Logit models and logistic regressions for social networks: I. An introduction to Markov graphs andp
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Spanning nearly sixty years of research, statistical network analysis has passed through (at least) two generations of researchers and models. Beginning in the late 1930's, the first generation of research dealt with the distribution of various network statistics, under a variety of null models. The second generation, beginning in the 1970's and continuing into the 1980's, concerned models, usually for probabilities of relational ties among very small subsets of actors, in which various simple substantive tendencies were parameterized. Much of this research, most of which utilized log linear models, first appeared in applied statistics publications.
But recent developments in social network analysis promise to bring us into a third generation. The Markov random graphs of Frank and Strauss (1986) and especially the estimation strategy for these models developed by Strauss and Ikeda (1990; described in brief in Strauss, 1992), are very recent and promising contributions to this field. Here we describe a large class of models that can be used to investigate structure in social networks. These models include several generalizations of stochastic blockmodels, as well as models parameterizing global tendencies towards clustering and centralization, and individual differences in such tendencies. Approximate model fits are obtained using Strauss and Ikeda's (1990) estimation strategy.
In this paper we describe and extend these models and demonstrate how they can be used to address a variety of substantive questions about structure in social networks.
- Agresti, A. (1990) Categorical data analysis. John Wiley and Sons, New York
- Anderson, C. J., Wasserman, S. (1995) Logmultilinear models for valued social relations. Sociological Methods & Research 24: pp. 96-127
- Besag, J. (1974) Spatial interaction and the statistical analysis of lattice systems. Journal of the Royal Statistical Society 36: pp. 192-236
- Faust, K., Wasserman, S. (1992) Centrality and prestige: A review and synthesis. Journal of Quantitative Anthropology 4: pp. 23-78
- Fienberg, S. E. (1980) The analysis of cross-classified, categorical data. The MIT Press, Cambridge, MA
- Fienberg, S. E., Wasserman, S. Categorical data analysis of single sociometric relations. In: Leinhardt, S. eds. (1981) Sociological methodology 1981. Jossey-Bass, San Francisco, pp. 156-192
- Frank, O., Strauss, D. (1986) Markov random graphs. Journal of the American Statistical Association 81: pp. 832-842
- Holland, P. W., Leinhardt, S. (1973) The structural implications of measurement error in sociometry. Journal of Mathematical Sociology 3: pp. 85-111
- Holland, P. W., Leinhardt, S. The statistical analysis of local structure in social networks. In: Heise, D. R. eds. (1975) Sociological methodology 1976. Jossey-Bass, San Francisco, pp. 1-45
- Holland, P. W., & Leinhardt, S. (1977). Notes on the statistical analysis of social network data. Unpublished manuscript.
- Holland, P. W., Leinhardt, S. (1978) An omnibus test for social structure using triads. Sociological Methods & Research 7: pp. 227-256
- Holland, P. W., Leinhardt, S. Structural sociometry. In: Holland, P. W., Leinhardt, S. eds. (1979) Perspectives on social network research. Academic Press, New York, pp. 63-83
- Holland, P. W., Leinhardt, S. (1981) An exponential family of probability distributions for directed graphs. Journal of the American Statistical Association 76: pp. 33-65
- Iacobucci, D., Wasserman, S. (1990) Social networks with two sets of actors. Psychometrika 55: pp. 707-720
- Ising, E. (1925) Beitrag zur theorie des ferramagnetismus. Zeitschrift fur Physik 31: pp. 253-258
- Johnsen, E. C. (1985) Network macrostructure models for the Davis-Leinhardt set of empirical sociomatrices. Social Networks 7: pp. 203-224
- Johnsen, E. C. (1986) Structure and process: Agreement models for friendship formation. Social Networks 8: pp. 257-306
- Kindermann, R. P., Snell, J. L. (1980) On the relation between Markov random fields and social networks. Journal of Mathematical Sociology 8: pp. 1-13
- Koehly, L., & Wasserman, S. (1994). Classification of actors in a social network based on stochastic centrality and prestige. Manuscript submitted for publication.
- Pattison, P., & Wasserman, S. (in press). Logit models and logistic regressions for social networks: II. Extensions and generalizations to valued and bivariate relations.Journal of Quantitative Anthropology.
- Reitz, K. P. (1982) Using log linear analysis with network data: Another look at Sampson's monastery. Social Networks 4: pp. 243-256
- Ripley, B. (1981) Spatial statistics. Wiley, New York
- Sampson, S. F. (1968) A novitiate in a period of change: An experimental and case study of relationships. Department of Sociology, Cornell University, Ithaca, NY
- Snijders, T. A. B. (1991) Enumeration and simulation methods for 0–1 matrices with given marginals. Psychometrika 56: pp. 397-417
- Speed, T. P. (1978) Relations between models for spatial data, contingency tables, and Markov fields on graphs. Supplement Advances in Applied Probability 10: pp. 111-122
- Strauss, D. (1977) Clustering on colored lattices. Journal of Applied Probability 14: pp. 135-143
- Strauss, D. (1986) On a general class of models for interaction. SIAM Review 28: pp. 513-527
- Strauss, D. (1992) The many faces of logistic regression. The American Statistician 46: pp. 321-327
- Strauss, D., Ikeda, M. (1990) Pseudolikelihood estimation for social networks. Journal of the American Statistical Association 85: pp. 204-212
- Vickers, M. (1981) Relational analysis: An applied evaluation. Department of Psychology, University of Melbourne, Australia
- Vickers, M., Chan, S. (1981) Representing classroom social structure. Victoria Institute of Secondary Education, Melbourne
- Walker, M. E. (1995).Statistical models for social support networks: Application of exponential models to undirected graphs with dyadic dependencies. Unpublished doctoral dissertation, University of Illinois, Department of Psychology.
- Wang, Y. J., Wong, G. Y. (1987) Stochastic blockmodels for directed graphs. Journal of the American Statistical Association 82: pp. 8-19
- Wasserman, S. (1978) Models for binary directed graphs and their applications. Advances in Applied Probability 10: pp. 803-818
- Wasserman, S. (1987) Conformity of two sociometric relations. Psychometrika 52: pp. 3-18
- Wasserman, S., Faust, K. (1994) Social network analysis: Methods and applications. Cambridge University Press, Cambridge, England
- Wasserman, S., Galaskiewicz, J. (1984) Some generalizations ofp1: External constraints, interactions, and non-binary relations. Social Networks 6: pp. 177-192
- Wasserman, S., Iacobucci, D. (1986) Statistical analysis of discrete relational data. British Journal of Mathematical and Statistical Psychology 39: pp. 41-64
- Logit models and logistic regressions for social networks: I. An introduction to Markov graphs andp
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