Goodness of fit of logistic models for random graphs

Pierre Latouche (1) , Stéphane Robin (2) , Sarah Ouadah (2)

1 SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)
2 MIA-Paris - Mathématiques et Informatique Appliquées

Logistic models for random graphs are commonly used to study binary networks when covariate information is available. After estimating the logistic parameters, one of the main questions which arises in practice is to assess the goodness of fit of the corresponding model. To address this problem, we add a general term, related to the graphon function of W-graph models, to the logistic function. Such an extra term aims at characterizing the residual structure of the network, that is not explained by the covariates. We approximate this new generic logistic model using a class of models with blockwise constant residual structure. This framework allows to derive a Bayesian procedure from a model based selection context using goodness-of-fit criteria. All these criteria depend on marginal likelihood terms for which we do provide estimates relying on two series of variational approximations. Experiments on toy data are carried out to assess the inference procedure. Finally, two real networks from social sciences and ecology are studied to illustrate the proposed methodology.

Mots clés: Random graphs; logistic regression; W -graph model; variational ap-proximations

Domaines: Statistiques [math.ST]

Pierre Latouche, Stéphane Robin, Sarah Ouadah. Goodness of fit of logistic models for random graphs. 2015. ⟨hal-01187890⟩