The Interaction Model and Relative Location Variables

References

• Three reviews cover the relevant background literature: Gerald A. P. Carrothers. “An Historical Review of the Gravity and Potential Concepts of Human Interaction,” Journal A. I. P., XXII (1956), 94–102.
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• Walter Isard et al., Methods of Regional Analysis; an Introduction to Regional Science (Cambridge, Massachusetts: The M. I. T. Press 1960), Chapter II.
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• Gunnar Olsson, Distance and Human Interaction—A Review and Bibliography (Regional Science Research Institute, Philadelphia, Penn. Bibliography Series Number Two, 1965).
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• Peter Haggett, Locational Analysis in Human Geography (London: Edward Arnold (Publishers) Ltd., 1965), 40–47.
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• Claes-Fredrik Claeson, “En Korologisk Publikanalys” Geografiska Annaler, 46 (1964), 1–130, and “A Two- Stage Model of In-Migration To Urban Centres: Deductive Development of a Variant of the Gravity Formulation,” Geografiska Annaler, 51B (1969), 127–138.
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• Olof Wärneryd, Interdependence in Urban Systems (Göteborg: Regionkonsult Aktiebolag, 1968).
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• Stuart Carter Dodd, “The Interactance Hypothesis. A Gravity Model Fitting Physical Masses and Human Groups,” American Sociological Review, 15 (1950), 245–56.
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• J. Ross Mackay, “The Interactance Hypothesis and Boundaries in Canada: A Preliminary Study,” Canadian Geographer, 11 (1958), 1–8.
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• James W. Simmons, Interprovincial Interaction Patterns in Canada (Research Paper No. 24, Centre for Urban and Community Studies, University of Toronto, 1970).
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• John N. H. Britton, Regional Analysis and Econmoic Geography (London: G. Bell and Sons, Ltd., 1967).
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• Patrick L. O'Sullivan, “Variations in Distance Friction in Great Britain,” Area, 2(1970), 36–39, it is to be noted that frictional exponents in this work vary appreciably from those in Martin Frost, Distribution Costs as a Factor in a Location of Industry Policy (London: London School of Economics and Political Science, Graduate School of Geography Discussion Paper No. 24, 1969).
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• Hans Linnemann, An Econometric Study of International Trade Flows (Amsterdam: North-Holland Publishing Co., 1966).
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• Robert N. Taaffe, “Interregional Passenger Movement in the Soviet Union,” The East Lakes Geographer, 3 (1967), 47–79.
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• Dyad is used here to refer to the existence of interaction between a pair of places; such a link, Tij, is distinguished from Tji (though these may be of equal flow value) on a directional basis. See Berry, “A Synthesis of Formal and Functional Regions using a General Field Theory of Spatial Behavior,” in Brian J. L. Berry and Duane F. Marble, Spatial Analysis (Englewood Cliffs, N. J.: Prentice-Hall, Inc., 1968), p. 420.
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• While linear programming models of flow systems—particularly The Transportation Problem—are truly systemic in character they are excluded from consideration here owing to their concern not with replicating (predicting) an existing flow structure in terms of a small number of parameters but with deriving an optimal set of flows.
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• S. A. Stouffer, “Intervening Opportunities: A Theory Relating Mobility and Distance,” American Sociological Review, V (1940), pp. 845–867 and, “Intervening Opportunities and Competing Migrants,” Journal of Regional Science, II (1960), pp. 1–26. See also Fred Strodtbeck, “Population Distance and Migration from Kentucky,” Sociometry, XIII (1950), pp. 123–130, and D. Michael Ray, Market Potential and Economic Shadow (Chicago, Illinois: Univeristy of Chicago, Department of Geography, Research Paper No. 101, 1965), 111–113.
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• Wallace E. Reed, Areal Interaction in India (Chicago, Illinois: University of Chicago, Dept. of Geography, Research Paper No. 110, 1967).
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• George W. Greenwood, Traffic Linkage Patterns between a Metropolitan Area and the Communities within its Region of Influence (University of Illinois, College of Engineering, Bulletin 488).
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• David L. Huff and Larry Blue, A Programmed Solution for Estimating Retail Sales Potentials Lawrence, Kansas: University of Kansas, Center for Regional Studies, no date).
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• Information on road movements has been obtained from a 107 × 107 zonal flow matrix originally compiled by the Ministry of Transport. The enquiry that produced the data for the matrix “covered four separate weeks in the period April, 1962 to January, 1963. A sample of vehicles was drawn for each survey week”. The sample enquiry results were expanded to provide annual estimates of the tonnage of goods moved by road transport—see Ministry of Transport, Survey of Road Goods Transport, 1962—Final Results, Part I (Statistical Paper No. 2, London: Her Majesty's Stationery Office, 1964). The forming of the regions was also influenced by the shape of the original survey zones that were amalgamated and by the structure of zones used in a rail survey: these data have been used with the road flow information in another investigation.
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• In 6 equations (of 92) the ratio of the population regression coefficient/standard error of the coefficient drops to the level of t expected at 0.1 probability, and in one instance, Southwest Wales, the population variable in both origin and destination equations contribute little to the relatively low levels of explanation. The two relevant equations produced coefficients of multiple determination of 0.46 and 0.59 for outflow and inflow vectors, respectively. This may be interpreted as a reflection of the low order of suitability of this variable to measure aggregate demand and supply for a region whose industrial structure is so dominated by petroleum refining (Milford Haven). Despite this problem the region is retained in subsequent calculations made for the flow matrix so that the analysis of connections in the system is complete.
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• Leslie Curry, in “Gravity Flows and Location: a Discussion”, mimeo, (Toronto: University of Toronto, 1969) is particularly concerned with this phenomenon.
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• The correlations between the three independent variables of equation (10) are as follows.
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• Correlations between the relative locative location variables and the other independent variables in equation (12) are as follows.
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• See footnote 3.
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• Edward J. Taaffe, “Air Transportation and United States Urban Distribution,” Geogr. Rev. 46 (1956), 219–238.
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