Visualizing analytical spatial autocorrelation components latent in spatial interaction data: An eigenvector spatial filter approach

Four decades ago, Curry (1972) argued that spatial autocorrelation (i.e., local distance and configuration effects) and distance decay (i.e., global distance effects) intermingle in the estimation of spatial interaction model specifications. Today, massive computer power available with a desktop PC offers the necessary resources to account for these spatial autocorrelation effects within spatial interaction. Simple gravity model respecifications have been analyzed by Griffith (2007) and by Fischer and Griffith (2008). These results have been extended to a doubly-constrained gravity model respecification by Griffith (2009a, 2009b). This paper summarizes results from a further refinement of this doubly-constrained respecification, namely differentiating within and between areal unit flows. In doing so, an eigenfunction-based spatial filter description of spatial autocorrelation is constructed, which lends itself to visualization of analytical spatial autocorrelation components. Results are illustrated with the 2000 journey-to-work dataset for the extended state of Pennsylvania, USA.

[1]  Manfred M. Fischer,et al.  Modeling Spatial Autocorrelation in Spatial Interaction Data: An Application to Patent Citation Data in the European Union , 2008 .

[2]  Geostatistical Methods in Geography: Applications in Human Geography: Geostatistical Methods in Geography , 2010 .

[3]  Daniel A. Griffith,et al.  Modeling spatial autocorrelation in spatial interaction data: empirical evidence from 2002 Germany journey-to-work flows , 2009, J. Geogr. Syst..

[4]  Daniel A. Griffith,et al.  Spatial Structure and Spatial Interaction: 25 Years Later , 2007 .

[5]  D. Griffith.  Effective Geographic Sample Size in the Presence of Spatial Autocorrelation , 2005 .

[6]  Daniel A. Griffith,et al.  Spatial Autocorrelation in Spatial Interaction , 2009 .

[7]  Frank J. Cesario,et al.  A new interpretation of the “normalizing” or “balancing” factors of gravity-type spatial models , 1977 .

[8]  Jason Dykes,et al.  Exploring spatial data representation with dynamic graphics , 1997 .

[9]  M. Aitkin,et al.  A method of fitting the gravity model based on the Poisson distribution. , 1982, Journal of regional science.

[10]  L. Curry.  A Spatial Analysis of Gravity Flows , 1972, The Random Spatial Economy and Its Evolution.

[11]  Yongwan Chun,et al.  Modeling network autocorrelation within migration flows by eigenvector spatial filtering , 2008, J. Geogr. Syst..

[12]  Geostatistical Methods in Geography: Applications in Physical Geography , 2010 .

[13]  Daniel A Griffith,et al.  Spatial modeling in ecology: the flexibility of eigenfunction spatial analyses. , 2006, Ecology.

[14]  Tony E. Smith,et al.  Gravity Models of Spatial Interaction Behavior , 1995 .

[15]  J. LeSage,et al.  Spatial Econometric Modeling of Origin-Destination Flows , 2008 .

[16]  Daniel A. Griffith,et al.  A spatial filtering specification for the auto-Poisson model , 2002 .

[17]  Michael Tiefelsdorf,et al.  The Exact Distribution of Moran's I , 1995 .

[18]  Alan Wilson,et al.  A statistical theory of spatial distribution models , 1967 .

[19]  Peter Nijkamp,et al.  Complexity and spatial networks : in search of simplicity , 2009 .

[20]  Yongwan Chun,et al.  Behavioral specifications of network autocorrelation in migration modeling: an analysis of migration flows by spatial filtering , 2007 .