Continuous time graph processes with known ERGM equilibria: contextual review, extensions, and synthesis

References

• Almquist, Z. W., & Butts, C. T. (2013). Dynamic network logistic regression: A logistic choice analysis of inter- and intra-group blog citation dynamics in the 2004 US presidential election. Political Analysis, 21, 430–448.
   PubMed Web of Science ®Google Scholar
• Baker, W. E. (1984). The social structure of a national securities market. The American Journal of Sociology, 89(4), 755–811.
   Web of Science ®Google Scholar
• Block, P., Stadtfeld, C., & Snijders, T. A. B. (2019). Forms of dependence: Comparing SAOMs and ERGMs from basic principles. Sociological Methods & Research, 48, 202–239.
   Web of Science ®Google Scholar
• Börgers, T., & Sarin, R. (1997). Learning through reinforcement and replicator dynamics. Journal of Economic Theory, 77(1), 1–14.
   Web of Science ®Google Scholar
• Burk, W. J., Steglich, C. E. G., & Snijders, T. A. B. (2007). Beyond dyadic interdependence: Actor-oriented models for co-evolving social networks and individual behaviors. International Journal of Behavioral Development, 31(4), 397–404.
   Web of Science ®Google Scholar
• Burt, R. S. (2000). Decay functions. Social Networks, 22(1), 1–28.
   Web of Science ®Google Scholar
• Burt, R. S. (2002). Bridge decay. Social Networks, 24(4), 333–363.
   Web of Science ®Google Scholar
• Butts, C. T. (2008). A relational event framework for social action. Sociological Methodology, 38(1), 155–200.
   Web of Science ®Google Scholar
• Butts, C. T. (2009). A behavioral micro-foundation for cross-sectional network models. ASA Annual Meeting Presentation.
   Google Scholar
• Butts, C. T. (2018). A perfect sampling method for exponential family random graph models. The Journal of Mathematical Sociology, 42(1), 17–36.
   Web of Science ®Google Scholar
• Butts, C. T. (2019). A dynamic process interpretation of the sparse ERGM reference model. The Journal of Mathematical Sociology, 43(1), 40–57.
   Web of Science ®Google Scholar
• Butts, C. T. (2020). A dynamic process reference model for sparse networks with reciprocity. The Journal of Mathematical Sociology.
   Web of Science ®Google Scholar
• Butts, C. T. (2021). Phase transitions in the edge/concurrent vertex model. The Journal of Mathematical Sociology, 43(3), 135–147.
   Google Scholar
• Butts, C. T., et al. (2017). Actor orientation and relational event models: A comment on Stadtfeld. Sociological Methodology, 47, 47–56.
   Web of Science ®Google Scholar
• Butts, C. T., & Almquist, Z. W. (2015). A flexible parameterization for baseline mean degree in multiple-network ERGMs. The Journal of Mathematical Sociology, 39(3), 163–167.
   PubMed Web of Science ®Google Scholar
• Byshkin, M., Stivala, A., Mira, A., Krause, R., Robins, G., & Lomi, A. (2016). Auxiliary parameter MCMC for exponential random graph models. Journal of Statistical Physics, 165(4), 740–754.
   Web of Science ®Google Scholar
• Carley, K. M. (1991). A theory of group stability. American Sociological Review, 56(3), 331–354.
   Web of Science ®Google Scholar
• Carnegie, N. B., Krivitsky, P. N., Hunter, D. R., & Goodreau, S. M. (2015). An approximation method for improving dynamic network model fitting. Journal of Computational and Graphical Statistics, 24(2), 502–519.
   PubMed Web of Science ®Google Scholar
• Cox, D. R. (1972). Regression models in life tables (with discussion). Journal of the Royal Statistical Society, Series B, 34, 187–220.
   Web of Science ®Google Scholar
• Crouch, B., Wasserman, S., & Trachtenburg, F. (1998). Markov chain Monte Carlo maximum likelihood estimation for p* social network models.
   Google Scholar
• de la Haye, K., Robins, G., Mohr, P., & Wilson, C. (2011). Homophily and contagion as explanations for weight similarities among adolescent friends. Journal of Adolescent Health, 49(4), 421–427.
   PubMed Web of Science ®Google Scholar
• Desmarais, B., & Cranmer, S. (2012). Statistical mechanics of networks: Estimation and uncertainty. Physica A: Statistical Mechanics and Its Applications, 391(4), 1865–1876.
   Web of Science ®Google Scholar
• Diesser, E. M., Freites, J. A., Tobias, D. J., & Butts, C. T. (2023). Network Hamiltonian models for unstructured protein aggregates, with application to γD-crystallin. The Journal of Physical Chemistry B, 127(3), 685–697.
   PubMed Web of Science ®Google Scholar
• Feld, S. (1981). The focused organization of social ties. The American Journal of Sociology, 1015–1035. 1986.
   Web of Science ®Google Scholar
• Freeman, L. C., Freeman, S. C., & Michaelson, A. G. (1988). On human social intelligence. Journal of Social and Biological Structure, 11, 415–425.
   Google Scholar
• Gibson, C. B., & Butts, C. T. (2023). Effects of temporal resolution adjustments on dynamic sexual contact models. Social Networks, 73, 104–113.
   Web of Science ®Google Scholar
• Grazioli, G., Yu, Y., Unhelkar, M. H., Martin, R. W., & Butts, C. T. (2019). Network-based classification and modeling of amyloid fibrils. The Journal of Physical Chemistry B, 123(26), 5452–5462.
   PubMed Web of Science ®Google Scholar
• Grimmett, G. R., & Stirzaker, D. R. (1992). Probability and Random Processes. Clarendon Press.
   Google Scholar
• Häggström, O., & Jonasson, J. (1999). Phase transition in the random triangle model. Journal of Applied Probability, 36, 1101–1115.
   Web of Science ®Google Scholar
• Handcock, M. S. (2003). Statistical models for social networks: Inference and degeneracy. In R. Breiger, K. M. Carley, & P. Pattison (Eds.), Dynamic Social Network Modeling and Analysis (pp. 229–240). National Academies Press.
   Google Scholar
• Handcock, M. S., & Gile, K. J. (2010). Modeling networks with sampled data. The Annals of Applied Statistics, 4(1), 5–25.
   PubMed Web of Science ®Google Scholar
• Hanneke, S., & Xing, E. P. (2007). Discrete temporal models of social networks. In E. M. Airoldi & E. an Stephen. D. M. B. Fienberg, A. Goldenberg, E. P. Xing, and A. X. Zheng, Eds., Statistical Network Analysis: Models, Issues, and New Directions: ICML 2006 Workshop on Statistical Network Analysis, Pittsburgh, PA, USA, June 29, 2006, Revised Selected Papers, volume 4503 of Lecture Notes in Computer Science, pages 115–125. Springer-Verlag.
   Google 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), S4–25.
   Google Scholar
• Holland, P. W., & Leinhardt, S. (1977). A dynamic model for social networks. The Journal of Mathematical Sociology, 5(1), 5–20.
   Web of Science ®Google Scholar
• Hummon, N. P., & Fararo, T. J. (1995). Actors and networks as objects. Social Networks, 17, 1–26.
   Web of Science ®Google Scholar
• Hunter, D. R., Handcock, M. S., Butts, C. T., Goodreau, S. M., & Morris, M. (2008). Ergm: A package to fit, simulate and diagnose exponential-family models for networks. Journal of Statistical Software, 24(3).
   Google Scholar
• Kahneman, D., & Tversky, A. (1979). Prospect theory: An analysis of decision under risk. Econometrica, 47(2), 263–291.
   Web of Science ®Google Scholar
• Katz, L., & Proctor, C. H. (1959). The concept of configuration of interpersonal relations in a group as a time-dependent stochastic process. Psychometrika, 24, 317–327.
   Web of Science ®Google Scholar
• Klumb, C., Goodreau, S., & Morris, M. (2022). Revisiting the edges dissolution approximation. Working Paper, University of Washington.
   Google Scholar
• Koskinen, J., Caimo, A., & Lomi, A. (2015). Simultaneous modeling of initial conditions and time heterogeneity in dynamic networks: An application to foreign direct investments. Network Science, 3(1), 58–77.
   Google Scholar
• Koskinen, J. H., Robins, G. L., Wang, P., & Pattison, P. E. (2013). Bayesian analysis for partially observed network data, missing ties, attributes and actors. Social Networks, 35(4), 514–527.
   Web of Science ®Google Scholar
• Koskinen, J. H., & Snijders, T. A. (2007). Bayesian inference for dynamic social network data. Journal of Statistical Planning and Inference, 137(12): 3930–3938. 5th St. Petersburg Workshop on Simulation, Part {II}
   Web of Science ®Google Scholar
• Krivitsky, P. N. (2012a). Exponential-family random graph models for valued networks. Electronic Journal of Statistics, 6, 1100–1128.
   PubMed Web of Science ®Google Scholar
• Krivitsky, P. N. (2012b). Modeling of dynamic networks based on egocentric data with durational information. Upenn Department of Statistics: Technical Reports and Preprints, 12(1), 1–32.
   Google Scholar
• Krivitsky, P. N., & Handcock, M. S. (2014). A separable model for dynamic networks. Journal of the Royal Statistical Society, Series B, 76(1), 29–46.
   Google Scholar
• Krivitsky, P. N., Handcock, M. S., & Morris, M. (2011). Adjusting for network size and composition effects in exponential-family random graph models. Statistical Methodology, 8(4), 319–339.
   PubMedGoogle Scholar
• Krivitsky, P. N., & Kolaczyk, E. D. (2015). On the question of effective sample size in network modeling: An asymptotic inquiry. Statistical Science, 30, 184–198.
   PubMed Web of Science ®Google Scholar
• Krivitsky, P. N., & Morris, M. (2017). Inference for social network models from egocentrically sampled data, with application to understanding persistent racial disparities in HIV prevalence in the US. The Annals of Applied Statistics, 11(1), 427–455.
   PubMed Web of Science ®Google Scholar
• Lawson, B. G., & Park, S. (2000). Asynchronous time evolution in an artificial society model. Journal of Artificial Societies and Social Simulation, 3(1).
   Web of Science ®Google Scholar
• Lerner, J., Indlekofer, N., Nick, B., & Brandes, U. (2013). Conditional independence in dynamic networks. Journal of Mathematical Psychology, 57(6), 275–283.
   Web of Science ®Google Scholar
• Lospinoso, J., & Snijders, T. A. (2019). Goodness of fit for stochastic actor-oriented models. Methodological Innovations, 12(3), 2059799119884282.
   Google Scholar
• Lusher, D., Koskinen, J., & Robins, G. (2012). Exponential Random Graph Models for Social Networks: Theory, Methods, and Applications. Cambridge University Press.
   Google Scholar
• Lütkepohl, H. (1993). Introduction to Multivariate Time Series Analysis. Springer-Verlag.
   Google Scholar
• Mayhew, B. H. (1984). Chance and necessity in sociological theory. The Journal of Mathematical Sociology, 9, 305–339.
   Web of Science ®Google Scholar
• Mele, A. (2010). A structural model of segregation in social networks. NET Institute Working Paper No. 10-16.
   Google Scholar
• Mele, A. (2017). A structural model of dense network formation. Econometrica, 85(3), 825–850.
   Web of Science ®Google Scholar
• Morris, M., Handcock, M. S., & Hunter, D. R. (2008). Specification of exponential-family random graph models: Terms and computational aspects. Journal of Statistical Software, 24(4), 1–24.
   PubMedGoogle Scholar
• Morris, M., Kurth, A. E., Hamilton, D. T., Moody, J., & Wakefield, S. (2009). Concurrent partnerships and HIV prevalence disparities by race: Linking science and public health practice. American Journal of Public Health, 99(6), 1023–1031.
   PubMed Web of Science ®Google Scholar
• Niezink, N. M. D., & Snijders, T. A. B. (2017). Co-evolution of social networks and continuous actor attributes. The Annals of Applied Statistics, 11, 1948–1973.
   Web of Science ®Google Scholar
• Park, J., & Newman, M. (2004). Solution of the 2-star model of a network. Physical Review E, 70, 066146.
   Web of Science ®Google Scholar
• Perry, P. O., & Wolfe, P. J. (2013). Point process modelling for directed interaction networks. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 75, 821–849.
   Web of Science ®Google Scholar
• Radin, C., & Yin, M. (2013). Phase transitions in exponential random graphs. Annals of Applied Probability, 23(6), 2458–2471.
   Web of Science ®Google Scholar
• Robins, G. L., & Pattison, P. E. (2001). Random graph models for temporal processes in social networks. The Journal of Mathematical Sociology, 25, 5–41.
   Web of Science ®Google Scholar
• Robins, G. L., Pattison, P. E., & Woolcock, J. (2005). Small and other worlds: Network structures from local processes. The American Journal of Sociology, 110(4), 894–936.
   Web of Science ®Google Scholar
• Schaefer, D. R., & Kreager, D. A. (2020). New on the block: Analyzing network selection trajectories in a prison treatment program. American Sociological Review, 85(4), 709–737.
   PubMed Web of Science ®Google Scholar
• Schweinberger, M. (2011). Instability, sensitivity, and degeneracy of discrete exponential families. Journal of the American Statistical Association.
   PubMed Web of Science ®Google Scholar
• Schweinberger, M., Krivitsky, P. N., Butts, C. T., & Stewart, J. (2020). Exponential-family models of random graphs: Inference in finite-, super-, and infinite-population scenarios. Statistical Science, 35(4), 627–662.
   Web of Science ®Google Scholar
• Schweinberger, M., & Snijders, T. A. B. (2007). Markov models for digraph panel data: Monte Carlo-based derivative estimation. Computational Statistics & Data Analysis, 51, 4465–4483.
   Web of Science ®Google Scholar
• Sijtsema, J. J., Ojanen, T., Veenstra, R., Lindenberg, S., Hawley, P. H., & Little, T. D. (2010). Forms and functions of aggression in adolescent friendship selection and influence: A longitudinal social network analysis. Social Development, 19(3), 515–534.
   Web of Science ®Google Scholar
• Skvoretz, J. (1985). Random and biased networks: Simulations and approximations. Social Networks, 7, 256–261.
   Web of Science ®Google Scholar
• Snijders, T. A. B. (1996). Stochastic actor-oriented models for network change. The Journal of Mathematical Sociology, 23, 149–172.
   Google Scholar
• Snijders, T. A. B. (2001). The statistical evaluation of social network dynamics. Sociological Methodology, 31, 361–395.
   Web of Science ®Google Scholar
• Snijders, T. A. B. (2002). Markov chain Monte Carlo estimation of exponential random graph models. Journal of Social Structure, 3(2).
   Google Scholar
• Snijders, T. A. B., & Duijn, M. A. J. V. (1997). Simulation for statistical inference in dynamic network models. In R. Conte, R. Hegselmann, & P. Terna (Eds.), Simulating Social Phenomena (pp. 493–512). Springer.
   Google Scholar
• Snijders, T. A. B., Koskinen, J., & Schweinberger, M. (2010). Maximum likelihood estimation for social network dynamics. The Annals of Applied Statistics, 4, 567–588.
   PubMed Web of Science ®Google Scholar
• Stadtfeld, C. (2012). Events in Social Networks: A Stochastic Actor-oriented Framework for Dynamic Event Processes in Social Networks. KIT Scientific Publishing.
   Google Scholar
• Stadtfeld, C., Hollway, J., & Block, P. (2017). Dynamic network actor models: Investigating coordination ties through time. Sociological Methodology, 47(1), 1–40.
   Google Scholar
• Steglich, C., Snijders, T. A. B., & Pearson, M. (2010). Dynamic networks and behavior: Separating selection from influence. Sociological Methodology, 40(1), 329–393.
   Web of Science ®Google Scholar
• Stivala, A. D., Koskinen, J. H., Rolls, D. A., Wang, P., & Robins, G. L. (2016). Snowball sampling for estimating exponential random graph models for large networks. Social Networks, 47, 167–188.
   Web of Science ®Google Scholar
• Strauss, D. (1986). On a general class of models for interaction. SIAM Review, 28(4), 513–527.
   Web of Science ®Google Scholar
• Vu, D., Asuncion, A., Hunter, D., & Smyth, P. (2011a). Dynamic egocentric models for citation networks. In Proceedings of the 28th International Conference on Machine Learning (ICML 2011), pages 857–864. International Machine Learning Society.
   Google Scholar
• Vu, D., Asuncion, A., Hunter, D., & Smyth, P. (2011b). Dynamic egocentric models for citation networks. In Proceedings of the 2011 International Conference on Neural Information Processing Systems (NIPS).
   Google Scholar
• Wang, J., & Atchadé, Y. F. (2014). Approximate Bayesian computation for exponential random graph models for large social networks. Communications in Statistics-Simulation and Computation, 43(2), 359–377.
   Web of Science ®Google Scholar
• Wasserman, S. S. (1980). A stochastic model for directed graphs with transition rates determined by reciprocity. Sociological Methodology, 11, 392–412.
   Google Scholar
• Weerman, F. M. (2011). Delinquent peers in context: A longitudinal network analysis of selection and influence effects. Criminology, 49(1), 253–286.
   Web of Science ®Google Scholar
• Young, H. P. (1998). Individual Strategy and Social Structure: An Evolutionary Theory of Institutions. Princeton University Press.
   Google Scholar
• Yu, Y., Grazioli, G., Unhelkar, M., Martin, R. W., & Butts, C. T. (2020). Network Hamiltonian models reveal pathways to amyloid fibril formation. Nature Scientific Reports, 10, 15668.
   PubMed Web of Science ®Google Scholar