Network Autocorrelation and Spatial Filtering

Abstract

Geographical flows have been frequently modeled with gravity type spatial interaction models. The estimation of spatial interaction models is often achieved with regression techniques, including linear regression and Poisson/negative binomial regression based on the nature of the observations under the independence assumption among observations. Recent studies show, with a development of neighborhood structure among network flows, that geographical flows such as population migration tend to have a significant level of correlation. This phenomenon, called network autocorrelation, leads to a violation of the independence assumption and raises a necessity of a proper modeling method which can account for network autocorrelation. The eigenvector spatial filtering method furnishes a way to incorporate network autocorrelation in linear regression and generalized linear regression. Specifically, the eigenvector spatial filtering method can be utilized to describe positive autocorrelation in Poisson/negative binomial regression, whereas their counterpart auto models are able to describe only negative autocorrelation due to the integrability condition. This chapter discusses different specifications of eigenvector spatial filtering to model network autocorrelation in a spatial interaction modeling framework. These methods are illustrated with applications with interregional commodity flows and interstate migration flows in the U.S.