Statistical Analysis of Discrete Relational Data

Abstract

Social interaction data record the intensity of the relationship, or frequency of interaction, between two individual actors. Recent methods for analysing such data have treated these relational variables as continuous. A more appropriate method, described here, views these dyadic interactions as variables in multidimensional discrete cross-classified arrays, thus permitting analysis by log-linear models.

These methods extend previous approaches to social interaction data, which were limited to binary relations, by focusing on discrete-valued relations. Dyadic interactions, measured for a single discrete relational variable, are modelled stochastically using tendencies towards expansiveness (actor-effects), popularity (partner-effects) and reciprocity. Actor-characteristic variables may be used to group actors into a substantive partition, thus simplifying the analysis and subsequent interpretations.