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Social Networks with Two Sets of Actors

Published online by Cambridge University Press:  01 January 2025

Dawn Iacobucci  and
Stanley Wasserman
Dawn Iacobucci*
Affiliation:
Department of Marketing, Kellogg Graduate School of Management, Northwestern University
Stanley Wasserman
Affiliation:
Departments of Psychology and Statistics, University of Illinois at Urbana-Champaigh
*
Requests for reprints should be sent to Dawn Iacobucci, Department of Marketing, Kellogg Graduate School of Management, Northwestern University, 2001 Sheridan Road, Evanston, IL, 60208.
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Abstract

Traditional network research analyzes relational ties within a single group of actors: the models presented in this paper involve relational ties exist beteen two distinct sets of actors. Statistical models for traditional networks in which relations are measured within a group simplify when modeling unidirectional relations measured between groups. The traditional paradigm results in a one-mode socionatrix; the network paradigm considered in this paper results in a two-mode socionatrix; A statistical model is presented, illustrated on a sample data set, and compared to its traditional counterpart. Extensions are discussed, including those that model multivariate relations simultaneously, and those that allow for the inclustion of attributes of the individuals in the group.

Keywords

relational databipartite graphssociomatrixcategorical data analysis
Type
Original Paper
Information
Psychometrika , Volume 55 , Issue 4 , December 1990 , pp. 707 - 720
Copyright
Copyright © 1990 The Psychometric Society

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Footnotes

We thank the Editor and two anonymous reviewers for their helpful comments. We are also grateful to George Barnett for allowing us to analyze his data.

References

Allison, P. D., & Liker, J. K. (1982). Analyzing sequential categorical data on dyadic interactions: A comment on Gottman. Psychological Bulletin, 91, 393–403.CrossRefGoogle Scholar
Arbie, P. A., Boorman, S. A., & Levitt, P. R. (1978). Constructing blockmodels: How and why. Journal of Mathematical Psychology, 17, 21–63.CrossRefGoogle Scholar
Bondy, J. A., & Murty, U. S. R. (1976). Graph theory with applications, New York: North-Holland.CrossRefGoogle Scholar
Draper, N., & Smith, H. (1981). Applied regression analysis 2nd ed.,, New York: Wiley.Google Scholar
Fararo, T. J., & Doreian, P. (1984). Tripartite structural analysis: Generalizing the Breiger-Wilson formalism. Social Networks, 6, 141–175.CrossRefGoogle Scholar
Fienberg, S. E. (1980). The analysis of cross-classified categorical data 2nd ed.,, Cambirdge, MA: The MIT Press.Google Scholar
Fienberg, S. E., Meyer, M. M., & Wasserman, S. (1985). Statistical analysis of multiple sociometric relations. Journal of the American Statistical Association, 80, 51–67.CrossRefGoogle Scholar
Fienberg, S. E., & Wasserman, S. (1981). Categorical data analysis of single sociometric relations. In Lienhardt, S. (Eds.), Sociological methdology (pp. 156–192). San Francisco: Jossey-Bass.Google Scholar
Frank, O., & Strauss, D. (1986). Markov graphs. Jorunal of the American Statistical Association, 81, 832–842.CrossRefGoogle Scholar
Friedland, M. H., Barnett, G. A., & Danowski, J. A. (1988, Februray). The network structure of American industrial and service organizations based upon shared public relations and advertising firms. Paper presented to the Sunbelt Social Networks Conference, Can Diego, CA.Google Scholar
Galaskiewicz, J. (1985). Social organizations of an urban grant economy: A study of business philanthropy and nonprofit organizations, Orlando, FL: Academic Press.Google Scholar
Gorsuch, R. L. (1983). Factor analysis 2nd ed., Hillsdale, NJ: Lawrence Erlbaum.Google Scholar
Gottman, J. M. (1979). Detecting cyclicity in social interaction. Psychological Bulletin, 86, 338–348.CrossRefGoogle Scholar
Hage, P., & Harary, F. (1983). Structural models in anthropology, Cambridge: Cambridge University Press.Google Scholar
Harman, H. H. (1976). Modern factor anlaysis 3rd ed., Chicago: The University of Chicago Press.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.CrossRefGoogle Scholar
Hubert, L. J., & Baker, F. B. (1978). Evaluating the conformity of sociometric measurements. Psychometrika, 43, 31–41.CrossRefGoogle Scholar
Iacobucci, D. (1989). Modeling multivariate sequential dyadic inteactions. Social Networks, 11, 315–362.CrossRefGoogle Scholar
Iacobucci, D., & Wasserman, S. (1988). A general framework for the statistical analysis of sequential dyadic interaction data. Psychological Bulletin, 103, 379–390.CrossRefGoogle Scholar
Kenny, D. A., LaVoie, L. (1984). The social relations model. In Berkowitz, L. (Eds.), Advances in experimental social psychology, 18 (pp. 141–182). New York: Academic Press.Google Scholar
Knoke, D., & Kuklinski, J. H. (1982). Network analysis, Beverly Hills: Sage.Google Scholar
Kruskal, J. B., & Wish, M. (1978). Multidimensional scaling, Beverly Hills: Sage.CrossRefGoogle Scholar
Lorrain, F., & White, H. C. (1971). The structural equivalence of individuals in social networks. Journal of Mathematical Sociology, 1, 49–80.CrossRefGoogle Scholar
McDonald, R. P. (1985). Factor analysis and related methods, Hillsdale, NJ: Lawrence Erlbaum.Google Scholar
Sampson, S. F. (1968). A novitiate in a period of change: An experimental and case study of relationships. Unpublished doctoral dissertation, Cornell University, Department of Sociology.Google Scholar
Scheffé, H. (1959). The analysis of variance, New York: Wiley.Google Scholar
Strauss, D., & Ikeda, M. (1990). Pseudolikelihood estimation for social networks. Journal of the American Statistical Association, 85, 204–212.CrossRefGoogle Scholar
Torgerson, W. S. (1958). Theory and methods of scaling, New York: Wiley.Google Scholar
Tucker, L. R. (1963). Implications of factor analysis of three-way matrices for measurement of change. In Harris, C. W. (Eds.), Problems in measuring change (pp. 122–137). Madison: University of Wisconsin Press.Google Scholar
Tucker, L. R. (1966). Some mathematical notes on three-mode factor analysis. Psychometrika, 31, 279–311.CrossRefGoogle ScholarPubMed
Tucker, L. R. (1972). Relations between multidimensional scaling and three-mode factor analysis. Psychometrika, 37, 3–27.CrossRefGoogle Scholar
Wasserman, S. (1987). Conformity of two sociometric relations. Psychometrika, 52, 3–18.CrossRefGoogle Scholar
Wasserman, S., & Anderson, C. (1987). Stochastic a posteriori blockmodels: Construction and assessment. Social Networks, 9, 1–36.CrossRefGoogle Scholar
Wasserman, S., & Fuast, K. (1990). Social network analysis: Methods and applications, New York: Cambridge University Press.Google Scholar
Wasserman, S., & Iacobucci, D. (1986). Statistical analysis of discrete relational data. British Journal of Mathematical and Statistical Psychology, 39, 41–64.CrossRefGoogle Scholar
Wasserman, S., & Iacobucci, D. (1988). Sequential social network data. Psychometrika, 53, 261–282.CrossRefGoogle Scholar
Wasserman, S., & Iacobucci, D. (in press). Statistical modeling of one-mode and two-mode networks: Simultaneous analysis of graphs and bipartite graphs. British Jorunal of Mathematical and Statistical Psychology.Google Scholar
Wasserman, S., & Weaver, S. O. (1985). Statistical analysis of binary relational data: Parameter estimation. Journal of Mathematical Psychology, 29, 406–427.CrossRefGoogle Scholar
White, H. C., Boorman, S. A., & Breiger, R. L. (1976). Social structure from multiple networks I: Blockmodels of roles and positions. American Journal of Sociology, 81, 730–780.CrossRefGoogle Scholar
Wilson, T. P. (1982). Relational networks: An extension of sociometric concepts. Social Networks, 4, 105–116.CrossRefGoogle Scholar
Wong, G. (1989, April). Maximum likelihood estimation of the p1model. Paper presented at the Stockholm Conference on Random Graphs and Applications. Stockholm, Sweden.Google Scholar