Modelos exponenciais para grafos aleatórios valorados

Abstract

Exponential Random Graph Models (ERGM) are statistical models for network structure, which allows us to make inferences about the generating process of such structures. They are based on three main statistics: edges, k-stars and triangles. Hunter and Handcock (2006) present a method for estimation of the parameters of the ERGM model for simple graphs through MCMC simulations, as well as the covariance matrix of the estimated parameters. The main objective of this work is to extend this method to valued random graphs, whose edge values are not constrained to zero or one. We extend the algorithm proposed by Hunter and Handcock (2006) to Exponential Random Graph Model for valued networks (ERGM-V) proposed by Krivitsky (2012) and implement it to the model where the values of the edges are Poisson. We also implemented the algorithm proposed by Krivitsky (2012) for simulation of valued random graphs. The results for simulation studies are satisfactory. For the uniparametric model, with independent edges, all of the simulations converged. By inserting a correlation measure between the observations, the convergence depends greatly on the initial parameter vector set for the simulations. However, in all of the cases where there was convergence of the algorithm, both uniparametric and biparametric, we observed that it was efficient to estimate the parameters of the model.