A p* primer: Logit models for social networks

Carolyn Jane Anderson, Stanley Wasserman, Bradley Crouch

Research output: Contribution to journalArticle

Abstract

A major criticism of the statistical models for analyzing social networks developed by Holland, Leinhardt, and others [Holland, P.W., Leinhardt, S., 1977. 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, pp. 33-65 (with discussion); Fienberg, S.E., Wasserman, S., 1981. Categorical data analysis of single sociometric relations. In: Leinhardt, S. (Ed.), Sociological Methodology 1981, San Francisco: Jossey-Bass, pp. 156-192; Fienberg, S.E., Meyer, M.M., Wasserman, S., 1985. Statistical analysis of multiple sociometric relations. Journal of the American Statistical Association, 80, pp. 51-67; Wasserman, S., Weaver, S., 1985. Statistical analysis of binary relational data: Parameter estimation. Journal of Mathematical Psychology. 29, pp. 406-427; Wasserman, S., 1987. Conformity of two sociometric relations. Psychometrika. 52, pp. 3-18] is the very strong independence assumption made on interacting individuals or units within a network or group. This 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. Pseudolikelihood 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., Pattison, P., 1996. Logit models and logistic regressions for social networks: I. An introduction to Markov random graphs and p*. Psychometrika. 60, pp. 401-426] present a derivation and extension of these models, this paper is a primer on how to use these important breakthroughs to model the relationships between actors (individuals, units) within a single network and provides an extension of the models to multiple networks. The models for multiple networks permit researchers to study how groups are similar and/or how they are different. The models for single and multiple networks and the modeling process are illustrated using friendship data from elementary school children from a study by Parker and Asher [Parker, J.G., Asher, S.R., 1993. Friendship and friendship quality in middle childhood: Links with peer group acceptance and feelings of loneliness and social dissatisfaction. Developmental Psychology. 29, pp. 611-621].

Original languageEnglish (US)
Pages (from-to)37-66
Number of pages30
JournalSocial Networks
Volume21
Issue number1
DOIs
StatePublished - Jan 1999

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Social Support
social network
Logistic Models
Netherlands
Bass
Peer Group
friendship
Loneliness
statistical analysis
San Francisco
Statistical Models
Emotions
mathematical psychology
Research Personnel
Psychology
weaver
developmental psychology
peer group
conformity
schoolchild

ASJC Scopus subject areas

  • Anthropology
  • Sociology and Political Science
  • Social Sciences(all)
  • Psychology(all)

Cite this

A p* primer : Logit models for social networks. / Anderson, Carolyn Jane; Wasserman, Stanley; Crouch, Bradley.

In: Social Networks, Vol. 21, No. 1, 01.1999, p. 37-66.

Research output: Contribution to journalArticle

Anderson, Carolyn Jane ; Wasserman, Stanley ; Crouch, Bradley. / A p* primer : Logit models for social networks. In: Social Networks. 1999 ; Vol. 21, No. 1. pp. 37-66.
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