Statistical models for social network dynamics

The study of social network dynamics has become an increasingly important component of many disciplines in the social sciences. In the past decade, statistical models and methods have been proposed which permit researchers to draw statistical inference on these dynamics. This thesis builds on one such family of models, the stochastic actor oriented model (SAOM) proposed by Snijders [2001]. Goodness of fit for SAOMs is an area that is only just beginning to be filled in with appropriate methods. This thesis proposes a Mahalanobis distance based, Monte Carlo goodness of fit test that can depend on arbitrary features of the observed network data and covariates. As remediating poor fit can be a difficult process, a modified model distance (MMD) estimator is devised that can help researchers to choose among a set of model elaborations. In practice, panel data is typically used to draw SAOM-based inference. This thesis also proposes a score-type test for time heterogeneity between the waves in the panel that is computationally cheap and fits into a convenient, forward model selecting workflow. Next, this thesis proposes a rigorous method for aggregating so-called relational event data (e.g. emails and phone calls) by extending the SAOM family to a family of hidden Markov models that suppose a latent social network is driving the observed relational events. Finally, this thesis proposes a measurement model for SAOMs inspired by error-in-variables (EiV) models employed in an array of disciplines. Like the relational event aggregation model, the measurement model is a hidden Markov model extension to the SAOM family. These models allow the researcher to specify the form of the mesurement error and buffer against potential attenuating biases and other problems that can arise if the errors are ignored