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Likelihoods for fixed rank nomination networks

Published online by Cambridge University Press:  20 December 2013

PETER HOFF ,
BAILEY FOSDICK ,
ALEX VOLFOVSKY  and
KATHERINE STOVEL
PETER HOFF
Affiliation:
Departments of Statistics and Biostatistics, University of Washington, Seattle, WA 98195, USA (e-mail: [email protected])
BAILEY FOSDICK
Affiliation:
Statistical and Applied Mathematical Sciences Institute, Research Triangle Park, NC 27709, USA (e-mail: [email protected])
ALEX VOLFOVSKY
Affiliation:
Department of Statistics, Harvard University, Cambridge, MA 02138, USA (e-mail: [email protected])
KATHERINE STOVEL
Affiliation:
Department of Sociology, University of Washington, Seattle, WA 98195, USA (e-mail: [email protected])
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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, asks study participants to nominate and rank at most a small number of contacts or friends, leaving the existence of 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. To investigate this possibility, we compare Bayesian parameter estimates obtained from a likelihood for complete binary networks with those obtained from likelihoods that are derived from the FRN scheme, and therefore accommodate the ranked and censored nature of the data. We show analytically and via simulation that the binary likelihood can provide misleading inference, particularly for certain model parameters that relate network ties to characteristics of individuals and pairs of individuals. We also compare these different likelihoods in a data analysis of several adolescent social networks. For some of these networks, the parameter estimates from the binary and FRN likelihoods lead to different conclusions, indicating the importance of analyzing FRN data with a method that accounts for the FRN survey design.

Keywords

censoringlatent variablemarginal likelihoodmissing dataordinal dataranked datanetworksocial relations model
Type
Research Article
Information
Network Science , Volume 1 , Issue 3 , December 2013 , pp. 253 - 277
Copyright
Copyright © Cambridge University Press 2013 

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