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

• Activity Number: 229
• Type: Topic Contributed
• Date/Time: Monday, July 30, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Health Policy Statistics Section
• Author(s): Pavel Krivitsky*+ and Carter T. Butts
• Companies: Penn State University and University of California at Irvine
• Keywords: ERGM ; social networks ; ranks ; weighted networks ; transitivity ; mutuality

Abstract

Rank-order sociometric data, in which each actor ranks the others according to some criterion, have a long history in the social sciences, particularly in observation of network processes involving personal preferences like liking and advice-seeking. However, the most common approach to analysis, particularly model-based, of rank network data has been to dichotomize ranks by thresholding, losing information and potentially introducing biases. We propose a class of exponential-family models for representing rank-order relational data directly and derive sufficient statistics of ranks to model properties commonly observed in social networks, including homophily, mutuality, and triadic effects; as well as to model evolution of rankings over time. We apply the framework to evolution of relations in an acquaintance process and to assessing factors affecting accuracy of a respondent ranking others on amount of past interaction.