Abstract
Regional analysts are often faced with the task of forecasting future flows. The ability to carry out such a task is often limited to a reliance on either a Markovian assumption or other techniques that use only one or two observed flow matrices. This paper explores alternative methods that may be used to combine the information contained in an observed temporal sequence of flow matrices. Information theoretic principles, lag structures, and constant causative matrix operators are among the techniques discussed. These methods are applied and evaluated using inter-regional migration flow data for the United States.
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References
Bartholomew, D. 1973.Stochastic models for social processes. New York: John Wiley.
Batty, M. and March, L. 1976. The method of residues in urban modelling.Environment and Planning A 8: 189–214.
Blumen, I., Kogan, M. and McCarthy, P. 1955.The industrial mobility of labor as a probability process. Cornell Studies of Industrial and Labor Relations, Volume 6. Ithaca: Cornell University Press.
Collins, L. 1972.Industrial migration in Ontario: forecasting aspects of industrial activity through Markov chain analysis. Catalogue 31–509, Ottawa: Statistics Canada.
Engels, R. and Healy, K. 1981. Measuring interstate migration flows: an origin-destination network based on Internal Revenue Service records.Environment and Planning A 13: 1345–60.
Fotheringham, A. S. 1983a. A new set of spatial interaction models: the theory of competing destinations.Environment and Planning A 15: 15–36.
Fotheringham, A. S. 1983b. Some theoretical aspects of destination choice and their relevance to production-constrained gravity models.Environment and Planning A 15: 1121–32.
Gale, S. 1972. Stochastic stationarity and the analysis of geographical mobility.Papers Presented to the 22nd International Congress of the International Geographical Union, ed. P. Adams and F. Helleinen Montreal: University of Toronto Press.
Harary, F., Lipstein, B. and Styan, G. 1970. A matrix approach to nonstationary chains.Operations Research 18: 1168–81.
Haynes, K. E. and Phillips, F. Y. 1982. Constrained minimum-discrimination-information: a unifying tool for modeling spatial and individual choice behavior.Environment and Planning A 14: 1341–54.
Isserman, A., Plane, D. and McMillen, D. 1982. Internal migration in the United States: an evaluation of federal data.Review of Public Data Use 10: 285–311.
Knudsen, D. 1983. An analysis of temporal evolution in a spatial interaction system: a new look at U.S. commodity flows. Paper presented at the Annual Meeting of the Association of American Geographers, Denver, Colorado.
Kullback, S. 1959.Information theory and statistics. New York: John Wiley.
Ledent, J. 1978. Stable growth in the nonlinear components-of-change model of interregional population growth and distribution. RM-78-28, International Institute for Applied Systems Analysis, Laxenburg, Austria.
Lipstein, B. 1968. Test marketing: a perturbation in the market place.Management Science Series B 14: 437–48.
McFarland, D. 1970. Intra-generational social mobility as a Markov process: including a time-stationary Markovian model that explains observed declines in mobility rates over time.American Sociological Review 35: 463–76.
Plane, D. 1982. An information theoretic approach to the estimation of migration flows.Journal of Regional Science 22: 441–56.
Pullman, N. and Styan, G. 1973. The convergence of Markov chains with nonstationary transition probabilities and constant causative matrix.Stochastic Processes and Their Applications 1: 279–85.
Rogers, A. 1967. Estimating interregional population and migration operators from interregional population distributions.Demography 4: 515–31.
Rogers, A. and von Rabenau, B. 1970. Estimation of interregional in- and out-migration flows from place-of-birth-by-residence data. Working Paper Number 127, Institute of Urban and Regional Development, University of California, Berkeley.
Rogerson, P. 1979. Prediction: a modified Markov chain approach.Journal of Regional Science 19: 469–78.
Shannon, C. E. and Weaver, W. 1949.The mathematical theory of communication. Urbana: University of Illinois Press.
Singer, G. and Spilerman, S. 1979. Clustering on the main diagonal in mobility matrices. InSociological Methodology ed. K. Schuessler, pp. 172–208. San Francisco: Jossey-Bass.
Snickars, F. and Weibull, J. 1977. A minimum information principle: theory and practice.Regional Science and Urban Economics 7: 137–68.
Spilerman, S. 1972. The analysis of mobility processes by the introduction of independent variables into a Markov Chain.American Sociological Review 37: 277–94.
U.S. Bureau of the Census. 1977. Geographical mobility: March 1975 to March 1976.Current Population Reports P-20, Number 305.
U.S. Bureau of the Census. 1978a.The Current Population Survey: Design and Methodology. Technical Paper 40.
U.S. Bureau of the Census. 1978b. Geographical mobility: March 1975 to March 1977.Current Population Reports P-20, Number 320.
U.S. Bureau of the Census. 1979. Geographical mobility: March 1975 to March 1978.Current Population Reports P-20, Number 331.
U.S. Bureau of the Census. 1980. Geographical mobility: March 1975 to March 1979.Current Population Reports P-20, Number 353.
U.S. Bureau of the Census. 1981. Geographical mobility: March 1975 to March 1980.Current Population Reports P-20, Number 368.
U.S. Bureau of the Census. 1983. Geographical mobility: March 1980 to March 1981.Current Population Reports P-20, Number 377.
Vining, D. 1975. The spatial distribution of human populations and its characteristic evolution over time: some recent evidence from Japan.Papers of the Regional Science Association 35: 157–78.
Webber, M. J. 1979.Information theory and urban spatial structure. London: Croom Helm.
White, H. 1970.Chains of opportunity. Cambridge, Massachusetts: Harvard University Press.
Willekens, F. and Rogers, A. 1978.Spatial population analysis: methods and computer programs. Research report 78-18, Laxenburg, Austria: International Institute for Applied Systems Analysis.
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Rogerson, P.A., Plane, D.A. Modeling temporal change in flow matrices. Papers of the Regional Science Association 54, 147–164 (1984). https://doi.org/10.1007/BF01940130
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DOI: https://doi.org/10.1007/BF01940130