The Impact of Partial Markov Bases on the Goodness-of-Fit of Network Models

• Activity Number: 439
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Xiaolin Yang*+ and Stephen E. Fienberg and Alessandro Rinaldo
• Companies: Carnegie Mellon Univ and Department of Statistics, Carnegie Mellon University and Carnegie Mellon University
• Keywords: network model ; ERGM ; goodness of fit ; algebraic geometry

Abstract

The goodness of fit of a network model is an important problem to consider when analyzing social network data. In the family of Exponential Random Graph Models, this problem corresponds to what minimal sufficient statistics terms should be included in the model. One way of doing this is to construct a random walk over the fiber and compute the test statistics from the MLEs of all these networks. When the sample space is too large, sampling from the conditional distribution of a network given the minimal sufficient statistics can approximate this procedure. However, sometimes complete Markov bases moves are difficult to identify. Instead we can define a subset of Markov moves that can generate all networks for most sufficient statistics. The question is whether there are significant differences between the distributions of the test statistics using subset and complete set of moves. In this paper, we show our study by experiments on the p1 model whose complete Markov bases have been found. Furthermore, we define a subset of Markov bases moves for Markov random graph models and evaluate the performance. We want to show how well the subset of Markov bases approximate the whole bases.