MODELS FOR EVOLVING FIXED NODE NETWORKS - MODEL-FITTING AND MODEL TESTING

Researchers in social networks are becoming increasingly interested in how networks evolve over time. There are theories that bear on the ev olution of networks, but virtually no statistical methodology which su pports the comparative evaluation of these theories. In this paper, we present explicit probability models for networks that change over tim e, covering a range of simple but significant qualitative behavior. Ma ximum likelihood estimates of model parameters which describe the rate of change of the network are derived, and some of their sampling prop erties are elucidated. To calculate these estimates the researcher mus t have measurements upon the trajectory of a network - these are the v alues of the network at successive time points. We also describe goodn ess-of-fit tests for assessing model adequacy, and use Newcomb's datas et to illustrate the methodology.