Modeling Network Autocorrelation in Space-Time Migration Flow Data: An Eigenvector Spatial Filtering Approach

Gravity-type spatial interaction models have been popularly utilized in modeling cross-sectional migration data, but their misspecification also has been raised in the literature. This misspecification issue principally concerns an insufficient accounting of underlying effects of spatial structure, including the presence of network autocorrelation among migration flows. Recent studies reveal that spatial interaction models are significantly improved by incorporating network autocorrelation in log-linear or Poisson regression estimation techniques, which are common estimation methods for spatial interaction models. However, when migration flows are structured as a panel data set from multiple time periods, the data set is likely to display temporal correlation within each measurement unit (here, each flow between a dyad of an origin and a destination) as well as network autocorrelation within each time period. Hence, spatial interaction models should be explicitly specified to account for these two different types of correlation structure. Using the eigenvector spatial filtering technique, this article outlines how to model network autocorrelation among migration flows structured through multiple time spans in either a linear or a generalized linear mixed model. An analysis of annual U.S. interstate migration data reported by the U.S. Internal Revenue Service shows that incorporation of two different types of autocorrelation leads to an improvement of model fitting and more intuitive parameter estimates.