Likelihoods for fixed rank nomination networks with applications to friendship networks from Add Health


Volfovsky, Alexander; Hoff, Peter D.; Fosdick, Bailey K.; & Stovel, Katherine (2014). Likelihoods for fixed rank nomination networks with applications to friendship networks from Add Health. 2014 Add Health Users Conference. Bethesda, MD.


Many studies that gather social network data use survey methods that lead to censored, missing or otherwise incomplete information. For example, Add Health employs the popular fixed rank nomination (FRN) scheme, asking 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 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 from Wave 1 of Add Health. 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.


Reference Type

Conference proceeding

Book Title

2014 Add Health Users Conference


Volfovsky, Alexander
Hoff, Peter D.
Fosdick, Bailey K.
Stovel, Katherine

Year Published


City of Publication

Bethesda, MD

Reference ID