Disaster response on September 11, 2001 through the lens of statistical network analysis

The rescue and relief operations triggered by the September 11, 2001 attacks on the World Trade Center in New York City demanded collaboration among hundreds of organisations. To shed light on the response to the September 11, 2001 attacks and help to plan and prepare the response to future disasters, we study the inter-organisational network that emerged in response to the attacks. Studying the inter-organisational network can help to shed light on (1) whether some organisations dominated the inter-organisational network and facilitated communication and coordination of the disaster response; (2) whether the dominating organisations were supposed to coordinate disaster response or emerged as coordinators in the wake of the disaster; and (3) the degree of network redundancy and sensitivity of the inter-organisational network to disturbances following the initial disaster. We introduce a Bayesian framework which can answer the substantive questions of interest while being as simple and parsimonious as possible. The framework allows organisations to have varying propensities to collaborate, while taking covariates into account, and allows to assess whether the inter-organisational network had network redundancy-in the form of transitivity-by using a test which may be regarded as a Bayesian score test. We discuss implications in terms of disaster management.

[1]  Michael I. Jordan,et al.  Variational inference for Dirichlet process mixtures , 2006 .

[2]  Tom A. B. Snijders,et al.  Manual for BLOCKS version 1 . 8 , 2004 .

[3]  P. Pattison,et al.  New Specifications for Exponential Random Graph Models , 2006 .

[4]  Edoardo M. Airoldi,et al.  Mixed Membership Stochastic Blockmodels , 2007, NIPS.

[5]  O. Barndorff-Nielsen.  Information and Exponential Families in Statistical Theory , 1980 .

[6]  P. Green,et al.  On Bayesian Analysis of Mixtures with an Unknown Number of Components (with discussion) , 1997 .

[7]  Calyampudi R. Rao.  Large sample tests of statistical hypotheses concerning several parameters with applications to problems of estimation , 1948, Mathematical Proceedings of the Cambridge Philosophical Society.

[8]  A. Rinaldo,et al.  On the geometry of discrete exponential families with application to exponential random graph models , 2008, 0901.0026.

[9]  Edoardo M. Airoldi,et al.  Stochastic Block Models of Mixed Membership , 2006 .

[10]  Paul Erdös,et al.  On random graphs, I , 1959 .

[11]  Karl Pearson F.R.S..  X. On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling , 2009 .

[12]  J. Besag.  Spatial Interaction and the Statistical Analysis of Lattice Systems , 1974 .

[13]  David R. Hunter,et al.  Curved exponential family models for social networks , 2007, Soc. Networks.

[14]  Tom A. B. Snijders,et al.  Markov Chain Monte Carlo Estimation of Exponential Random Graph Models , 2002, J. Soc. Struct..

[15]  S. Koschade.  A Social Network Analysis of Jemaah Islamiyah: The Applications to Counterterrorism and Intelligence , 2006 .

[16]  ON SOME OPTIMALITY PROPERTIES OF FISHER-RAO SCORE FUNCTION IN TESTING AND ESTIMATION , 2001 .

[17]  Xiao-Li Meng,et al.  Posterior Predictive $p$-Values , 1994 .

[18]  David J. C. MacKay,et al.  Information Theory, Inference, and Learning Algorithms , 2004, IEEE Transactions on Information Theory.

[19]  P. Diaconis,et al.  Estimating and understanding exponential random graph models , 2011, 1102.2650.

[20]  M. Handcock,et al.  Likelihood-based inference for stochastic models of sexual network formation. , 2004, Theoretical population biology.

[21]  Allan Sly,et al.  Mixing time of exponential random graphs. , 2011 .

[22]  Jure Leskovec,et al.  Community Structure in Large Networks: Natural Cluster Sizes and the Absence of Large Well-Defined Clusters , 2008, Internet Math..

[23]  Anil K. Bera,et al.  Rao's score, Neyman's C(α) and Silvey's LM tests: an essay on historical developments and some new results , 2001 .

[24]  Christopher Steven Marcum,et al.  Interorganizational Collaboration in the Hurricane Katrina Response* , 2012, J. Soc. Struct..

[25]  Lancelot F. James,et al.  Gibbs Sampling Methods for Stick-Breaking Priors , 2001 .

[26]  T. Snijders,et al.  Estimation and Prediction for Stochastic Blockstructures , 2001 .

[27]  D. Hunter,et al.  Goodness of Fit of Social Network Models , 2008 .

[28]  Alberto Caimo,et al.  Bayesian inference for exponential random graph models , 2010, Soc. Networks.

[29]  Carter T. Butts,et al.  Emergent Coordinators in the World Trade Center Disaster , 2005, International Journal of Mass Emergencies & Disasters.

[30]  Allan Sly,et al.  Random graphs with a given degree sequence , 2010, 1005.1136.

[31]  Peter D. Hoff,et al.  Latent Space Approaches to Social Network Analysis , 2002 .

[32]  A. Neath.  Testing Statistical Hypotheses (3rd ed.). E. L. Lehmann and Joseph P. Romano , 2006 .

[33]  J. Møller,et al.  An efficient Markov chain Monte Carlo method for distributions with intractable normalising constants , 2006 .

[34]  Peter D. Hoff,et al.  Bilinear Mixed-Effects Models for Dyadic Data , 2005 .

[35]  Thomas Brendan Murphy,et al.  Variational Bayesian inference for the Latent Position Cluster Model , 2009, NIPS 2009.

[36]  R. Paap,et al.  The Bayesian Score Statistic , 2000 .

[37]  Garry Robins,et al.  Analysing exponential random graph (p-star) models with missing data using Bayesian data augmentation , 2010 .

[38]  David R. Hunter,et al.  Model-Based Clustering of Large Networks , 2012, The annals of applied statistics.

[39]  M E J Newman,et al.  Community structure in social and biological networks , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[40]  P. Holland,et al.  An Exponential Family of Probability Distributions for Directed Graphs , 1981 .

[41]  D. Krackhardt.  Graph theoretical dimensions of informal organizations , 1994 .

[42]  S. Koschade.  A Social Network Analysis of Jemaah Islamiyah: The Applications to Counter-Terrorism and Intelligence , 2006 .

[43]  Adrian E. Raftery,et al.  Representing degree distributions, clustering, and homophily in social networks with latent cluster random effects models , 2009, Soc. Networks.

[44]  J. F. C. Kingman,et al.  Information and Exponential Families in Statistical Theory , 1980 .

[45]  M. Schweinberger.  Instability, Sensitivity, and Degeneracy of Discrete Exponential Families , 2011, Journal of the American Statistical Association.

[46]  M. Newman,et al.  Random graphs with arbitrary degree distributions and their applications. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[47]  S. Chib,et al.  Marginal Likelihood From the Metropolis–Hastings Output , 2001 .

[48]  D. M. Titterington,et al.  Variational approximations in Bayesian model selection for finite mixture distributions , 2007, Comput. Stat. Data Anal..

[49]  Eric D. Kolaczyk,et al.  Statistical Analysis of Network Data: Methods and Models , 2009 .

[50]  C. Butts,et al.  Responder Communication Networks in the World Trade Center Disaster: Implications for Modeling of Communication Within Emergency Settings , 2007 .

[51]  K. Pearson.  On the Criterion that a Given System of Deviations from the Probable in the Case of a Correlated System of Variables is Such that it Can be Reasonably Supposed to have Arisen from Random Sampling , 1900 .

[52]  E. Lehmann.  Testing Statistical Hypotheses , 1960 .

[53]  P. Green,et al.  Corrigendum: On Bayesian analysis of mixtures with an unknown number of components , 1997 .

[54]  Jun S. Liu,et al.  Monte Carlo strategies in scientific computing , 2001 .

[55]  Stanley Wasserman,et al.  Social Network Analysis: Methods and Applications , 1994, Structural analysis in the social sciences.

[56]  J. Eugene Haas,et al.  Complex Organizations: A Sociological Perspective , 1973 .

[57]  Carter T. Butts,et al.  Bernoulli Graph Bounds for Generalrandom Graphs , 2011 .

[58]  Kathleen M. Carley,et al.  A structural perspective on the emergence of network organizations , 1999 .

[59]  E. Jaynes.  Information Theory and Statistical Mechanics , 1957 .

[60]  T. Snijders,et al.  p2: a random effects model with covariates for directed graphs , 2004 .

[61]  P. Bickel,et al.  A nonparametric view of network models and Newman–Girvan and other modularities , 2009, Proceedings of the National Academy of Sciences.

[62]  A. Raftery,et al.  Model‐based clustering for social networks , 2007 .

[63]  M. Stephens.  Dealing with label switching in mixture models , 2000 .

[64]  L. Comfort,et al.  Coordination in Rapidly Evolving Disaster Response Systems , 2004 .

[65]  M. Handcock.  Center for Studies in Demography and Ecology Assessing Degeneracy in Statistical Models of Social Networks , 2005 .

[66]  Erik Auf der Heide,et al.  Disaster Response: Principles of Preparation and Coordination , 1989 .

[67]  Ove Frank,et al.  http://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained , 2007 .

[68]  L. Tierney.  Markov Chains for Exploring Posterior Distributions , 1994 .

[69]  D. Hunter,et al.  Inference in Curved Exponential Family Models for Networks , 2006 .

[70]  Maurizio Dapor.  Monte Carlo Strategies , 2020, Transport of Energetic Electrons in Solids.

[71]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[72]  Christian Tallberg.  A BAYESIAN APPROACH TO MODELING STOCHASTIC BLOCKSTRUCTURES WITH COVARIATES , 2004 .

[73]  David Strauss.  On a general class of models for interaction , 1986 .

[74]  T. Snijders,et al.  10. Settings in Social Networks: A Measurement Model , 2003 .

[75]  Martina Morris,et al.  ergm: A Package to Fit, Simulate and Diagnose Exponential-Family Models for Networks. , 2008, Journal of statistical software.

[76]  J. Jonasson.  The random triangle model , 1999, Journal of Applied Probability.