Likelihoods for fixed rank nomination networks

TL;DR

This paper demonstrates that using standard binary network models on fixed rank nomination data can lead to misleading inferences, emphasizing the need for likelihoods that account for the censored and ranked data structure.

Contribution

The paper introduces and compares likelihood methods for fixed rank nomination network data, highlighting the importance of modeling the censored and ranked nature of such data.

Findings

Binary likelihood can produce misleading parameter estimates.

Likelihood accounting for FRN design yields different, potentially more accurate inferences.

Analysis of adolescent networks shows the impact of model choice on conclusions.

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 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 parameter estimates obtained from a likelihood for complete binary networks to those from a likelihood that is derived from the FRN scheme, and therefore recognizes the ranked and censored nature of the data. We show analytically and via simulation that the binary likelihood can provide misleading inference, at least 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.