References
W. W. Bunge, Jr.,Theoretical Geography (Lund: Gleerup, 1963), p. 151. Emphasis in Bunge's work is on comparisons of observed patterns with theoretically derived patterns.
R. Bachi, “Standard Distance Measures and Related Methods for Spatial Analysis,”Papers of the Regional Science Association, X (1962), pp. 83–132.
D. Neft, “Statistical Analysis for Areal Distributions,” Ph. D. thesis, Columbia University, 1962, 286 pp.
H. H. McCarty,et al, “The Measurement of Association in Industrial Geography,” Department of Geography, State University of Iowa, 1956, mimeographed.
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A. H. Robinson and R. A. Bryson, “A Method for Describing Quantitatively the Correspondence of Geographical Distributions,”Annals, Association of American Geographers, XXXXVII (1957), pp. 379–91.
Ordinary correlation, of course, also requires such a priori pairings. Bachi,op. cit. “, p. 122, comments on a possible strategy in cases for which a natural pairing does not exist.
Aside from the obvious ecological situations, see the biological mappings given in D'Arcy W. Thompson,On Growth and Form (Bonner Abridgement), (Cambridge: University Press), 1961, pp. 268–325.
The formulation in terms of complex variables can be traced to C. F. Gauss. Also see: M. Masuamya, “Correlation between Tensor Quantities,”Proceedings, Physico-Mathematical Society of Japan, 3rd Series, XXI (1939), pp. 638–47.
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Nearest neighbor methods have also been employed for such comparisons; see M. F. Dacey, “Order Neighbor Statistics for a Class of Random Patterns in Multidimensional Space,”Annals, Association of American Geographers, LIII, 4 (1963), pp. 505–15.
See Court,op. cit., A. Court, “Wind Correlation and Regression,”Scientific Report #3, United States Air Force Contract 19 (604)-2060, AFCRC TN-58-230 (1958), 16 pp. and Lenhard,et al,op. cit. R. W. Lenhard, Jr., A. Court, and H. Salmela, “Reply,”Journal of Applied Meteorology, II, 6 (1963), pp. 812–15.
Court,op. cit. A. Court, “Wind Correlation and Regression,”Scientific Report #3, United States Air Force Contract 19 (604)-2060, AFCRC TN-58-230 (1958), 16 pp.
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Ellison,op. cit.“, p. 95 gives the treatment for vectors. The conformal transformation defined by a complex polynomial is employed in photogrammetry; see G. H. Schut, “Development of Programs for Strip and Block Adjustment at the National Research Council of Canada,”Photogrammetric Engineering, XXX, 2 (1964), pp. 283–91. Bunge has suggested as geographically interesting a least squares approach to the problem of forcing distributions into Christaller's hexagonal central place pattern. A differential equation defining the restrictions on the transformation for this problem is given in W. R. Tobler, “Geographical Area and Map Projections,”The Geographical Review, LIII, 1 (1963), pp. 59–78.
This is not strictly true. See R. L. Miller and J. S. Kahn,Statistical Analysis in the Geological Sciences (New York: John Wiley & Sons, 1962), p. 204.
Ellison,op. cit.“, p. 95.
W. Isard,Methods of Regional Analysis (New York: John Wiley & Sons, 1960).
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The author is indebted to Professors W. Bunge, Jr., A. Court, and J. Nystuen for discussions of this topic and for pointing out errors in an earlier version of this paper.
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Tobler, W.R. Computation of the correspondence of geographical patterns. Papers of the Regional Science Association 15, 131–139 (1965). https://doi.org/10.1007/BF01947869
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DOI: https://doi.org/10.1007/BF01947869