Exponential-Family Random Graph Models for Rank-Order Relational Data

Abstract: Rank-order relational data, in which each actor ranks the others according to some criterion, often arise from sociometric measurements of judgment (e.g., self-reported interpersonal interaction) or preference (e.g., relative liking). We propose a class of exponential-family models for rank-order relational data and derive a new class of sufficient statistics for such data, which assume no more than within-subject ordinal properties. Application of MCMC MLE to this family allows us to estimate effects for a variety of plausible mechanisms governing rank structure in cross-sectional context, and to model the evolution of such structures over time. We apply this framework to model the evolution of relative liking judgments in an acquaintance process, and to model recall of relative volume of interpersonal interaction among members of a technology education program.