Dec 3

2:30 pm

## Estimation and Examination of Longitudinal Social Network Data Covariance Structures

### Anton Westveld

General Exam

University of Washington - Department of Statistics

Social network data consist of measured relations among a set of actors. This type of data allows for the empirical investigation of the interconnectivity of the actors, which is a cornerstone of social science theory. This talk will focus on data generated from the repeated interaction of pairs of actors (temporal dyadic data) resulting in an outcome for each actor at each time point. Examples of such data arise in many disciplines. Yearly trade levels between nations is a primary example of longitudinal social network data; every year the amount each nation sends (exports) and receives (imports) is recorded. Other examples include: conflicts between nations, migration, friendship relations, tournaments and games, and data generated from experimental game theory.

Previous studies have generally focused on modeling the temporal correlation or the network correlation. In this talk, I propose statistical methodology that accounts for both types of correlation. In particular, in order to accommodate both types of correlation structure, I expand the social network contributions of Warner et al. (1979), Wong (1982), Gill and Swartz (2001), and Hoff (2002), all of which used random effects to account for (1) correlation of actions having the same sender, (2) correlation of actions having the same receiver, and (3) correlation due to reciprocity of actions among pairs of actors. Their models are expanded to a longitudinal social network model by assuming the random effects are correlated through time. A method of moments estimation procedure is developed to allow for semi-parametric estimation of the covariances. Based upon the estimates of the covariances, the auto-correlation functions and the partial auto-correlations can be plotted to gain insight into the temporal correlation structure leading to ARMA model selection.