Likelihoods for Fixed-Rank Nomination Networks

• Activity Number: 49
• Type: Invited
• Date/Time: Sunday, August 4, 2013 : 4:00 PM to 5:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Peter David Hoff*+
• Companies: University of Washington
• Keywords: censoring ; missing data ; ordinal data ; ranked data ; social network ; social relations model

Abstract

Many studies that gather social network data use survey methods that lead to censored, missing or otherwise incomplete information. For example, the popular fixed rank nomination (FRN) scheme, often used in studies of schools and businesses, allows study participants to nominate and rank at most a small number of contacts or friends, leaving the existence other relations uncertain. However, most statistical models are formulated in terms of completely observed binary networks. Statistical analyses of FRN data with such models ignore the censored and ranked nature of the data and could potentially result in misleading statistical inference. We compare parameter estimates obtained from a likelihood for complete binary networks to those from a likelihood that is derived from the FRN scheme, and show that the binary likelihood can provide misleading inference, at least for certain model parameters. In an analysis of several adolescent social networks, the parameter estimates from the binary and FRN likelihoods lead to substantively different conclusions, indicating the importance of analyzing FRN data with a method that accounts for the FRN survey design.