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Statistical Models for Social Networks

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Data Analysis, Classification, and Related Methods

Abstract

Recent developments in statistical models for social networks reflect an increasing theoretical focus in the social and behavioral sciences on the interdependence of social actors in dynamic, network-based social settings (e.g., Abbott, 1997; White, 1992, 1995). As a result, a growing importance has been accorded the problem of modeling the dynamic and complex interdependencies among network ties and the actions of the individuals whom they link. Included in this problem is the identification of cohesive subgroups, or classifications of the individuals. The early focus of statistical network modeling on the mathematical and statistical properties of Bernoulli and dyad-independent random graph distributions has now been replaced by efforts to construct theoretically and empirically plausible parametric models for structural network phenomena and their changes over time.

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References

  • ABBOTT, A. (1997): Of time and space: the contemporary relevance of the Chicago School. Social Forces, 75, 1149–1182.

    Google Scholar 

  • ANDERSON, C., WASSERMAN, S. & FAUST, K. (1992): Building stochastic blockmodels. Social Networks, 14, 137–161.

    Article  Google Scholar 

  • BESAG, J.E. (1974): Spatial interaction and the statistical analysis of lattice systems. Journal of the Royal Statistical Society, Series B, 36, 96–127.

    Google Scholar 

  • BOLLOBAS, B.(1985): Random Graphs. London: Academic Press.

    Google Scholar 

  • van de Bunt, G., van Duijn, M., & Snijders, T.A.B.(1995): Friendship networks and rational choice. In M.G. Everett K. & K. Rennolls (eds.), Proceedings of the International Conference on Social Networks, Volume I, London, 6th-10th July, 1995. Greenwich: University of Greenwich Press.

    Google Scholar 

  • CARTWRIGHT, D. & HARARY, F. (1979): Balance and cluster ability: An overview. In P. W. Holland & S. Leinhardt, (eds.), Perspectives on Social Network Research, pages 25–50. New York: Academic Press.

    Google Scholar 

  • CROUCH, B., & WASSERMAN, S. (1998): Fitting P*: Monte Carlo maximum likelihood estimation. Paper presented at International Conference on Social Networks, Sitges, Spain, May 28–31.

    Google Scholar 

  • DAVIS, J. A. (1967): Clustering and structural balance in graphs. Human Relations, 20, 181–187.

    Article  Google Scholar 

  • DAVIS, J.A. (1979): The Davis/Holland/Leinhardt studies: An overview. In P. W. Holland & S. Leinhardt, (eds.), Perspectives on Social Network Research, pages 51–62. New York: Academic Press.

    Google Scholar 

  • DOREIAN, P.(1982):Maximum likelihood methods for linear models. Sociological Methods & Research, 10, 243–269.

    Article  Google Scholar 

  • DOREIAN, P., & STOKMAN, F. (1997): Evolution of Social Networks. Amsterdam: Gordon & Breach.

    Google Scholar 

  • EMIRBAYER, M. (1997): Manifesto for a relational sociology. American Journal of Sociology. 103, 281–317.

    Article  Google Scholar 

  • EMIRBAYER, M., & Goodwin, J.(1994): Network analysis, culture, and the problem of agency. American Journal of Sociology, 99, 1411–1454.

    Article  Google Scholar 

  • ERDÖS, P.(1959): Graph theory and probability, I. Canadian Journal of Mathematics, 11, 34’38.

    Google Scholar 

  • ERDÖS, P.(1961): Graph theory and probability, II. Canadian Journal of Mathematics, 13, 346–352.

    Article  Google Scholar 

  • ERDÖS, P., & RENYI, A. (1960): On the evolution of random graphs. Publications of the Mathematical Institute of the Hungarian Academy of Sciences, 5, 17–61.

    Google Scholar 

  • FAUST, K., & SKVORETZ, J. (1999): Logit models for affiliation networks. In M. Becker, & M. Sobel (eds.), Sociological Methodology 1999, pages 253–280. New York: Basil Black well.

    Google Scholar 

  • FIENBERG, S. E., MEYER, M. M., & WASSERMAN, S. (1985): Statistical analysis of multiple sociornetric relations. Journal of the American Statistical Association, 80, 51–67.

    Article  Google Scholar 

  • FIENBERG, S., & WASSERMAN, S. (1981): Categorical data analysis of single sociornetric relations. In S. Leinhardt (ed.), Sociological Methodology 1981, pages 156–192. San Francisco: Jossey-Bass.

    Google Scholar 

  • FRANK, O. (1977): Estimation of graph totals. Scandinavian Journal of Statistics, 4, 81–89.

    Google Scholar 

  • FRANK, O. (1980): Sampling and inference in a population graph. International Statistical Review, 48, 33–41.

    Article  Google Scholar 

  • FRANK, O. (1981): A survey of statistical methods for graph analysis. In S. Leinhardt (ed.), Sociological Methodology 1981, pages 110–155. San Francisco: Jossey-Bass.

    Google Scholar 

  • FRANK O. (1989): Random graph mixtures. Annals of the New York Academy of Science. 576: Graph Theory and its Applications, pages 192–199. New York: East and West.

    Google Scholar 

  • FRANK, O., & Nowicki, K. (1993): Exploratory statistical analysis of networks. In J. Gimbel, J.W. Kennedy, & L. V. Quintas (eds.), Quo Vadis Graph Theory? A Source Book for Challenges and Directions. Amsterdam: North-Holland, (also Annals of Discrete Mathematics, 55, 349–366.).

    Google Scholar 

  • FRANK, O., & Strauss, D. (1986): Markov graphs. Journal of the American Statistical Association, 81, 832–842.

    Article  Google Scholar 

  • FRIEDKIN, N. (1998): A Structural Theory of Social Influence. New York: Cambridge University Press.

    Book  Google Scholar 

  • GEYER, C., & THOMPSON, E (1992): Constrained Monte Carlo maximum likelihood for dependent data. Journal of the Royal Statistical Society, Series B, 54, 657–699.

    Google Scholar 

  • GILBERT, E. N. (1959): Random graphs. Annals of Mathematical Statistics, 30, 1141–1144.

    Article  Google Scholar 

  • GRANOVETTER, M. (1973): The strength of weak ties. American Journal of Sociology, 78, 1360–1380.

    Article  Google Scholar 

  • HOLLAND, P. W., LASKEY, K. B., & LEINHARDT, S. (1983): Stochastic block- models: some first steps. Social Networks, 5, 109–137.

    Article  Google Scholar 

  • HOLLAND, P. W., & LEINHARDT, S. (1970): A method for detecting structure in sociornetric data. American Journal of Sociology, 70, 492–513.

    Article  Google Scholar 

  • HOLLAND, P. W. & LEINHARDT, S. (1975): The statistical analysis of local structure in social networks. In D. R. Heise (ed.), Sociological Methodology 1976, pp. 1–45. San Francisco: Jossey-Bass.

    Google Scholar 

  • HOLLAND, P. W., & LEINHARDT, S. (1981): An exponential family of probability distributions for directed graphs. Journal of the American Statistical Association, 76, 33–50.

    Article  Google Scholar 

  • HUBERT, L. J., & BAKER, F. B. (1978): Evaluating the conformity of sociornetric measurements. Psychometrika, 43, 31–41.

    Article  Google Scholar 

  • IACOBUCCI, D., & WASSERMAN, S. (1988): A general framework for the statistical analysis of sequential dyadic interaction data. Psychological Bulletin, 103, 379–390.

    Article  Google Scholar 

  • KATZ, L., & POWELL, J. H. (1953): A proposed index of conformity of one sociornetric measurement to another. Psychometrika, 18, 249–256.

    Article  Google Scholar 

  • KATZ, L., & POWELL, J. H. (1957): Probability distributions of random variables associated with a structure of the sample space of sociometric investigations. Annals of Mathematical Statistics, 28, 442–448.

    Article  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.

    Article  Google Scholar 

  • LAURITZEN, S. (1996): Graphical Models. Oxford: Oxford University Press.

    Google Scholar 

  • LAZEGA, E. and VAN DUIJN, M. (1997): Position in formal structure, personal characteristics and choices of advisors in a law firm: A logistic regression model for dyadic network data. Social Networks, 19, 375–397.

    Article  Google Scholar 

  • LAZEGA, E., & PATTISON, P. (1999): Multiplexity, generalized exchange and cooperation in organizations. Social Networks, 21, 67–90.

    Article  Google Scholar 

  • LEENDERS, R. (1995): Models for network dynamics: A Markovian framework. Journal of Mathematical Sociology, 20, 1–21.

    Article  Google Scholar 

  • LEENDERS, R. (1996): Evolution of friendship and best friendship choices. Journal of Mathematical Sociology, 21, 133–148.

    Article  Google Scholar 

  • LINDENBERG, S. (1997): Grounding groups in theory: functional, cognitive and structural interdependencies. Advances in Group Processes, 14, 281–331.

    Google Scholar 

  • MANTEL, N. (1967): The detection of disease clustering and a generalized regression approach. Cancer Research, 27, 209–220.

    Google Scholar 

  • MARSDEN, P., & FRIEDKIN, N. (1994): Network studies of social influence. In S. Wasserman J. & Galaskiewicz (eds.), Advances in Social Network Analysis (pages 3–25). Thousand Oaks, CA: Sage.

    Google Scholar 

  • PATTISON, P., MISCHE, A., & ROBINS, G.L. (1998): The plurality of social relations: k-partite representations of interdependent social forms. Keynote address, Conference on Ordinal and Symbolic Data Analysis, Amherst, Sept. 28–30.

    Google Scholar 

  • PATTISON, P. E., & WASSERMAN, S. (1999): Logit models and logistic regressions for social networks, II. Multivariate relations. British Journal of Mathematical and Statistical Psychology, 52, 169–194.

    Article  Google Scholar 

  • PATTISON, P., WASSERMAN, S., ROBINS, G.L., & KANFER, A.M. (in press): Statistical evaluation of algebraic constraints for social networks. Journal of Mathematical Psychology.

    Google Scholar 

  • RAPOPORT, A. (1949): Outline of a probabilistic approach to animal sociology, I. Bulletin of Mathematical Biophysics, 11, 183–196.

    Article  Google Scholar 

  • ROBINS, G.L., PATTISON, P., & ELLIOTT, P. (in press): Network models for social influence processes. Psychometrika.

    Google Scholar 

  • ROBINS, G.L., PATTISON, P., & WASSERMAN, S. (1999): Logit models and logistic regressions for social networks, III. Valued relations. Psychometrika, 64, 371–394.

    Article  Google Scholar 

  • SNIJDERS, T. A. B. (1991): Enumeration and simulation methods for 0–1 matrices with given marginals. Psychometrika, 56, 397–417.

    Article  Google Scholar 

  • SNIJDERS, T. A. B. (1996): Stochastic actor-oriented models for network change. Journal of Mathematical Sociology, 21, 149–172.

    Article  Google Scholar 

  • SNIJDERS, T. A. B., & NOWICKI, K. (1997): Estimation and prediction for stochastic blockmodels for graphs with latent block structure. Journal of Classification, 14, 75–100.

    Article  Google Scholar 

  • SNIJDERS, T.A.B., & VAN DUIJN, M.A.J. (1997). Simulation for statistical inference in dynamic network models. In R. Conte, R, Hegselmann, & P. Terna (eds.), Simulating Social Phenomena (pages 493–512). Berlin: Springer-Verlag.

    Google Scholar 

  • STRAUSS, D. (1986): On a general class of models for interaction. SIAM Review, 28, 513–527.

    Article  Google Scholar 

  • STRAUSS, D., & IKEDA, M. (1990): Pseudolikelihood estimation for social networks. Journal of the American Statistical Association, 85, 204–212.

    Article  Google Scholar 

  • VAN DE BUNT, G., VAN DUIJN, M., & SNIJDERS, T. A. B. (1999): Friendship networks through time: an actor-oriented dynamic statistical network model. Computational and Mathematical Organization Theory, 5, 167–192.

    Article  Google Scholar 

  • VAN DUIJN, M., & SNIJDERS, T. A. B. (1997): p 2: a random effects model for directed graphs. Unpublished manuscript.

    Google Scholar 

  • WANG, Y. Y., & WONG, G. Y. (1987): Stochastic blockmodels for directed graphs. Journal of the American Statistical Association, 82, 8–19.

    Article  Google Scholar 

  • WASSERMAN, S. (1977): Random directed graph distributions and the triad census in social networks. Journal of Mathematical Sociology, 5, 61–86.

    Article  Google Scholar 

  • WASSERMAN, S. (1979): A stochastic model for directed graphs with transition rates determined by reciprocity. In K. Schuessler (ed.) Sociological Methodology 1980, pages 392–412. San Francisco: Jossey-Bass.

    Google Scholar 

  • WASSERMAN, S. (1980): Analyzing social networks as stochastic processes. Journal of the American Statistical Association, 75, 280–294.

    Article  Google Scholar 

  • WASSERMAN, S. (1987): Conformity of two sociornetric relations. Psychometrika, 52, 3–18.

    Article  Google Scholar 

  • WASSERMAN, S., & FAUST, K. (1994): Social Network Analysis: Methods and Applications. New York: Cambridge University Press.

    Google Scholar 

  • WASSERMAN, S., & GALASKIEWICZ, J. (1984): Some generalizations of pn External constraints, interactions, and non-binary relations. Social Networks, 6, 177–192.

    Article  Google Scholar 

  • WASSERMAN, S., & IACOBUCCI, D. (1986): Statistical analysis of discrete relational data. British Journal of Mathematical and Statistical Psychology, 39, 41–64.

    Article  Google Scholar 

  • WASSERMAN, S., & IACOBUCCI, D. (1988): Sequential social network data. Psychometrika, 53, 262–282.

    Article  Google Scholar 

  • WASSERMAN, S., & PATTISON, P. E. (1996): Logit models and logistic regressions for social networks, I. An introduction to Markov random graphs and p*. Psychometrika, 60, 401–425.

    Article  Google Scholar 

  • WASSERMAN, S., & PATTISON, P. E. (in press): Multivariate Random Graph Distributions. Springer Lecture Note Series in Statistics.

    Google Scholar 

  • WATTS, D. (1999): Networks, dynamics, and the small-world phenomenon. American Journal of Sociology, 105, 493–527.

    Article  Google Scholar 

  • WATTS, D., & STROGATZ, S. (1998): Collective dynamics of ‘small-world’ networks. Nature, 393, 440–442.

    Article  Google Scholar 

  • WHITE, H. C. (1992): Identity and Control. Princeton, NJ: Princeton University Press.

    Google Scholar 

  • WHITE, H. C. (1995): Network switchings and Bayesian forks: reconstructing the social and behavioral sciences. Social Research, 62, 1035–1063.

    Google Scholar 

  • WHITE, H. C., BOORMAN, S., & BREIGER, R. L. (1976): Social structure from multiple networks, I. Blockmodels of roles and positions. American Journal of Sociology, 81, 730–780.

    Article  Google Scholar 

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Wasserman, S., Pattison, P. (2000). Statistical Models for Social Networks. In: Kiers, H.A.L., Rasson, JP., Groenen, P.J.F., Schader, M. (eds) Data Analysis, Classification, and Related Methods. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59789-3_46

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  • DOI: https://doi.org/10.1007/978-3-642-59789-3_46

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67521-1

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