The General Linear Model and Spatial Autoregressive Models

  • Daniel A. Griffith
Part of the Advances in Spatial Science book series (ADVSPATIAL)

Abstract

Specific instances of the general linear model (GLM) have already been implemented within spatial statistics. Griffith (1978) summarizes how to write the simple one- way ANOVA model in the presence of spatial autocorrelation, more recently extending this to N-way ANOVA and unbalanced designs [Griffith (1992b)]. This recent article highlights the need for more work on mixed and random effects unbalanced design models, which is the case in traditional statistics as well. Griffith (1979) describes how to write the one-way MANOVA model for geo-referenced data, more recently extending this to N-way MANOVA and unbalanced designs [Griffith (1992b)], too. His initial findings in this case are consistent with the perspective promoted by Haining (1991). Griffith (1989) has also outlined spatial Statistical two-groups discriminant function analysis and ANCO VA models [see also Anselin (1988), for a spatial econometric implementation of this latter model]. Other attempts along these lines are found in Switzer (1985), who has devised a spatial principal components analysis, Mardia (1988) and Griffith (1988), who have constructed multivariate geo-referenced data models, and Wartenberg (1985), who has formulated a cross-Moran Coefficient (cross-MC). And, Cressie and Hilterbrand (1993) have studied the problem of multivariate geo-statistics. What remains explicitly unaddressed is treatment of canonical correlation, and a spatial Statistical fc-groups discriminant function analysis model (which should relate to the eigenvectors of the aforementioned spatially adjusted MANOVA model).

Keywords

Covariance Turkey Autocorrelation Prefix Estima 

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References

  1. Anselin, L.,Spatial Econometrics: Methods and Models, Dordrecht: Kluwer, 1988.Google Scholar
  2. Anselin, L., Moran Scatterplots as a Means to Visualize Instability in Spatial Autocorrelation, in:Position Papers: NCGIA Exploratory Spatial Data Analysis and GIS Workshop, Santa Barbara, 1993.Google Scholar
  3. Arbia, G .,Using Spatial Data to Characterize Short-term Dynamic Economic Models, paper presented to the annual North American Regional Science Association meetings, Santa Barbara, 1989.Google Scholar
  4. Barnett, V. and T. Lewis,Outliers in Statistical Data, New York: Wiley, 1984 (2nd ed.).Google Scholar
  5. Belsley, D., E. Kuh and R. Welsch,Regression Diagnostics, New York: Wiley, 1980.CrossRefGoogle Scholar
  6. Cliff, A. and J. Ord,Spatial Processes, London: Pion, 1981.Google Scholar
  7. Cressie, N. and J. Hilterbrand,Multivariate Spatial Statistics in a GIS, Iowa State University, Department of Statistics, 1993 (mimeo).Google Scholar
  8. Emerson, J. and M. Stoto, Transforming Data, in: D. Hoaglin, F. Mosteller and J. Turkey (eds.),Understanding Robust and Exploratory Data Analysis, New York: Wiley, 1983.Google Scholar
  9. Gastel, M. van and J. Paelinck, Computation of Box-Cox Transform Parameters: A New Method and its Applications to Spatial Econometrics, 1995 (this issue).Google Scholar
  10. Griffith, D., A Spatially Adjusted ANOVA Model,Geographical Analysis, 10, 296–301, 1978.CrossRefGoogle Scholar
  11. Griffith, D., Urban Dominance, Spatial Structure and Spatial Dynamics: Some Theoretical Conjectures and Empirical Implications,Economic Geography, 55, 95–113, 1979.CrossRefGoogle Scholar
  12. Griffith, D.,Advanced Spatial Statistics, Dordrecht: Kluwer, 1988.CrossRefGoogle Scholar
  13. Griffith, D.,Spatial Regression Analysis on the PC: Spatial Statistics Using MINITAB, Ann Arbor, Michigan: Institute of Mathematical Geography, Discussion Paper #1, 1989.Google Scholar
  14. Griffith, D., What is Spatial Autocorrelation? Reflections on the Past 25 Years of Spatial Statistics,l’Espace Geographique, 21, 265–280, 1992a.Google Scholar
  15. Griffith, D., A Spatially Adjusted N-way ANOVA Model,Regional Science and Urban Economics, 22, 347–369, 1992b.CrossRefGoogle Scholar
  16. Griffith, D., Simplifying the Normalizing Factor in Spatial Autoregressions for Irregular Lattices,Papers in Regional Science, 71, 71–86, 1992c.CrossRefGoogle Scholar
  17. Griffith, D., Estimating Missing Values in Spatial Urban Census Data,The Operational Geographer, 10, 23–26, 1992d.Google Scholar
  18. Haining, R., Bivariate Correlation with Spatial Data,Geographical Analysis, 23, 210–227, 1991.CrossRefGoogle Scholar
  19. Haining, R., D. Griffith and R. Bennett, A Statistical Approach to the Problem of Missing Spatial Data Using a First-Order Markov Model,The Professional Geographer, 36, 338–345, 1984.CrossRefGoogle Scholar
  20. Johnson, R. and D. Wichern,Applied Multivariate Statistical Analysis, Englewood Cliffs: Prentice Hall, 1992 (3rd ed.).Google Scholar
  21. Little, R. and D. Rubin,Statistical Analysis with Missing Data, New York: Wiley, 1987.Google Scholar
  22. Mardia, K., Multi-Dimensional Multivariate Gaussian Markov Random Fields with Application to Image Processing,Journal of Multivariate Analysis, 24, 265–284, 1988.CrossRefGoogle Scholar
  23. Rousseeuw, P. and A. Leroy,Robust Regression & Outlier Detection, New York: Wiley, 1987.CrossRefGoogle Scholar
  24. Switzer, P., MIN/MAX Autocorrelation Factors for Multivariate Spatial Imagery, in: L. Billard (ed.),Computer Science and Statistics: The Interface, Amsterdam: North-Holland, 1985.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Daniel A. Griffith
    • 1
  1. 1.Syracuse UniversitySyracuseUSA

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