# Flow autocorrelation: a dyadic approach

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## Abstract

The paper proposes and investigates a new index of flow autocorrelation, based upon a generalization of Moran’s I, and made of two ingredients. The first one consists of a family of spatial weights matrix, the *exchange matrix*, possessing a freely adjustable parameter interpretable as the age of the network, and controlling for the distance decay range. The second one is a matrix of chi-square dissimilarities between outgoing or incoming flows. Flows have to be adjusted, that is their diagonal part must first be calibrated from their off-diagonal part, thanks to a new iterative procedure procedure aimed at making flows as independent as possible. Commuter flows in Western Switzerland as well as migration flows in Western US illustrate the statistical testing of flow autocorrelation, as well as the computation, mapping and interpretation of local indicators of flow autocorrelation. We prove the present dyadic formalism to be equivalent to the “origin-based” tetradic formalism found in alternative studies of flow autocorrelation.

## JEL Classification

C21 C23 R12## References

- Anselin L (1995) Local indicators of spatial association—LISA. Geogr Anal 27:93–115CrossRefGoogle Scholar
- Bavaud F (1998) Models for Spatial Weights: A Systematic Look. Geographical Analysis 30:153–171CrossRefGoogle Scholar
- Bavaud F (2013) Testing spatial autocorrelation in weighted networks: the modes permutation test. J Geogr Syst 15:233–247CrossRefGoogle Scholar
- Bavaud F (2014) “Spatial weights: constructing weight-compatible exchange matrices from proximity matrices”. In: Duckham M. et al. (Eds.): GIScience 2014, LNCS 8728, pp. 81–96. SpringerGoogle Scholar
- Behrens K, Ertur C, Koch W (2012) Dual gravity: using spatial econometrics to control for multilateral resistance. J Appl Econom 27:773–794CrossRefGoogle Scholar
- Berger J, Snell JL (1957) On the concept of equal exchange. Behav Sci 2:111–118CrossRefGoogle Scholar
- Berglund S, Karlström A (1999) Identifying local spatial association in flow data. J Geogr Syst 1:219–236CrossRefGoogle Scholar
- Bishop YM, Fienberg SE, Holland PW (1975) Discrete multivariate analysis: theory and practice. The MIT Press, CambridgeGoogle Scholar
- Bivand RS, Pebesma EJ, Gómez-Rubio V, Pebesma EJ (2008) Applied spatial data analysis with R. Springer, New YorkGoogle Scholar
- Black WR (1992) Network autocorrelation in transportation network and flow systems. Geogr Anal 24:207–222CrossRefGoogle Scholar
- Black WR, Thomas I (1998) Accidents on Belgiums motorways: a network autocorrelation analysis. J Trans Geogr 6:23–31CrossRefGoogle Scholar
- Bolduc D, Laferriere R, Santarossa G (1995) Spatial autoregressive error components in travel flow models: an application to aggregate mode choice. In: Anselin L, Florax RJ (eds) New directions in spatial econometrics. Springer, Berlin, pp 96–108CrossRefGoogle Scholar
- Brandsma AS, Ketellapper RH (1979) A biparametric approach to spatial autocorrelation. Environ Plan A 11:51–58CrossRefGoogle Scholar
- Chung FRK (1997) Spectral graph theory. AMS, ProvidenceGoogle Scholar
- Cover T, Thomas J (1991) Elements of information theory. Wiley, HobokenCrossRefGoogle Scholar
- Cliff AD, Ord JK (1981) Spatial processes. Pion, Thousand OaksGoogle Scholar
- Fischer MM, Griffith DA (2008) Modeling spatial autocorrelation in spatial interaction data: an application to patent citation in the European Union. J Reg Sci 48(5):969–989CrossRefGoogle Scholar
- Hillberry R, Hummels D (2008) Trade responses to geographic frictions: a decomposition using micro-data. Eur Econ Rev 52:527–550CrossRefGoogle Scholar
- Kondor RI, Lafferty J (2002) Diffusion kernels on graphs and other discrete input spaces. In: ICML, vol 2, pp 315–322Google Scholar
- LeSage J, Pace RK (2008) Spatial econometric modeling of origin-destination flows. J Reg Sci 48:941–967CrossRefGoogle Scholar
- LeSage J, Polasek W (2008) Incorporating transportation network structure in spatial econometric models of commodity flows. Spatial Econ Anal 3:225–245CrossRefGoogle Scholar
- Llano-Verduras C, Minondo A, RequenaSilvente F (2011) Is the border effect an artefact of geographical aggregation? World Econ 34:1771–1787CrossRefGoogle Scholar
- Polasek W, Sellner R (2010) Spatial Chow–Lin methods for data completion in econometric flow models (No. 255). Reihe Ökonomie/Economics Series, Institut für Höhere Studien (IHS)Google Scholar
- Tiefelsdorf M, Braun G (1999) Network autocorrelation in poisson regression residuals: inter-district migration patterns and trends within Berlin. In: paper presented at the 11th European colloquium on quantitative and theoretical geography, Durham City, England, September 3–7Google Scholar