Network models for social influence processes

This paper generalizes thep* class of models for social network data to predict individual-level attributes from network ties. Thep* model for social networks permits the modeling of social relationships in terms of particular local relational or network configurations. In this paper we present methods for modeling attribute measures in terms of network ties, and so constructp* models for the patterns of social influence within a network. Attribute variables are included in a directed dependence graph and the Hammersley-Clifford theorem is employed to derive probability models whose parameters can be estimated using maximum pseudo-likelihood. The models are compared to existing network effects models. They can be interpreted in terms of public or private social influence phenomena within groups. The models are illustrated by an empirical example involving a training course, with trainees' reactions to aspects of the course found to relate to those of their network partners.This research was supported by grants from the Australian Research Council. The authors would like to acknowledge the help of Stanley Wasserman, Janice Langan-Fox and Larry Hubert, and would like to thank four anonymous reviewers for their helpful comments. Earlier versions of this article were presented at the North American Conference of the Psychometric Society, Lawrence, Kansas, June, 1999, and at the Australasian Mathematical Psychology Conference, Brisbane, Australia, December 1999.