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.
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Allison, P. D., & Liker, J. K. (1982). Analyzing sequential categorical data on dyadic interactions: A comment on Gottman.Psychological Bulletin, 91, 393–403.
Arbie, P. A., Boorman, S. A., & Levitt, P. R. (1978). Constructing blockmodels: How and why.Journal of Mathematical Psychology, 17, 21–63.
Bondy, J. A., & Murty, U. S. R. (1976).Graph theory with applications. New York: North-Holland.
Draper, N., & Smith, H. (1981).Applied regression analysis (2nd ed.). New York: Wiley.
Fararo, T. J., & Doreian, P. (1984). Tripartite structural analysis: Generalizing the Breiger-Wilson formalism.Social Networks, 6, 141–175.
Fienberg, S. E. (1980).The analysis of cross-classified categorical data (2nd ed.). Cambirdge, MA: The MIT Press.
Fienberg, S. E., Meyer, M. M., & Wasserman, S. (1985). Statistical analysis of multiple sociometric relations.Journal of the American Statistical Association, 80, 51–67.
Fienberg, S. E., & Wasserman, S. (1981). Categorical data analysis of single sociometric relations. In S. Lienhardt (Ed.),Sociological methdology (pp. 156–192). San Francisco: Jossey-Bass.
Frank, O., & Strauss, D. (1986). Markov graphs.Jorunal of the American Statistical Association, 81, 832–842.
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.
Galaskiewicz, J. (1985).Social organizations of an urban grant economy: A study of business philanthropy and nonprofit organizations. Orlando, FL: Academic Press.
Gorsuch, R. L. (1983).Factor analysis (2nd ed.). Hillsdale, NJ: Lawrence Erlbaum.
Gottman, J. M. (1979). Detecting cyclicity in social interaction.Psychological Bulletin, 86. 338–348.
Hage, P., & Harary, F. (1983).Structural models in anthropology. Cambridge: Cambridge University Press.
Harman, H. H. (1976).Modern factor anlaysis (3rd ed.). Chicago: The University of Chicago Press.
Holland, P. W., & Leinhardt, S. (1981). An exponential family of probability distributions for directed graphs.Journal of the American Statistical Association, 76, 33–50.
Hubert, L. J., & Baker, F. B. (1978). Evaluating the conformity of sociometric measurements.Psychometrika, 43, 31–41.
Iacobucci, D. (1989). Modeling multivariate sequential dyadic inteactions.Social Networks, 11, 315–362.
Iacobucci, D., & Wasserman, S. (1988). A general framework for the statistical analysis of sequential dyadic interaction data.Psychological Bulletin, 103, 379–390.
Kenny, D. A., & LaVoie, L. (1984). The social relations model. In L. Berkowitz (Ed.),Advances in experimental social psychology, 18 (pp. 141–182). New York: Academic Press.
Knoke, D., & Kuklinski, J. H. (1982).Network analysis. Beverly Hills: Sage.
Kruskal, J. B., & Wish, M. (1978).Multidimensional scaling. Beverly Hills: Sage.
Lorrain, F., & White, H. C. (1971). The structural equivalence of individuals in social networks.Journal of Mathematical Sociology, 1, 49–80.
McDonald, R. P. (1985).Factor analysis and related methods. Hillsdale, NJ: Lawrence Erlbaum.
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.
Scheffé, H. (1959).The analysis of variance. New York: Wiley.
Strauss, D., & Ikeda, M. (1990). Pseudolikelihood estimation for social networks.Journal of the American Statistical Association, 85, 204–212.
Torgerson, W. S. (1958).Theory and methods of scaling. New York: Wiley.
Tucker, L. R. (1963). Implications of factor analysis of three-way matrices for measurement of change. In C. W. Harris (Ed.).Problems in measuring change (pp. 122–137). Madison: University of Wisconsin Press.
Tucker, L. R. (1966). Some mathematical notes on three-mode factor analysis.Psychometrika, 31, 279–311.
Tucker, L. R. (1972). Relations between multidimensional scaling and three-mode factor analysis.Psychometrika, 37, 3–27.
Wasserman, S. (1987). Conformity of two sociometric relations.Psychometrika, 52, 3–18.
Wasserman, S., & Anderson, C. (1987). Stochastic a posteriori blockmodels: Construction and assessment.Social Networks, 9, 1–36.
Wasserman, S., & Fuast, K. (1990).Social network analysis: Methods and applications. New York: Cambridge University Press.
Wasserman, S., & Iacobucci, D. (1986). Statistical analysis of discrete relational data.British Journal of Mathematical and Statistical Psychology, 39, 41–64.
Wasserman, S., & Iacobucci, D. (1988). Sequential social network data.Psychometrika, 53, 261–282.
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.
Wasserman, S., & Weaver, S. O. (1985). Statistical analysis of binary relational data: Parameter estimation.Journal of Mathematical Psychology, 29, 406–427.
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.
Wilson, T. P. (1982). Relational networks: An extension of sociometric concepts.Social Networks.4, 105–116.
Wong, G. (1989, April).Maximum likelihood estimation of the p 1 model. Paper presented at the Stockholm Conference on Random Graphs and Applications. Stockholm, Sweden.
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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.
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Iacobucci, D., Wasserman, S. Social networks with two sets of actors. Psychometrika 55, 707–720 (1990). https://doi.org/10.1007/BF02294618
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DOI: https://doi.org/10.1007/BF02294618