Abstract
A cross-product statistic is used to demonstrate that spatial interaction models are a special case of a general model of spatial autocorrelation. A series of traditional measures of spatial autocorrelation is shown to have a cross-product form. Several interaction models are shown to have a similar form. A general spatial statistic is developed which indicates that the relationship between the two types of models is particularly strong when the focus is on measurements from a single point.
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References
Anselin L (1988) Spatial econometrics: methods and models. Kluwer, Dordrecht
Cliff AD, Ord JK (1969) The problem of spatial autocorrelation. In: Scott A (ed) Studies in regional science. Pion, London, pp 25–55
Cliff AD, Ord JK (1973) Spatial autocorrelation. Pion, London
Fotheringham AS (1983) A new set of spatial-interaction models: the theory of competing distances. Environ Plan A 15:15–36
Geary RC (1954) The contiguity ratio and statistical mapping. Inc Stat 5:115–145
Getis A (1984) Interaction modeling using second-order analysis. Environ Plan A 16:173–183
Getis A, Ord JK (1992) The analysis of spatial association by use of distance statistics. Geogr Anal 24:189–206
Haining RP (1977) Model specification in stationary random fields. Geogr Anal 9:107–129
Haining RP (1978) Estimating spatial-interaction models. Environ Plan A 10:305–320
Haynes KE, Fotheringham AS (1984) Gravity and spatial interaction models. Sage, Newbury Park, CA
Hubert L (1977) Generalized proximity function comparisons. Br J Math Stat Psychol 31:179–182
Hubert L, Golledge RG (1982) Measuring association between spatially defined variables: Tjostheim’s index and some generalizations. Geogr Anal 14:273–278
Hubert L, Golledge RG, Costanzo C (1981) Generalized procedures for evaluating spatial autocorrelation. Geogr Anal 13:224–233
Moran PAP (1948) The interpretation of statistical maps. J R Stat Soc B 10:243–251
Ord JK (1975) Estimation methods for models of spatial interaction. J Am Stat Assoc 70:120–126
Tobler WR (1983) An alternate formulation for spatial-interaction modeling. Environ Plan A 15:693–703
Whittle P (1954) On stationary processes in the plane. Biometrika 41:434–449
Wilson A (1970) Inter-regional commodity flows: entropy maximizing approaches. Geogr Anal 3:255–282
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Getis, A. (2010). Spatial Interaction and Spatial Autocorrelation: A Cross-Product Approach. In: Anselin, L., Rey, S. (eds) Perspectives on Spatial Data Analysis. Advances in Spatial Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01976-0_2
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DOI: https://doi.org/10.1007/978-3-642-01976-0_2
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