Structural Modelling of Dynamic Networks and Identifying Maximum Likelihood

TL;DR

This paper develops a probabilistic nonnegative matrix factorization method for nonlinear dynamic network models, introducing a new maximum likelihood approach for consistent estimation and asymptotic analysis of the network effects.

Contribution

It introduces a novel probabilistic NMF method and a maximum likelihood estimator for dynamic network models, with theoretical guarantees and asymptotic properties.

Findings

Consistent estimation of the network matrix parameters.

Asymptotic distribution derived for the estimators.

Efficiency bounds established for the maximum likelihood estimator.

Abstract

This paper considers nonlinear dynamic models where the main parameter of interest is a nonnegative matrix characterizing the network (contagion) effects. This network matrix is usually constrained either by assuming a limited number of nonzero elements (sparsity), or by considering a reduced rank approach for nonnegative matrix factorization (NMF). We follow the latter approach and develop a new probabilistic NMF method. We introduce a new Identifying Maximum Likelihood (IML) method for consistent estimation of the identified set of admissible NMF's and derive its asymptotic distribution. Moreover, we propose a maximum likelihood estimator of the parameter matrix for a given non-negative rank, derive its asymptotic distribution and the associated efficiency bound.