Abstract
A new method is proposed for the statistical analysis of dyadic social interaction data measured over time. The data to be studied are assumed to be realizations of a social network of a fixed set of actors interacting on a single relation. The method is based on loglinear models for the probabilities for various dyad (or actor pair) states and generalizes the statistical methods proposed by Holland and Leinhardt (1981), Fienberg, Meyer, & Wasserman (1985), and Wasserman (1987) for social network data. Two statistical models are described: the first is an “associative” approach that allows for the study of how the network has changed over time; the second is a “predictive” approach that permits the researcher to model one time point as a function of previous time points. These approaches are briefly contrasted with earlier methods for the sequential analysis of social networks and are illustrated with an example of longitudinal sociometric data.
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References
Agresti, A. (1984).Analysis of ordinal categorical data. New York: John Wiley & Sons.
Allison, P. D., & Liker, J. D. (1982). Analyzing sequential categorical data on dyadic interactions.Psychological Bulletin, 91, 393–403.
Arabie, P. (1984). Validation of sociometric structure by data on individuals' attributes.Social Networks, 6, 373–403.
Arabie, P., & Carroll, J. D. (1980). MAPCLUS: A mathematical programming approach to fitting the ADCLUS model.Psychometrika, 45, 211–236.
Baker, R. J., & Nelder, J. A. (1978).The GLIM system, Release 3: Generalized linear interactive modeling. Oxford: The Numerical Algorithms Group.
Berkowitz, S. D. (1982).An introduction to structural analysis: The network approach to social research. Toronto: Butterworths.
Bernard, H. R., & Killworth, P. D. (1979). Deterministic models of social networks. In P. W. Holland & S. Leinhardt (Eds.),Perspectives on social network research (pp. 165–186). New York: Academic Press.
Bishop, Y. M. M., Fienberg, S. E., & Holland, P. W. (1975).Discrete multivariate analysis: Theory and practice. Cambridge, MA: The MIT Press.
Budescu, D. V. (1984). Tests of lagged dominance in sequential dyadic interaction.Psychological Bulletin, 96, 402–414.
Burt, R. S. (1980). Models of network structure.Annual Review of Sociology, 6, 79–141.
Fienberg, S. E. (1980).The Analysis of cross-classified, categorical data (2nd ed.). Cambridge, MA: The MIT Press.
Fienberg, S. E. (1985). Multivariate directed graphs in statistics. In S. Kotz & N. L. Johnson (Ed.),Encyclopedia of statistical sciences (Vol. 6, pp. 40–43). New York: John Wiley & Sons.
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. Leinhardt (Ed.),Sociological methodology 1981 (pp. 156–192). San Francisco: Jossey-Bass.
Gottman, J. M. (1979).Marital interactions: Experimental investigations. New York: Academic Press.
Gottman, J. M., & Ringland, J. T. (1981). The analysis of dominance and bidirectionality in social development.Child Development, 52, 393–412.
Haberman, S. J. (1978).Analysis of qualitative data, (Vol. 1). New York: Academic Press.
Haberman, S. J. (1979).Analysis of qualitative data (Vol. 2). New York: Academic Press.
Hage, P., & Harary, F. (1983).Structural models in anthropology. Cambridge, England: Cambridge University Press.
Holland, P. W., & Leinhardt, S. (1977). A dynamic model for social networks.Journal of Mathematical Sociology, 5, 5–20.
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. (1978). Generalized proximity function comparisons.British Journal of Mathematical and Statistical Psychology, 31, 179–192.
Hubert, L. J. (1979). Generalized concordance.Psychometrika, 44, 135–142.
Hubert, L. J., & Baker, F. B. (1978). Evaluating the conformity of sociometric measurements.Psychometrika, 43, 31–41.
Hubert, L. J., & Schultz, J. V. (1976). Quadratic assignment as a general data analysis strategy.British Journal of Mathematical and Statistical Psychology, 29, 190–241.
Iacobucci, D., & Wasserman, S. (1987). Dyadic social interactions.Psychological Bulletin, 102, 293–306.
Iacobucci, D., & Wasserman, S. (1988). A general framework for the statistical analysis of sequential dyadic interaction data.Psychological Bulletin, 103, 279–390.
Katz, L., & Powell, J. H. (1953). A proposed index for the conformity of one sociometric measurement to another.Psychometrika, 18, 249–256.
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.
Knoke, D., & Kuklinski, J. H. (1982).Network Analysis. Beverly Hills, CA: Sage Publications.
Koehler, K., & Larntz, K. (1980). An empirical investigation of goodness-of-fit statistics for sparse multinomials.Journal of the American Statistical Association, 75, 336–344.
Meyer, M. M. (1982). Transforming contingency tables.Annals of Statistics, 10, 1172–1181.
Noma, E., & Smith, D. R. (1985). Benchmark for the blocking of sociometric data.Psychological Bulletin, 97, 583–591.
Payne, C. D. (1985).The GLIM system release 3.77: Generalized linear interactive modelling manual. Oxford: The Numerical Algorithms Group.
Rice, R. E., & Richards, W. D. Jr. (1985). An overview of network analysis methods and programs. In B. Cervin & M. J. Voigt (Eds.)Progress in communication sciences (Vol. VI, pp. 105–165). Norwood, NJ: Ablex.
Sampson, S. F. (1968).A Novitiate in a period of change: An experimental and case study of social relationships. Unpublished doctoral dissertation, Department of Sociology, Cornell University.
Shepard, R. N., & Arabie, P. (1979). Additive clustering: Representation of similarities as combinations of discrete overlapping properties.Psychological Review, 86, 87–123.
Wampold, B. E. (1984). Tests of dominance in sequential categorical data.Psychological Bulletin, 96, 424–429.
Wampold, B. E., & Margolin, G. (1982). Nonparametric strategies to test the independence of behavioral states in sequential data.Psychological Bulletin, 92, 755–765.
Wasserman, S. (1978). Models for binary directed graphs and their applications.Advances in Applied Probability, 10, 803–818.
Wasserman, S. (1980). Analyzing social networks as stochastic processes.Journal of the American Statistical Association, 75, 280–294.
Wasserman, S. (1987). Conformity of two sociometric relations.Psychometrika, 52, 3–18.
Wasserman, S., & Anderson, C. (1987). Stochastica posteriori blockmodels: Construction and assessment.Social Networks, 9, 1–36.
Wasserman, S., & Iacobucci, D. (1986). Statistical analysis of discrete relational data.British Journal of Mathematical and Statistical Psychology, 39, 41–64.
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Research support provided by National Science Foundation Grant #SES84-08626 to the University of Illinois at Urbana-Champaign and by a predoctoral traineeship awarded to the second author by the Quantitative Methods Program of the Department of Psychology, University of Illinois at Urbana-Champaign, funded by ADAHMA, National Research Service Award #MH14257. We thank the editor and three anonymous referees for helpful comments.
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Wasserman, S., Iacobucci, D. Sequential social network data. Psychometrika 53, 261–282 (1988). https://doi.org/10.1007/BF02294137
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DOI: https://doi.org/10.1007/BF02294137