A Performance Comparison of Intersection and Union Rules for Integrating Self-Reports of Social Relationships

• In Event: 260 - Section on Mathematical Sociology Paper Session. Advances in Mathematical Sociology

Abstract

Network inference is the problem of inferring an unknown graph from a set of error prone observations (Butts, 2003). The most familiar example of the network inference problem arises when attempting to integrate self-reports from subjects, (Drabek et al., 1981; Wellman, 1971; Robins, 1994), and poses a challenge for the analyst: given two reports on the state of a relationship, what is to be done when informants disagree? Krackhardt (1987) formalized two strategies for the analysis of such data (leading to estimators of the underlying network): regard an edge as present if either party reports it (the union rule); or regard an edge as present if and only if both parties report it (the intersection rule). There has been little investigation of how the rules perform on empirical data, and on the relative performance of these rules in inferring network structure under realistic conditions. This paper seeks to address this gap, employing interpersonal networks whose structures can be well-estimated through hierarchical Bayesian models (Butts, 2003) to assess the accuracy of these simpler (but more widely applicable) rules. Our findings demonstrate that the intersection rule outperforms the union rule for the networks studied, a surprising result, given that our informants are more prone to false negatives than false positives. We resolve this discrepancy by showing that the sparsity of the network is key to the performance of both rules, with the intersection rule dominating the union rule for networks wherein the opportunities for false positives outweigh the opportunities for false negatives.

Author

• Francis Lee, University of California-Irvine