Estimating the correlation in network disturbance models

TL;DR

This paper analyzes the challenges of estimating correlation in network disturbance models, revealing bias issues with maximum likelihood and proposing a more stable, intuitive estimator for the correlation parameter.

Contribution

It identifies the limitations of maximum likelihood estimation in dense networks and introduces a new estimator that reduces bias in correlation estimation.

Findings

Maximum likelihood estimates of $ ho$ are biased and unstable in dense graphs.

The proposed estimator shows significantly less bias in simulations.

The paper discusses implications for the Network Effects Model.

Abstract

The Network Disturbance Model of Doreian (1989) expresses the dependency between observations taken at the vertices of a network by modelling the correlation between neighbouring vertices, using a single correlation parameter $\rho$. It has been observed that estimation of $\rho$ in dense graphs, using the method of Maximum Likelihood, leads to results that can be both biased and very unstable. In this paper, we sketch why this is the case, showing that the variability cannot be avoided, no matter how large the network. We also propose a more intuitive estimator of $\rho$, which shows little bias. The related Network Effects Model is briefly discussed.