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Continuous-time statistical models for network panel data

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SNAW04 - Dynamic Networks

For the statistical analysis of network panel data even with as little as 2 waves, it is very fruitful to use models that assume a continuous-time Markov network process, observed only at the moments of observation for the panel. This is analogous to the use of continuous-time models for classical (non-network) panel data proposed by Bergstrom, Singer, and others. For network data such an approach was proposed already by Coleman in 1964. The advantage of this approach is that it provides a simple way to represent the feedback that is inherent in network dynamics, and the model can be defined by just specifying the conditional probability of a tie change, given the current state of the network.

This approach is used in the Stochastic Actor-Oriented Model of Snijders (2001) and in the Longitudinal Exponential Random Graph Model of Snijders & Koskinen (2013). The first of these is actor-oriented, i.e., tie changes are modelled as choices by actors, which among their outgoing tie variables to toggle; the second is tie-oriented, i.e., tie changes are modelled as toggles of single tie variables. Both are generalized linear models for the (unobserved) continuous-time process, with all the practical modelling flexibility of such models. Estimation for panel data is more involved, requiring a simulation approach. Estimators have been developed along several lines, including Method of Moments, Generalized Method of Moments, Maximum Likelihood, and Bayesian, and are available in the R package RSiena. This package is widely applied in empirical social network studies in the social sciences.            
This presentation treats the basic definition of the model and some of its extensions, e.g., co-evolution of multivariate networks. Some open problems, from a mathematical and from an applied perspective, will be mentioned.            

References  

  • Ruth M. Ripley, Tom A.B. Snijders, Zsófia Boda, András Vörös, and Paulina Preciado, 2016. Manual for SIENA version 4.0. Oxford: University of Oxford, Department of Statistics; Nuffield College. http://www.stats.ox.ac.uk/siena/   
  • Tom A.B. Snijders, 2001. The statistical evaluation of social network dynamics. Sociological Methodology, 31, 361-395.
  • Tom A.B. Snijders and Johan Koskinen, 2013. “Longitudinal Models”. Chapter 11 (pp. 130-140) in D. Lusher, J. Koskinen, and G. Robins, Exponential Random Graph Models for Social Networks, Cambridge: Cambridge University Press.  
  • T om A.B. Snijders, Gerhard G. van de Bunt, G. G., and Christian E.G. Steglich, 2010. Introduction to actor-based models for network dynamics. Social Networks, 32, 44–60.  




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