Algebraic statistics for a directed random graph model with reciprocation
Abstract
The p_1 model is a directed random graph model used to describe dyadic interactions in a social network in terms of effects due to differential attraction (popularity) and expansiveness, as well as an additional effect due to reciprocation. In this article we carry out an algebraic statistics analysis of this model. We show that the p_1 model is a toric model specified by a multi-homogeneous ideal. We conduct an extensive study of the Markov bases for p_1 models that incorporate explicitly the constraint arising from multi-homogeneity. Our results are directly relevant to the estimation and conditional goodness-of-fit testing problems in p_1 models.
Keywords
Cite
@article{arxiv.0909.0073,
title = {Algebraic statistics for a directed random graph model with reciprocation},
author = {Sonja Petrović and Alessandro Rinaldo and Stephen E. Fienberg},
journal= {arXiv preprint arXiv:0909.0073},
year = {2015}
}
Comments
22 pages. 4 figures depicting relevant Markov moves. One section removed from previous version.