ASSESSMENT OF STOCHASTIC APPROXIMATION METHODS AND OF DEGENERACY DIAGNOSTIC TOOLS IN EXPONENTIAL RANDOM GRAPH MODELS

Abstract

In recent decades there has been an enormous growth of interest in the notion of social network and the methods of Social Network Analysis (SNA). The methodology developed in the field of network analysis has been categorized into descriptive methods and statistical methods. The statistical methods may be organized into two parts; the first group consists of dyadic and triadic methods which represent statistical models for subgraphs and the second group of statistical models for entire graphs and digraphs. In this work we pay attention to the Exponential Random Graph Models (ERGMs), the statistical models which provide a general framework for modeling dependent data where the dependence can be thought of as a neighborhood effect. The present manuscript is based on two main motivations. Firstly, we are interested to examine model diagnostics and check for degeneracy of ERGMs using different methods and functions. Secondly, we aim to evaluate and compare results obtained for networks of various sizes from three different estimation procedures such as Newton-Raphson, Robbins-Monro and Stepping.