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Many studies that gather social network data use survey methods that lead tocensored, missing or otherwise incomplete information. For example, the popularfixed rank nomination (FRN) scheme, often used in studies of schools andbusinesses, asks study participants to nominate and rank at most a small numberof contacts or friends, leaving the existence other relations uncertain.However, most statistical models are formulated in terms of completely observedbinary networks. Statistical analyses of FRN data with such models ignore thecensored and ranked nature of the data and could potentially result inmisleading statistical inference. To investigate this possibility, we compareparameter estimates obtained from a likelihood for complete binary networks tothose from a likelihood that is derived from the FRN scheme, and thereforerecognizes the ranked and censored nature of the data. We show analytically andvia simulation that the binary likelihood can provide misleading inference, atleast for certain model parameters that relate network ties to characteristicsof individuals and pairs of individuals. We also compare these differentlikelihoods in a data analysis of several adolescent social networks. For someof these networks, the parameter estimates from the binary and FRN likelihoodslead to different conclusions, indicating the importance of analyzing FRN datawith a method that accounts for the FRN survey design.

Likelihoods for fixed rank nomination networks