Statistical models for social network data

Social network graphs are used to display interactions of actors. Often statistical summaries from social network graphs are used to predict future interactions or are related to other measurements on the actors. This dissertation considers two statistical problems involving social network data: bias caused by missing data, and dynamics of social networks over time.;Many social network data sets have missing data from nonrespondents or censoring. Most researchers analyze complete cases only, thereby assuming that all missing observations are not interacting. This causes estimated network-level statistics such as degree or closeness to be biased. A multiple imputation method is proposed that uses latent actor effects as well as reciprocity estimates to impute missing values in the adjacency matrix. The multiple imputation method is shown to reduce bias in estimated quantities.;Q-connectivity graphs display interactions of a target actor who is observed multiple times. They differ from social network graphs by concentrating on one target actor and displaying persistence of interactions between the target actor and peer actors. A two-stage stochastic model is developed for data from Q-connectivity graphs, where the first stage models probabilities of interaction between two actors, and the second stage models probabilities of at least three actors interacting. The model employs fixed effects for observed characteristics of each actor and random effects to capture the heterogeneity between actors. It is shown that the model accounts for the dynamic social networks over time and for the multiple observations of the same actor. The model is applied to data on children's play patterns, and shows differences in estimated latent sociability among the children.