The statistical analysis of social networks is increasingly used to understand social processes and patterns. The association between social relationships and individual behaviors is of particular interest to sociologists, psychologists, and public health researchers. Several recent network studies make use of the fixed choice design (FCD), which induces missing edges in the network data. Because of the complex dependence structure inherent in networks, missing data can pose very difficult problems for valid statistical inference. In this article, we introduce novel methods for accounting for the FCD censoring and introduce a new survey design, which we call the augmented fixed choice design (AFCD). The AFCD adds considerable information to analyses without unduly burdening the survey respondent, resulting in improvements over the FCD, and other existing estimators. We demonstrate this new method through simulation studies and an analysis of alcohol use in a network of undergraduate students living in a residence hall.

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