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Separable and semiparametric network-based counting processes applied to the international combat aircraft trades

Published online by Cambridge University Press:  20 September 2021

Cornelius Fritz Open the ORCID record for Cornelius Fritz [Opens in a new window] ,
Paul W. Thurner  and
Göran Kauermann
Cornelius Fritz*
Affiliation:
Department of Statistics, LMU Munich, Munich, Germany (e-mail: goeran.kauermann@stat.uni-muenchen.de)
Paul W. Thurner
Affiliation:
Geschwister Scholl Institute of Political Science, LMU Munich, Munich, Germany (e-mail: paul.thurner@gsi.uni-muenchen.de)
Göran Kauermann
Affiliation:
Department of Statistics, LMU Munich, Munich, Germany (e-mail: goeran.kauermann@stat.uni-muenchen.de)
*
*Corresponding author. Email: cornelius.fritz@stat.uni-muenchen.de
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Abstract

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We propose a novel tie-oriented model for longitudinal event network data. The generating mechanism is assumed to be a multivariate Poisson process that governs the onset and repetition of yearly observed events with two separate intensity functions. We apply the model to a network obtained from the yearly dyadic number of international deliveries of combat aircraft trades between 1950 and 2017. Based on the trade gravity approach, we identify economic and political factors impeding or promoting the number of transfers. Extensive dynamics as well as country heterogeneities require the specification of semiparametric time-varying effects as well as random effects. Our findings reveal strong heterogeneous as well as time-varying effects of endogenous and exogenous covariates on the onset and repetition of aircraft trade events.

Keywords

arms trade networkcombat aircraftlongitudinal network analysisrelational event model
Type
Research Article
Information
Network Science , Volume 9 , Issue 3 , September 2021 , pp. 291 - 311
Creative Commons
Creative Common License - CCCreative Common License - BYCreative Common License - NCCreative Common License - ND
This is an Open Access article, distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives licence (http://creativecommons.org/licenses/by-nc-nd/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is unaltered and is properly cited. The written permission of Cambridge University Press must be obtained for commercial re-use or in order to create a derivative work.
Copyright
© The Author(s), 2021. Published by Cambridge University Press

Footnotes

Action Editor: Stanley Wasserman

References

Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19(6), 716–723.CrossRefGoogle Scholar
Akerman, A., & Seim, A. L. (2014). The global arms trade network 1950–2007. Journal of Comparative Economics, 42(3), 535–551.CrossRefGoogle Scholar
Almquist, Z. W., & Butts, C. T. (2014). Logistic network regression for scalable analysis of networks with joint edge/vertex dynamics. Sociological Methodology, 44(1), 273–321.CrossRefGoogle ScholarPubMed
Bastian, M., Heymann, S., & Jacomy, M. (2009). Gephi: An open source software for exploring and manipulating networks. In Third international AAAI conference on weblogs and social media.Google Scholar
Bauer, V., Harhoff, D., & Kauermann, G. (2021). A smooth dynamic network model for patent collaboration data. In AStA advances in statistical analysis.CrossRefGoogle Scholar
Boschee, E., Lautenschlager, J., O’Brien, S., Shellman, S., & Starz, J. (2018). ICEWS automated daily event data. Retrieved from https://doi.org/10.7910/DVN/QI2T9A (visited 2019-09-23).CrossRefGoogle Scholar
Box-Steffensmeier, J. M., Christenson, D. P., & Morgan, J. W. (2018). Modeling unobserved heterogeneity in social networks with the frailty exponential random graph model. Political Analysis, 26(1), 3–19.CrossRefGoogle Scholar
Breslow, N. E., & Clayton, D. G. (1993). Approximate inference in generalized linear mixed models. Journal of the American Statistical Association, 88(421), 9–25.Google Scholar
Butts, C. T. (2008). A relational event framework for social action. Sociological Methodology, 38(1), 155–200.CrossRefGoogle Scholar
Butts, C. T., & Marcum, C. S. (2017). A relational event approach to modeling behavioral dynamics. In Pilny, A., & Poole, M. S. (Eds.), Group processes (pp. 51–92). Cham: Springer.CrossRefGoogle Scholar
Cranmer, S. J., Desmarais, B. A., & Menninga, E. J. (2012). Complex dependencies in the alliance network. Conflict Management and Peace Science, 29(3), 279–313.CrossRefGoogle Scholar
Csardi, G., & Nepusz, T. (2006). The igraph software package for complex network research. InterJournal, Complex Systems, 1695(5), 1–9.Google Scholar
Davis, J. A. (1970). Clustering and hierarchy in interpersonal relations: Testing two graph theoretical models on 742 sociomatrices. American Sociological Review, 35(5), 843–851.CrossRefGoogle Scholar
de Boor, C. (2001). A practical guide to splines. New York: Springer.Google Scholar
Desmarais, B. A., & Cranmer, S. J. (2012). Statistical inference for valued-edge networks: The generalized exponential random graph model. PLoS ONE, 7(1), 1–12.CrossRefGoogle ScholarPubMed
Eilers, P. H. C., & Marx, B. D. (1996). Flexible smoothing with B-splines and penalties. Statistical Science, 11(2), 89–102.CrossRefGoogle Scholar
Forsberg, R. (1994). The arms production dilemma: Contraction and restraint in the world combat aircraft industry. Cambridge: MIT Press.Google Scholar
Forsberg, R. (1997). The contraction of the world military aircraft industry. In M. Kaldor, B. Vashee, & G. Scheder (Eds.), The end of military for dism: Restructuring the global military sector. London: Bloomsbury.Google Scholar
Friedman, M. (1982). Piecewise exponential models for survival data with covariates. Annals of Statistics, 10(1), 101–113.CrossRefGoogle Scholar
Fritz, C., Lebacher, M., & Kauermann, G. (2020). Tempus volat, hora fugit: A survey of tie-oriented dynamic network models in discrete and continuous time. Statistica Neerlandica, 74(3), 275–299.CrossRefGoogle Scholar
Gjessing, H. K., Røysland, K., Pena, E. A., & Aalen, O. O. (2010). Recurrent events and the exploding Cox model. Lifetime Data Analysis, 16(4), 525–546.CrossRefGoogle ScholarPubMed
Goldenberg, A., Zheng, A. X., Fienberg, S. E., & Airoldi, E. M. (2010). A survey of statistical network models. Foundations and Trends in Machine Learning, 2(2), 129–233.CrossRefGoogle Scholar
Greven, S., & Kneib, T. (2010). On the behaviour of marginal and conditional AIC in linear mixed models. Biometrika, 97(4), 773–789.CrossRefGoogle Scholar
Hanneke, S., Fu, W., & Xing, E. P. (2010). Discrete temporal models of social networks. Electronic Journal of Statistics, 4, 585–605.CrossRefGoogle Scholar
Hoeffler, C., & Mérand, F. (2016). Buying a fighter jet: European lessons for Canada. Canadian Foreign Policy Journal, 22(3), 262–275.CrossRefGoogle Scholar
Hoffman, M., Block, P., Elmer, T., & Stadtfeld, C. (2020). A model for the dynamics of face-to-face interactions in social groups. Network Science, 8(S1), 1–22.CrossRefGoogle Scholar
Holland, P., & Leinhardt, S. (1971). Transitivity in structural models of small groups. Comparative Group Studies, 2(2), 107–124.CrossRefGoogle Scholar
Holland, P., & Leinhardt, S. (1977). A dynamic model for social networks. The Journal of Mathematical Sociology, 5(1), 5–20.CrossRefGoogle Scholar
Hunter, D. R., Goodreau, S. M., & Handcock, M. S. (2008). Goodness of fit of social network models. Journal of the American Statistical Association, 103(481), 248–258.CrossRefGoogle Scholar
Kalbfleisch, J. D., & Prentice, R. L. (2002). The statistical analysis of failure time data. Hoboken: Wiley.CrossRefGoogle Scholar
Kauermann, G., Krivobokova, T., & Fahrmeir, L. (2009). Some asymptotic results on generalized penalized spline smoothing. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 71(2), 487–503.CrossRefGoogle Scholar
Kauermann, G., & Opsomer, J. D. (2011). Data-driven selection of the spline dimension in penalized spline regression. Biometrika, 98(1), 225–230.CrossRefGoogle Scholar
Kim, B., Lee, K. H., Xue, L., & Niu, X. (2018). A review of dynamic network models with latent variables. Statistics Surveys, 12, 105–135.CrossRefGoogle ScholarPubMed
Kleiber, C., & Zeileis, A. (2016). Visualizing count data regressions using rootograms. The American Statistician, 70(3), 296–303.CrossRefGoogle Scholar
Kleinberg, J. M. (1999). Authoritative sources in a hyperlinked environment. Journal of the ACM, 46(5), 604–632.CrossRefGoogle Scholar
Kolaczyk, E. D. (2009). Statistical analysis of network data. Methods and models. New York: Springer.CrossRefGoogle Scholar
Kolaczyk, E. D. (2017). Topics at the frontier of statistics and network analysis: (Re)visiting the foundations. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Kreiß, A., Mammen, E., & Polonik, W. (2019). Nonparametric inference for continuous-time event counting and link-based dynamic network models. Electronic Journal of Statistics, 13(2), 2764–2829.CrossRefGoogle Scholar
Krivitsky, P. N. (2012). Exponential-family random graph models for valued networks. Electronic Journal of Statistics, 6, 1100–1128.CrossRefGoogle Scholar
Krivitsky, P. N, & Handcock, M. S. (2014). A separable model for dynamic networks. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 76(1), 29–46.CrossRefGoogle ScholarPubMed
Krivitsky, P. N., Handcock, M. S., Raftery, A. E., & Hoff, P. D. (2009). Representing degree distributions, clustering, and homophily in social networks with latent cluster random effects models. Social Networks, 31(3), 204–213.CrossRefGoogle ScholarPubMed
Lazer, D., Pentland, A., Adamic, L., Aral, S., Barabási, A. L., Brewer, D., … Van Alstyne, M. (2009). Computational social science. Science, 323(5915), 721–723.CrossRefGoogle ScholarPubMed
Lebacher, M., Thurner, P. W., & Kauermann, G. (2020). Exploring dependence structures in the international arms trade network: A network autocorrelation approach. Statistical Modelling, 20(2), 195–218.CrossRefGoogle Scholar
Lebacher, M., Thurner, P. W., & Kauermann, G. (2021). A dynamic separable network model with actor heterogeneity: An application to global weapons transfers. Journal of Royal Statistical Society: Series A (Statistics in Society). Google Scholar
Leeds, B. A. (2019). Alliance treaty obligations and provisions (ATOP 4.01). Retrieved from http://www.atopdata.org/ (visited 2019-09-30).Google Scholar
Levine, P., Sen, S., & Smith, R. (1994). A model of the international arms market. Defence and Peace Economics, 5(1), 1–18.CrossRefGoogle Scholar
Li, Z., & Wood, S. N. (2020). Faster model matrix crossproducts for large generalized linear models with discretized covariates. Statistics and Computing, 30, 19–25.CrossRefGoogle Scholar
Lusher, D., Koskinen, J., & Robins, G. (2012). Exponential random graph models for social networks. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Marshall, M. G. (2017). Polity IV project: Political regime characteristics and transitions, 1800-2016. Retrieved from http://www.systemicpeace.org/inscrdata.html (visited 2019-09-16).Google Scholar
Martínez-Zarzoso, I., & Johannsen, F. (2019). The gravity of arms. Defence and Peace Economics, 30(1), 2–26.CrossRefGoogle Scholar
McFadden, D. (1973). Conditional logit analysis of qualitative choice behavior. In Zarembka, P. (Ed.), Frontiers in econometrics (pp. 105–142). New York: Academic Press.Google Scholar
Mehrl, M., & Thurner, P. W. (2020). Military technology and human loss in intrastate conflict: The conditional impact of arms imports. Journal of Conflict Resolution, 64(6), 1172–1196.CrossRefGoogle Scholar
Newman, M. E. J., Watts, D. J., & Strogatz, S. H. (2002). Random graph models of social networks. Proceedings of the National Academy of Sciences, 99(S1), 2566–2572.CrossRefGoogle Scholar
Nordhaus, W., Oneal, J. R., & Russett, B. (2012). The effects of the international security environment on national military expenditures: A multicountry study. International Organization, 66(3), 491–513.CrossRefGoogle Scholar
Opsahl, T., Agneessens, F., & Skvoretz, J. (2010). Node centrality in weighted networks: Generalizing degree and shortest paths. Social Networks, 32(3), 245–251.CrossRefGoogle Scholar
Opsahl, T., & Panzarasa, P. (2009). Clustering in weighted networks. Social Networks, 31(2), 155–163.CrossRefGoogle Scholar
Pamp, O., Dendorfer, F., & Thurner, P. W. (2018). Arm your friends and save on defense? The impact of arms exports on military expenditures. Public Choice, 177, 165–187.CrossRefGoogle Scholar
Robins, G., & Pattison, P. (2001). Random graph models for temporal processes in social networks. Journal of Mathematical Sociology, 25(1), 5–41.CrossRefGoogle Scholar
Robins, G., Pattison, P., & Wasserman, S. (1999). Logit models and logistic regressions for social networks: III. Valued relations. Psychometrika, 64(3), 371–394.CrossRefGoogle Scholar
Ruppert, D., Wand, M., & Carroll, R. J. (2003). Semiparametric regression. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Ruppert, D., Wand, M., & Carroll, R. J. (2009). Semiparametric regression during 2003–2007. Electronic Journal of Statistics, 3(3), 1193–1256.CrossRefGoogle ScholarPubMed
Saefken, B., Kneib, T., van Waveren, C.-S., & Greven, S. (2014). A unifying approach to the estimation of the conditional Akaike information in generalized linear mixed models. Electronic Journal of Statistics, 8(1), 201–225.CrossRefGoogle Scholar
Singer, J. D., Bremer, S., & Stuckey, J. (1972). Capability distribution, uncertainty, and major power war, 1820–1965. In B. Russett (Ed.), Peace, war, and numbers (pp. 19–48), vol. 19. Sage.Google Scholar
SIPRI. (2019). Military expenditure database. Retrieved from https://www.sipri.org/databases/milex (visited 2020-09-03).Google Scholar
SIPRI. (2020a). Arms transfers database. Retrieved from https://www.sipri.org/databases/armstransfers (visited 2020-03-09).Google Scholar
SIPRI. (2020b). Arms transfers database: Sources and methods. Retrieved from https://www.sipri.org/databases/ armstransfers/sources-and-methods (visited 2020-03-09).Google Scholar
Snijders, T. A. B. (1996). Stochastic actor-oriented models for network change. Journal of Mathematical Sociology, 21, 149–172.CrossRefGoogle Scholar
Snijders, T. A. B. (2003). Accounting for degree distribution in empirical analysis of network dynamics. In Dynamic social network modeling and analysis: Workshop summary and papers (pp. 146–161). The National Academies Press.Google Scholar
Snijders, T. A. B. (2017). Comment: Modeling of coordination, rate functions, and missing ordering information. Sociological Methodology, 47(1), 41–47.CrossRefGoogle Scholar
Snijders, T. A. B., & van Duijn, M. (1997). Simulation for statistical inference in dynamic network models. In Conte, R., Hegselmann, R., & Terna, P. (Eds.), Simulating social phenomena. Cham: Springer.Google Scholar
Stadtfeld, C. (2012 ). Events in social networks: A stochastic actor-oriented framework for dynamic event processes in social networks. Ph.D. thesis, KIT.Google Scholar
Stadtfeld, C., Hollway, J., & Block, P. (2017). Dynamic network actor models: Investigating coordination ties through time. Sociological Methodology, 47(1), 1–40.CrossRefGoogle Scholar
Thiemichen, S., Friel, N., Caimo, A., & Kauermann, G. (2016). Bayesian exponential random graph models with nodal random effects. Social Networks, 46, 11–28.CrossRefGoogle Scholar
Thurner, P. W., Schmid, C. S., Cranmer, S. J., & Kauermann, G. (2019). Network interdependencies and the evolution of the international arms trade. Journal of Conflict Resolution, 63(7), 1736–1764.CrossRefGoogle Scholar
Tukey, J. W. (1977). Exploratory data analysis. London: Pearson.Google Scholar
Tutz, G., & Schmid, M. (2016). Modeling discrete time-to-event data. Cham: Springer.CrossRefGoogle Scholar
Vu, D., Hunter, D., Smyth, P., & Asuncion, A. (2011). Continuous-time regression models for longitudinal networks. In J. Shawe-Taylor, R. Zemel, P. Bartlett, F. Pereira, & K. Q. Weinberger (Eds.), Advances in neural information processing systems, vol. 24.Google Scholar
Vucetic, S. (2011). Canada and the F-35: What’s at stake? Canadian Foreign Policy Journal, 17(3), 196–203.CrossRefGoogle Scholar
Vucetic, S., & Nossal, K. R. (2012). The international politics of the F-35 Joint Strike Fighter. International Journal, 68(1), 3–12.CrossRefGoogle Scholar
Wasserman, S., & Faust, K. (1994). Social network analysis: methods and applications. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Whitehead, J. (1980). Fitting cox’s regression model to survival data using glim. Journal of the Royal Statistical Society: Series C (Applied Statistics), 29(3), 268.Google Scholar
Wood, S. N. (2006). On confidence intervals for generalized additive models based on penalized regression splines. Australian and New Zealand Journal of Statistics, 48(4), 445–464.CrossRefGoogle Scholar
Wood, S. N. (2017). Generalized additive models: An introduction with R. Boca Raton: CRC press.CrossRefGoogle Scholar
Wood, S. N., Li, Z., Shaddick, G., & Augustin, N. H. (2017). Generalized additive models for gigadata: Modeling the U.K. black smoke network daily data. Journal of the American Statistical Association, 112(519), 1199–1210.CrossRefGoogle Scholar
Wood, S. N., Pya, N., & Säfken, B. (2016). Smoothing parameter and model selection for general smooth models. Journal of the American Statistical Association, 111(516), 1548–1563.CrossRefGoogle Scholar
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