A p* primer: logit models for social networks

A major criticism of the statistical models for analyzing social networks d eveloped by Holland, Leinhardt, and others [Holland, P.W., Leinhardt, S., 1 977. Notes on the statistical analysis of social network data; Holland, P.W ., Leinhardt, S., 1981. An exponential family of probability distributions for directed graphs. Journal of the American Statistical Association. 76, p p. 33-65 (with discussion); Fienberg, S.E., Wasserman, S., 1981. Categorica l data analysis of single sociometric relations. In: Leinhardt,S. (Ed.), So ciological Methodology 1981, San Francisco: Jossey-Bass, pp. 156-192; Fienb erg, S.E., Meyer, M.M., Wasserman, S., 1985. Statistical analysis of multip le sociometric relations. Journal of the American Statistical Association, 80, pp. 51-67; Wasserman, S., Weaver, S., 1985. Statistical analysis of bin ary relational data: Parameter estimation. Journal of Mathematical Psycholo gy. 29, pp. 406-427; Wasserman, S., 1987. Conformity of two sociometric rel ations. Psychometrika. 52, pp. 3-18] is the very strong independence assump tion made on interacting individuals or units within a network or group. Th is limiting assumption is no longer necessary given recent developments on models for random graphs made by Frank and Strauss [Frank, O., Strauss, D., 1986. Markov graphs. Journal of the American Statistical Association. 81, pp. 832-842] and Strauss and Ikeda [Strauss, D., Ikeda, M., 1990. Pseudolik elihood estimation for social networks. Journal of the American Statistical Association. 85, pp. 204-212]. The resulting models are extremely flexible and easy to fit to data. Although Wasserman and Pattison [Wasserman, S., P attison, P., 1996. Legit models and logistic regressions for social network s: I. An introduction to Markov random graphs and p*. Psychometrika. 60, pp . 401-426] present a derivation and extension of these models, this paper i s a primer on how to use these important breakthroughs to model the relatio nships between actors (individuals, units) within a single network and prov ides an extension of the models to multiple networks. The models for multip le networks permit researchers to study how groups are similar and/or how t hey are different. The models for single and multiple networks and the mode ling process are illustrated using friendship data from elementary school c hildren from a study by Parker and Asher [Parker, J.G., Asher, S.R., 1993. Friendship and friendship quality in middle childhood: Links with peer grou p acceptance and feelings of loneliness and social dissatisfaction. Develop mental Psychology. 29, pp. 611-621].(C) 1999 Elsevier Science B.V. All righ ts reserved.