Goodness of Fit of Logistic Regression Models for Random Graphs. Issue 1 (2nd January 2018)

• Record Type: Journal Article
• Authors: Latouche, Pierre; Robin, Stéphane; Ouadah, Sarah
• Is Part Of: Journal of computational and graphical statistics. Volume 27:Issue 1(2018)
• Page Start: 98
• Page End: 109
• Publication Date: 2018-01-02
• Subjects: Logistic regression -- Random graphs -- Variational approximations -- W-graph model; Mathematical statistics -- Data processing -- Periodicals; Mathematical statistics -- Graphic methods -- Periodicals; 519.50285
• DOI: 10.1080/10618600.2017.1349663
• Languages: English
• ISSNs: 1061-8600

Abstract

ABSTRACT: Logistic regression is a natural and simple tool to understand how covariates contribute to explain the topology of a binary network. Once the model is fitted, the practitioner is interested in the goodness of fit of the regression to check if the covariates are sufficient to explain the whole topology of the network and, if they are not, to analyze the residual structure. To address this problem, we introduce a generic model that combines logistic regression with a network-oriented residual term. This residual term takes the form of the graphon function of a W -graph. Using a variational Bayes framework, we infer the residual graphon by averaging over a series of blockwise constant functions. This approach allows us to define a generic goodness-of-fit criterion, which corresponds to the posterior probability for the residual graphon to be constant. Experiments on toy data are carried out to assess the accuracy of the procedure. Several networks from social sciences and ecology are studied to illustrate the proposed methodology. Supplementary material for this article is available online.