Abstract
Analysts often ‘prioritize’ the independent variable(s) in their models in the sense that they entertain presuppositions as towhich variables are more/less important explanators of the dependent variables. The models constructed by expansions, are arrived at by redefming the parameters of an initial model into functions of expansion variables. Often these expanded models reflect a prioritization. This is the case if the initial model includes higher-priority explanators of the dependent variable(s), while the expansion variables and the terms in which they appear are lower priority refinements. Also, the initial model often articulates the primary theory that the expansions complement or widen.
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References
Anderson R.M. and May R.M. 1992., Infectious Diseases of Humans: Dynamics and Control,Oxford University Press.
Anselin L. 1988. Spatial Econometrics: Methods and Models, Dordrecht: Kluwer Academic.
Anselin L. 1992 Spatial Dependence and Spatial Heterogeneity: Model Specification Issues in the Spatial Expansion Paradigm, pp.334–354 in Applications of the Expansion Method, J.P. Jones III and E. Casetti (eds), Routledge, London and New York
Bailey N.T.J. 1957. The Mathematical Theory of Epidemics, Griffin: London
Bailey N.T.J. 1975. The Mathematical Theory of Infectious Diseases, Griffin: London Belsley D.A., Kuh E., and Welsch R.E. 1980. Regression Diagnostics: Identifying Influential Data and Sources of Collinearity, Wiley
Bowen J.L. 1994. Investigating the Relationship Between Foreign Aid and Economic Growth in Recipient Countries, Ph.D. Dissertation, UMI: Ann Arbor, Michigan
Bowen J.L. 1995. Foreign Aid and Economic Growth: An Empirical Analysis, Geographical Analysis, 27: 249–261.
Brookmeyer R. and Gail M.H. 1994. AIDS Epidemiology: A Quantitative Approach, Oxford University Press: New York Oxford
Brown D. and Rothery P. 1993. Models in Biology: Mathematics, Statistics and Computing, Wiley
Casetti E. 1972. Generating Models by the Expansion Method: Applications to Geographic Research, Geographical Analysis, 4: 81–91.
Casetti E. 1991. The Investigation of Parameter Drift by Expanded Regressions: Generalities and a ‘Family Planning’ Example, Environment and Planning A, 23: 1045–1061.
Casetti E. 1993. Spatial Analysis: Perspectives and Prospects, Urban Geography, 14: 526–537.
Casetti E. 1995. Spatial Mathematical Modeling and Regional Science, Papers In Regional Science, 74: 3–11.
Casetti E. 1996. The Expansion Method, Mathematical Modeling and Spatial Econometrics, Manuscript
Durbin J. 1953. A Note on Regression when there is Extraneous Information about One of the Coefficients, Journal of the American Statistical Association, 48: 799–808.
Fomby T.B., Hill R.C. and Johnson S.R.1984. Advanced Econometrics Methods, Springer-Verlag
Goldberger A.S. 1968. Topics in Regression Analysis,Macmillan: London Isham V. and Medley G. eds. 1996. Models for Infectious Human Deseases: Their Structure and Relation to DataCambridge University Press: Cambridge
Jewell N.P., Dietz K. and Farewell V.T. eds. 1992. AIDS Epidemiology: Methodological Issues, Birkhauser: Boston Basel Berlin
Judge G.G., Griffith W.E., Hill R.C., Lutkepohl H., and Lee T.C. 1985. The Theory and Practice of Econometrics, New York: Wiley
Kochanowski P. 1990. The Expansion Method as a Tool of Regional Analysis, Regional Science Perspectives, 20: 52–65.
Kristensen G. and Tkocz Z. 1994. The Determinants of Distance to Shopping Centers in an Urban Model Context. Journal of Regional Science, 34: 425–443.
Koutsoyiannis A. 1977. Theory of Econometrics,2nd ed. Macmillan Leamer E.E. 1983. Let’s Take the Con Out of Econometrics American Economic Review. 73:31–43
Learner E.E., 1985. Sensitivity Analyses would Help, American Economic Review, 75: 308–313.
Learner E.E. and Leonard H. 1983. Reporting the Fragility of Regression Estimates, Review of Economic and Statistics, 65: 306–317.
Levine R. and Renelt D. 1992. A Sensitivity Analysis of Cross-Country Growth Regressions, The American Economic Review. 82: 942–963.
Nagar A.L. and Kakwani N.C. 1964. The Bias and Moment Matrix of a Mixed Regression Estimator, Econometrica, 32: 389–402.
Rao C.R. and Toutenburg H. 1995. Linear Models: Least Squares and Alternatives. Springer Verlag: New York
Theil H. and Goldberger A.S. 1961. On Pure and Mixed Statistical Estimation in Economics. International Economic Review, 2: 65–78.
Theil H. 1963. On the Use of Incomplete Prior information in Regression Analysis, Journal of the American Statistical Association. 58: 401–414.
Theil H. 1971. Principles of Econometrics,Wiley
Toutenburg H. 1982. Prior Information in Linear Models Wiley
Vinod H.D. and Ullah A. 1981. Recent Advances in Regression Methods, Dekker: New York
Yancey T.A. Judge G.G. and Bock M.E. 1974. A Mean Square Error Test When Stochastic Restrictions Are Used in Regression, Communications in Statistics, 3: 755–768.
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Casetti, E. (1997). Mixed Estimation and the Expansion Method: An Application to the Spatial Modelling of the AIDS Epidemic. In: Fischer, M.M., Getis, A. (eds) Recent Developments in Spatial Analysis. Advances in Spatial Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03499-6_2
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