Journal of Conflict Resolution 36: 86–118.Google Scholar