Journal of Geographical Systems

, Volume 10, Issue 4, pp 317–344 | Cite as

Modeling network autocorrelation within migration flows by eigenvector spatial filtering

Original Article

Abstract

Although the assumption of independence among interaction flows frequently is engaged in spatial interaction modeling, in many circumstances it leads to misspecified models and incorrect inferences. An informed approach is to explicitly incorporate an assumed relationship structure among the interaction flows, and to explicitly model the network autocorrelation. This paper illustrates such an approach in the context of U.S. interstate migration flows. Behavioral assumptions, similar to those of the intervening opportunities or the competing destinations concepts, exemplify how to specify network flows that are related to particular origin–destination combinations. The stepwise incorporation of eigenvectors, which are extracted from a network link matrix, captures the network autocorrelation in a Poisson regression model specification context. Spatial autocorrelation in Poisson regression is measured by the test statistic of Jacqmin-Gadda et al. (Stat Med 16(11):1283–1297, 1997). Results show that estimated regression parameters in the spatial filtering interaction model become more intuitively interpretable.

Keywords

Network autocorrelation Spatial filtering Spatial interaction Eigenvector Migration 

JEL Classification

C21 R23 

Notes

Acknowledgments

The author thanks Michael Tiefelsdorf for useful comments on this research, and anonymous reviewers for their comments and suggestions.

References

  1. Almeida LMW, Goncalves MB (2001) A methodology to incorporate behavioral aspects in trip-distribution models with an application to estimate student flow. Environ Plan A 33(6):1125–1138CrossRefGoogle Scholar
  2. Anselin L, Griffith DA (1988) Do spatial effects really matter in regression analysis? Papers Reg Sci Assoc 65:11–34CrossRefGoogle Scholar
  3. Assuncao RM, Reis EA (1999) A new proposal to adjust Moran’s I for population density. Stat Med 18:2147–2162CrossRefGoogle Scholar
  4. Baxter M (1983) Estimation and inference in spatial interaction models. Progr Hum Geogr 7:40–59Google Scholar
  5. Berglund S, Karlstrom A (1999) Identifying local spatial association in flow data. J Geogr Syst 1(3):219–236CrossRefGoogle Scholar
  6. Black WR (1992) Network autocorrelation in transport network and flow systems. Geogr Anal 24(3):207–222Google Scholar
  7. Bolduc D, Dagenais MG, Gaudry MJI (1989) Spatially autocorrelated errors in origin–destination models: a new specification applied to aggregate mode choice. Transp Res Part B 23(5):361–372CrossRefGoogle Scholar
  8. Boots BN, Kanaroglou PS (1988) Incorporating the effects of spatial structure in discrete choice models of migration. J Reg Sci 28(4):495–509CrossRefGoogle Scholar
  9. Cadwallader MT (1992) Migration and residential mobility: macro and micro approaches. University of Wisconsin Press, MadisonGoogle Scholar
  10. Congdon P (1992) Aspects of general linear modelling of migration. Statistician 41:133–153CrossRefGoogle Scholar
  11. Congdon P (1993) Approaches to modelling overdispersion in the analysis of migration. Environ Plan A 25(10):1481–1510CrossRefGoogle Scholar
  12. Congdon P (2002a) A Bayesian approach to prediction using the gravity model with an application to patient flow modeling. Geogr Anal 32(3):205–224Google Scholar
  13. Congdon P (2002b) A model for mental health needs and resourcing small geographic areas: a multivariate spatial perspective. Geogr Anal 34(2):169–186CrossRefGoogle Scholar
  14. Cressie N, Chan HH (1989) Spatial modeling of regional variables. J Am Stat Assoc 84(405):393–401CrossRefGoogle Scholar
  15. Cushing BJ (1987) Location-specific amenities, topography, and population migration. Ann Reg Sci 21:74–85Google Scholar
  16. Davies PS, Greenwood MJ, Li H (2001) A conditional logit approach to U.S. state-to-state migration. J Reg Sci 41(2):337–360CrossRefGoogle Scholar
  17. de Jong P, Sprenger C, van Veen F (1984) On extreme values of Moran’s I and Geary’s C. Geogr Anal 16(1):17–24Google Scholar
  18. Fik TJ, Amey RG, Mulligan GF (1992) Labor migration amongst hierarchically competing and intervening origins and destinations. Environ Plan A 24:1271–1290CrossRefGoogle Scholar
  19. 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 (forthcoming)Google Scholar
  20. Flowerdew R (1991) Poisson regression modelling of migration. In: Stillwell J, Congdon P (eds) Migration models: macro and micro approaches. Belhaven, New York, pp 92–112Google Scholar
  21. Flowerdew R, Aitkin M (1982) A method of fitting the gravity model based on the Poisson distribution. J Reg Sci 22(2):191–202CrossRefGoogle Scholar
  22. Flowerdew R, Lovett A (1988) Fitting constrained Poisson regression models to inter-urban migration. Geogr Anal 20(4):297–307Google Scholar
  23. Fotheringham AS (1983) A new set of spatial-interaction models: the theory of competing destinations. Environ Plan A 15(1):15–36CrossRefGoogle Scholar
  24. Fotheringham AS (1986) Modelling hierarchical destination choice. Environ Plan A 18(3):401–418CrossRefGoogle Scholar
  25. Fotheringham AS (1991) Migration and spatial structure: the development of the competing destination model. In: Stillwell J, Congdon P (eds) Migration models: macro and micro approaches. Belhaven, New York, pp 57–72Google Scholar
  26. Fotheringham AS, O’Kelly ME (1989) Spatial interaction models: formulations and applications. Kluwer Academic Publishers, DordrechtGoogle Scholar
  27. Galle OR, Taeuber KE (1966) Metropolitan migration and intervening opportunities. Am Sociol Rev 31(1):5–13CrossRefGoogle Scholar
  28. Getis A (1990) Screening for spatial dependence in regression analysis. Papers Reg Sci Assoc 69:69–81CrossRefGoogle Scholar
  29. Getis A (1995) Spatial filtering in a regression framework: examples using data on urban crime, regional inequality, and government expenditures. In: Anselin L, Florax RJGM (eds) New directions in spatial econometrics. Springer, Berlin, pp 172–188Google Scholar
  30. Getis A, Griffith DA (2002) Comparative spatial filtering in regression analysis. Geogr Anal 34(2):130–140CrossRefGoogle Scholar
  31. Gleave D, Cordey-Hayes M (1977) Migration dynamics and labor market turnover. Prog Plan 8(1):1–95CrossRefGoogle Scholar
  32. Greenwood MJ (1985) Human migration: theory, models, and empirical studies. J Reg Sci 25(4):521–544CrossRefGoogle Scholar
  33. Griffith DA (1996) Spatial autocorrelation and eigenfunctions of the geographic weights matrix accompanying geo-reference data. Can Geogr 40(4):351–367CrossRefGoogle Scholar
  34. Griffith DA (2000) A linear regression solution to the spatial autocorrelation problem. J Geogr Syst 2(2):141–156CrossRefGoogle Scholar
  35. Griffith DA (2002) A spatial filtering specification of the auto-Poisson model. Stat Probab Lett 58(3):245–251CrossRefGoogle Scholar
  36. Griffith DA (2003) Spatial autocorrelation and spatial filtering: gaining understanding through theory and scientific visualization. Springer, BerlinGoogle Scholar
  37. Griffith DA (2004) A spatial filtering specification for the autologistic model. Environ Plan A 36(10):1791–1811CrossRefGoogle Scholar
  38. Griffith DA (2006) Hidden negative spatial autocorrelation. J Geogr Syst 8(4):335–355CrossRefGoogle Scholar
  39. Griffith DA (2007) Spatial structure and spatial interaction: 25 years later. Rev Reg Stud 37(1):28–38Google Scholar
  40. Guldmann JM (1999) Competing destinations and intervening opportunities interaction models of inter-city telecommunication. Papers Reg Sci 78(2):179–194CrossRefGoogle Scholar
  41. Haining R (1991) Bivariate correlation and spatial data. Geogr Anal 23(3):210–227Google Scholar
  42. Haining R (2003) Spatial data analysis: theory and practice. Cambridge University Press, CambridgeGoogle Scholar
  43. Hanson GH (1998) North American economic integration and industry location. Oxford Rev Econ Policy 14:30–44CrossRefGoogle Scholar
  44. Harary F (1999) Graph theory. Perseus Books, Reading, MAGoogle Scholar
  45. Homes JH, Haggett P (1977) Graph theory interpretation of flow matrices: a note on maximization procedures for identifying significant links. Geogr Anal 9(4):388–399Google Scholar
  46. Jacqmin-Gadda H, Commenges D, Nejjari C, Dartigues JF (1997) Tests of geographical correlation with adjustment for explanatory variables: an application to Dyspnoea in the elderly. Stat Med 16(11):1283–1297CrossRefGoogle Scholar
  47. Jayet H (1990) Spatial search processes and spatial interaction. 1. Sequential search, intervening opportunities, and spatial search equilibrium. Environ Plan A 22(5):583–599CrossRefGoogle Scholar
  48. Law J, Haining R (2004) Bayesian approach to modeling binary data: the case of high-intensity crime analysis. Geogr Anal 36(3):197–216CrossRefGoogle Scholar
  49. Liao PS (2001) Contextual analysis of rural migration intention: a comparison of Taiwanese and Pennsylvania data. Int J Comp Sociol 42(5):435–460CrossRefGoogle Scholar
  50. 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):293–310CrossRefGoogle Scholar
  51. Myers RH, Montgomery DC, Vining GG (2002) Generalized linear models with applications in engineering and the sciences. Wiley, New YorkGoogle Scholar
  52. Mulder CH, Hooimeijer P (1999) Residential relocations in the life course. In: van Wissen LJG, Dykstra PA (eds) Population issues: an interdisciplinary focus. Kluwer Academic Press, New York, pp 159–186Google Scholar
  53. Nelder JA, Wedderburn RWM (1972) Generalized linear models. J R Stat Soc Ser A 35(3):370–384Google Scholar
  54. Newbold KB (2005) Spatial scale, return and onward migration, and the Long-Boertlein index of repeat migration. Papers Reg Sci 84(2):281–290CrossRefGoogle Scholar
  55. Oden N (1995) Adjusting Moran’s I for population density. Stat Med 14(1):17–26CrossRefGoogle Scholar
  56. Plane DA (1984) Migration space: doubly constrained gravity model mapping of relative interstate separation. Ann Assoc Am Geogr 74(2):244–245CrossRefGoogle Scholar
  57. Prentice RL, Zhao LP (1991) Estimating equations for parameters in means and covariances of multivariate discrete and continuous responses. Biometrics 47(3):825–839CrossRefGoogle Scholar
  58. Ruiter ER (1967) Toward a better understanding of the intervening opportunities model. Transp Res 1:47–56CrossRefGoogle Scholar
  59. Shaw RP (1985) Intermetropolitan migration in Canada: changing determinants over three decades. NC Press, TorontoGoogle Scholar
  60. Schabenberger O, Gotway CA (2005) Statistical methods for spatial data analysis. Chapman & Hall/CRC, Boca RatonGoogle Scholar
  61. Schwartz A (1973) Interpreting the effects of distance on migration. J Polit Econ 81(5):1153–1169CrossRefGoogle Scholar
  62. Shvetsov VI, Dubov YA (1997) Expected distributions in the intervening opportunities model. Environ Plan A 29(7):1229–1241CrossRefGoogle Scholar
  63. Stouffer SA (1940) Intervening opportunities: a theory relating mobility and distance. Am Sociol Rev 5(6):845–867CrossRefGoogle Scholar
  64. Stouffer SA (1960) Intervening opportunities and competing migrants. J Reg Sci 2(1):1–26Google Scholar
  65. Tiefelsdorf M (2000) Modelling spatial processes: the identification and analysis of spatial relationships in regression residuals by means of Moran’s I. Springer, BerlinGoogle Scholar
  66. Tiefelsdorf M (2003) Misspecifications in interaction model distance decay relations: a spatial structure effect. J Geogr Syst 5(1):25–50CrossRefGoogle Scholar
  67. Tiefelsdorf M, Boots BN (1995a) The exact distribution of Moran’s I. Environ Plan A 27(6):985–999CrossRefGoogle Scholar
  68. Tiefelsdorf M, Boots BN (1995b) The specification of constrained interaction models using the SPSS Loglinear procedure. Geogr Syst 2(1):21–38Google Scholar
  69. Tiefelsdorf M, Griffith DA (2007) Semiparametric filtering of spatial autocorrelation: the eigenvector approach. Environ Plan A 39(5):1193–1221CrossRefGoogle Scholar
  70. Tiefelsdorf M, Griffith DA, Boots BN (1999) A variance-stabilizing coding scheme for spatial link matrices. Environ Plan A 31(1):165–180CrossRefGoogle Scholar
  71. US Department of Commerce (2002) National Oceanic and Atmospheric Administration, Environmental Data and Information Service. State, regional, and national monthly temperature (weighted by area), 1971–2000 (and previous normals periods). National Climatic Data Center, AshevilleGoogle Scholar
  72. Wakefield JC (2003) Sensitivity analyses for ecological regression. Biometrics 59(1):9–17CrossRefGoogle Scholar
  73. Wakefield JC, Best NG, Waller LA (2000) Bayesian approaches to disease mapping. In: Elliott P, Wakefield J, Best NG, Briggs DJ (eds) Spatial epidemiology: method and application. Oxford University Press, Oxford, pp 104–127Google Scholar
  74. Waldhör T (1996) The spatial autocorrelation coefficient Moran’s I under heteroscedasticity. Stat Med 15(7–9):887–892CrossRefGoogle Scholar
  75. Wilson AG (1970) Entropy in urban and regional modelling. Pion Limited, LondonGoogle Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.School of Economic, Political and Policy SciencesThe University of Texas at DallasRichardsonUSA

Personalised recommendations