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Spatial Autocorrelation and Spatial Interaction

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Encyclopedia of GIS

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Definition

Spatial interaction refers to all cases in which a relationship (a flow of persons, goods, communications, citations, and so on) is observed between pairs of spatial units. Differently from the standard areal or point units often analyzed in spatial science, spatial interaction data are denoted by their bilateral nature. They have an origin and a destination (in the particular case, the two being the same). Such origins and destinations may have observable characteristics. Moreover, each pair of spatial units may be described according to some measures of separation (such as distance) or of commonality (e.g., the presence of a common language). Such descriptors are typically employed in spatial interaction models, the most commonly used analytical framework for modeling flow data. Problems occur when the aforementioned descriptors exhibit correlation between the values of different spatial units or dyads which is due to the spatial configuration of the units themselves...

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References

  • Andersson M, Gråsjö U (2009) Spatial dependence and the representation of space in empirical models. Ann Reg Sci 43(1):159–180

    Article  Google Scholar 

  • Anselin L (1988) Spatial econometrics: methods and models. Kluwer Academic, Dordrecht/Boston

    Book  MATH  Google Scholar 

  • Arbia G (2006) Spatial econometrics: statistical foundations and applications to regional convergence. Springer, Heidelberg

    MATH  Google Scholar 

  • Arbia G (2014) A primer for spatial econometrics: with applications in R. Palgrave Macmillan, New York

    Book  Google Scholar 

  • Arbia G, Petrarca F (2013) Effects of scale in spatial interaction models. J Geogr Syst 15(3):249–264

    Article  Google Scholar 

  • Bavaud F (2013) Testing spatial autocorrelation in weighted networks: the modes permutation test. J Geogr Syst 15(3):233–247

    Article  Google Scholar 

  • Beenstock M, Felsenstein D (2016, forthcoming) Double spatial dependence in gravity models: migration from the European neighborhood to the European union. In: Patuelli R, Arbia G (eds) Spatial econometric interaction modelling. Springer, Heidelberg/Berlin

    Google Scholar 

  • Behrens K, Ertur C, Koch W (2012) ‘Dual’ gravity: using spatial econometrics to control for multilateral resistance. J Appl Econ 25(2):773–794

    Article  MathSciNet  Google Scholar 

  • Berglund S, Karlström A (1999) Identifying local spatial association in flow data. J Geogr Syst 1(3):219–236

    Article  Google Scholar 

  • Black WR (1992) Network autocorrelation in transport network and flow systems. Geogr Anal 24(3):207–222

    Article  Google Scholar 

  • Black WR, Thomas I (1998) Accidents on Belgium’s motorways: a network autocorrelation analysis. J Transp Geogr 6(3):23–31

    Article  Google Scholar 

  • Bolduc D, Laferrière R, Santarossa G (1992) Spatial autoregressive error components in travel flow models. Reg Sci Urban Econ 22(3):371–385

    Article  MATH  Google Scholar 

  • Burger M, van Oort F, Linders G-J (2009) On the specification of the gravity model of trade: zeros, excess zeros and zero-inflated estimation. Spat Econ Anal 4(3): 167–190

    Article  Google Scholar 

  • Chun Y (2008) Modeling network autocorrelation within migration flows by eigenvector spatial filtering. J Geogr Syst 10(4):317–344

    Article  Google Scholar 

  • Cliff AD, Martin RL, Ord JK (1974) Evaluating the friction of distance parameter in gravity models. Reg Stud 8(3–4):281–286

    Article  Google Scholar 

  • Cliff AD, Martin RL, Ord JK (1976) A reply to the final comment. Reg Stud 10(3):341–342

    Article  Google Scholar 

  • Congdon P (2010) Random-effects models for migration attractivity and retentivity: a Bayesian methodology. J R Stat Soc Ser A (Stat Soc) 173(4):755–774

    Article  MathSciNet  Google Scholar 

  • Cressie NAC (1993) Statistics for spatial data. Wiley, New York

    MATH  Google Scholar 

  • Curry L (1972) A spatial analysis of gravity flows. Reg Stud 6(2):131–147

    Article  Google Scholar 

  • Curry L, Griffith DA, Sheppard ES (1975) Those gravity parameters again. Reg Stud 9(3):289–96

    Article  Google Scholar 

  • Fischer MM, Griffith DA (2008) Modeling spatial autocorrelation in spatial interaction data: an application to patent citation data in the European union. J Reg Sci 48(5):969–989

    Article  Google Scholar 

  • Fischer MM, Reismann M, Scherngell T (2010) Spatial interaction and spatial autocorrelation. In: Anselin L, Rey SJ (eds) Perspectives on spatial data analysis. Advances in spatial science. Springer, Berlin/Heidelberg, pp 61–79

    Chapter  Google Scholar 

  • Fotheringham AS, Webber MJ (1980) Spatial structure and the parameters of spatial interaction models. Geogr Anal 12(1):33–46

    Article  Google Scholar 

  • Getis A (1991) Spatial interaction and spatial autocorrelation: a cross-product approach. Environ Plan A 23(9):1269–1277

    Article  MATH  Google Scholar 

  • Griffith DA (2000) A linear regression solution to the spatial autocorrelation problem. J Geogr Syst 2(2): 141–156

    Article  Google Scholar 

  • Griffith DA (2003) Spatial autocorrelation and spatial filtering: gaining understanding through theory and scientific visualization. Springer, Berlin/Heidelberg/New York

    Book  Google Scholar 

  • Griffith DA (2006) Assessing spatial dependence in count data: winsorized and spatial filter specification alternatives to the auto-Poisson model. Geogr Anal 38(2):160–179

    Article  Google Scholar 

  • Griffith DA (2007) Spatial structure and spatial interaction: 25 years later. Rev Reg Stud 37(1):28–38

    MathSciNet  Google Scholar 

  • Griffith DA (2010) The Moran coefficient for non-normal data. J Stat Plan Inference 140(11):2980–2990

    Article  MathSciNet  MATH  Google Scholar 

  • Griffith DA (2011) Visualizing analytical spatial autocorrelation components latent in spatial interaction data: an eigenvector spatial filter approach. Comput Environ Urban Syst 35(2):140–149

    Article  Google Scholar 

  • Griffith DA, Chun Y (2015) Spatial autocorrelation in spatial interactions models: geographic scale and resolution implications for network resilience and vulnerability. Netw Spat Econ 15(2):337–365

    Article  MathSciNet  MATH  Google Scholar 

  • Griffith DA, Fischer MM (2016, forthcoming) Constrained variants of the gravity model and spatial dependence: model specification and estimation issues. In: Patuelli R, Arbia G (eds) Spatial econometric interaction modelling. Springer, Heidelberg/Berlin

    Google Scholar 

  • Griffith DA, Jones KG (1980) Explorations into the relationship between spatial structure and spatial interaction. Environ Plan A 12(2):187–201

    Article  Google Scholar 

  • Haynes KE, Fotheringham AS (1984) Gravity and spatial interaction models. Sage Publications, Beverly Hills

    Google Scholar 

  • Jacqmin-Gadda H, Commenges D, Nejjari C, Dartigues J-F (1997) Tests of geographical correlation with adjustment for explanatory variables: an application to dyspnoea in the elderly. Stat Med 16(11):1283–1297

    Article  Google Scholar 

  • Krisztin T, Fischer MM (2015, forthcoming) The gravity model for international trade: specification and estimation issues. Spat Econ Anal 10(4):451–470

    Article  Google Scholar 

  • Lambert DM, Brown JP, Florax RJGM (2010) A two-step estimator for a spatial lag model of counts: theory, small sample performance and an application. Reg Sci Urban Econ 40(4):241–252

    Article  Google Scholar 

  • LeSage JP, Fischer MM (2010) Spatial econometric methods for modeling origin-destination flows. In: Fischer MM, Getis A (eds) Handbook of applied spatial analysis. Springer, Berlin/Heidelberg, pp 409–433

    Chapter  Google Scholar 

  • LeSage JP, Fischer MM (2016, forthcoming) Spatial regression-based model specifications for exogenous and endogenous spatial interaction. In: Patuelli R, Arbia G (eds) Spatial econometric interaction modelling. Springer, Heidelberg/Berlin

    Google Scholar 

  • LeSage JP, Fischer MM, Scherngell T (2007) Knowledge spillovers across Europe: evidence from a Poisson spatial interaction model with spatial effects. Pap Reg Sci 86(3):393–421

    Article  Google Scholar 

  • LeSage JP, Pace RK (2008) Spatial econometric modeling of origin-destination flows. J Reg Sci 48(5):941–967

    Article  Google Scholar 

  • LeSage JP, Pace RK (2009) Introduction to spatial econometrics. CRC Press, Boca Raton

    Book  MATH  Google Scholar 

  • LeSage JP, Satici E (2016, forthcoming) A Bayesian spatial interaction model variant of the Poisson pseudo-maximum likelihood estimator. In: Patuelli R, Arbia G (eds) Spatial econometric interaction modelling. Springer, Heidelberg/Berlin

    Google Scholar 

  • LeSage JP, Thomas-Agnan C (2015) Interpreting spatial econometric origin-destination flows models. J Reg Sci 55(2):188–208

    Article  Google Scholar 

  • Lin G, Zhang T (2007) Loglinear residual tests of Moran’s I autocorrelation and their applications to Kentucky breast cancer data. Geogr Anal 39(3):293–310

    Article  Google Scholar 

  • Metulini R, Patuelli R, Griffith DA (2015) Estimating a spatial filtering gravity model for bilateral trade: functional specifications and estimation challenges. In: Paper presented at the European trade study group 2015, Paris

    Google Scholar 

  • Moran P (1948) The interpretation of statistical maps. J R Stat Soc B 10:243–251

    MathSciNet  MATH  Google Scholar 

  • Neumayer E, Plümper T (2010) Spatial effects in dyadic data. Int Organ 64(1):145–166

    Article  Google Scholar 

  • Peeters D, Thomas I (2009) Network autocorrelation. Geogr Anal 41(4):436–443

    Article  Google Scholar 

  • Polasek W, Llano C, Sellner R (2012) Bayesian methods for completing data in spatial models. Rev Econ Anal 2(2):192–214

    Google Scholar 

  • Porojan A (2001) Trade flows and spatial effects: the gravity model revisited. Open Econ Rev 12(3):265–280

    Article  MATH  Google Scholar 

  • Roy JR, Thill J-C (2003) Spatial interaction modelling. Pap Reg Sci 83(1):339–361

    Article  Google Scholar 

  • Santos Silva JMC, Tenreyro S (2006) The log of gravity. Rev Econ Stat 88(4):641–658

    Article  Google Scholar 

  • Sellner R, Fischer MM, Koch M (2013) A spatial autoregressive Poisson gravity model. Geogr Anal 45(2):180–201

    Article  Google Scholar 

  •  Sen A, Smith TE (1995) Gravity models of spatial interaction behavior. Advances in spatial and network economics series. Springer, Heidelberg/New York

    Book  Google Scholar 

  • Sheppard ES, Griffith DA, Curry L (1976) A final comment on mis-specification and autocorrelation in those gravity parameters. Reg Stud 10(3):337–339

    Article  Google Scholar 

  • Thomas-Agnan C, LeSage JP (2014) Spatial econometric OD-flow models. In: Fischer MM, Nijkamp P (eds) Handbook of regional science. Springer, Berlin/Heidelberg, pp 1653–1673

    Chapter  Google Scholar 

  • Tiefelsdorf M (2003) Misspecifications in interaction model distance decay relations: a spatial structure effect. J Geogr Syst 5(1):25–50

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Economics, University of Bologna, via Angherá 22, 47921, Rimini, Italy

    Roberto Patuelli

  2. The Rimini Centre for Economic Analysis (RCEA), Rimini, Italy

    Roberto Patuelli

Authors
  1. Roberto Patuelli
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Correspondence to Roberto Patuelli .

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Editors and Affiliations

  1. University of Minnesota, Minneapolis, MN, USA

    Shashi Shekhar

  2. Management Science and Information Systems Department, Rutgers Business School, Rutgers, The State University of New Jersey, Newark, NJ, USA

    Hui Xiong

  3. Department of Management Sciences, Tippie College of Business, University of Iowa, Iowa City, IA, USA

    Xun Zhou

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Patuelli, R. (2017). Spatial Autocorrelation and Spatial Interaction. In: Shekhar, S., Xiong, H., Zhou, X. (eds) Encyclopedia of GIS. Springer, Cham. https://doi.org/10.1007/978-3-319-17885-1_1522

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