Abstract
The structural assumptions embedded in a particular form of a spatial connectivity or dependence matrix are often not explicitly treated in the statistical analysis of mixed regressive-spatial autoregressive models. This paper sees the evaluation of different structures as an application of tests on non-nested hypotheses. Several recently developed statistics are outlined and their appropriateness for spatial analysis discussed. The tests are illustrated empirically in simple models that incorporate spatial spill-over effects in the explanation of urban housing value.
Similar content being viewed by others
References
Aguirre-Torres, Victor and Gallant, A. Ronald. 1983. The null and non-null asymptotic distribution of the Cox test for multivariate nonlinear regression: alternatives and a new distribution-free Cox test.Journal of Econometrics 21, 1: 5–33.
Akaike, Hirotogu. 1981. Likelihood of a model and information criteria.Journal of Econometrics 16, 1: 3–14.
Anselin, Luc. 1980.Estimation methods for spatial autoregressive structures, Ithaca, NY: Regional Science Dissertation and Monograph Series #8, Cornell University.
Anselin, Luc. 1982. A note on small sample properties of estimators in a first-order spatial autoregressive model.Environment and Planning A 14, 8: 1023–30.
Anselin, Luc. 1983.A modified likelihood ratio test for the structure of interaction in spatial econometric models. The Ohio State University: Department of City and Regional Planning Working Paper WP 83-11.
Anselin, Luc. 1984. Specification tests and model selection for aggregate spatial interaction, an empirical comparison.Journal of Regional Science 24, 1: 1–15.
Arora, S. and Brown, M. 1977. Alternative approaches to spatial autocorrelation: an improvement over current practice.International Regional Science Review, 2, 1: 67–78.
Atkinson, A. C. 1970. A method for discriminating between models.Journal of The Royal Statistical Society B 32: 323–45.
Bartels, Cornelis P. A. 1979. Operational statistical methods for analysing spatial data. InExploratory and explanatory statistical analysis of spatial data, eds. C. Bartels and R. Ketellapper, pp. 5–50. Boston, Mass.: Martinus Nijhoff.
Bartels, C. and Hordijk, L. 1977. On the power of the generalized Moran contiguity coefficient in testing for spatial autocorrelation among regression disturbances.Regional Science and Urban Economics 7, 1/2: 83–101.
Bartels, C. and Ketellapper, R., eds. 1979.Exploratory and explanatory statistical analysis of spatial data. Boston, Mass. Martinus Nijhoff.
Bennett, R. J. 1979.Spatial time series. London: Pion.
Blommestein, Hans J. 1983. Specification and estimation of spatial econometric models. A discussion of alternative strategies for spatial economic modelling.Regional Science and Urban Economics 13, 2: 251–70.
Blommestein, Hans and Nijkamp, Peter. 1983.Testing the spatial scale and the dynamic structure in regional models. A contribution to spatial econometric specification analysis. Ekonomische Fakulteit, Vrije Universiteit Amsterdam: Serie Researchmemoranda 1983–16.
Bodson, P. and Peeters, D. 1975. Estimation of the coefficients of a linear regression in the presence of spatial autocorrelation. An application to a Belgian labour-demand function.Environment and Planning A 7, 4: 455–72.
Brandsma, A. S. and Ketellapper, R., 1979a. Biparametric approach to spatial autocorrelation.Environment and Planning A 11, 1: 51–58.
Brandsma, A. S. and Ketallapper, R. 1979a. Further evidence on alternative procedures for testing of spatial autocorrelation among regression disturbances. InExploratory and explanatory statistical analysis of spatial data, eds. C. Bartels and R. Ketellapper, pp. 113–36, Boston, Mass. Martinus Nijhoff.
Buck, Andrew J. and Hakim, Simon. 1981. Appropriate roles for statistical decision theory and hypothesis testing in model selection.Regional Science and Urban Economics 11, 1: 135–47.
Cliff, A. D. and Ord, J. K. 1973.Spatial autocorrelation. London: Pion.
Cliff, A. D. and Ord, J. K. 1981.Spatial processes, models and applications. London: Pion.
Cox, D. R. 1961. Tests of separate families of hypotheses.Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability 1: 105–23.
Cox, D. R. 1962. Further results on tests of separate families of hypotheses.Journal of The Royal Statistical Society B 24, 2: 406–24.
Dastoor, N. 1981. A note on the interpretation of the Cox procedure for non-nested hypotheses.Economics Letters 8: 113–20.
Davidson, Russell and MacKinnon, James. 1981. Several tests for model specification in the presence of alternative hypotheses.Econometrica 49, 3: 781–93.
Davidson, Russell and Mackinnon, James G. 1982. Some non-nested hypothesis tests and the relations among them.Review of Economic Studies 49: 551–65.
Ericsson, Neil R. 1983. Asymptotic properties of instrumental variables statistics for testing non-nested hypotheses.Review of Economic Studies 50: 287–304.
Fisher, Gordon R. 1983. Tests for two separate regressions.Journal of Econometrics 21, 1: 117–32.
Fisher, Gordon R. and McAleer, Michael. 1979. On the interpretation of the Cox test in econometrics.Economics Letters 4: 145–50.
Fisher, Gordon and McAleer, Michael. 1981. Alternative procedures and associated tests of significance for non-nested hypotheses.Jourral of Econometrics 16, 1: 103–19.
Fisher, W. 1971. Econometric estimation with spatial dependence.Regional Science and Urban Economics 1, 1: 19–40.
Gallant, A. Ronald and Jorgenson, D. W. 1979. Statistical inference for a system of non-linear implicit equations in the context of instrumental variable estimation.Journal of Econometrics 11, 2/3: 275–302.
Gaver, Kenneth M. and Geisel, Martin S. 1974. Discrimination among alternative models: Bayesian and non-Bayesian methods. InFrontiers in Econometrics, ed. P. Zarembka, pp. 49–77. New York. Academic Press.
Godfrey, L. G. 1983. Testing non-nested models after estimation by instrumental variables or least squares.Econometrica 51, 2: 355–65.
Godfrey, L. G. and Pesaran, M. H. 1983. Tests of non-nested regression models: small sample adjustrnents and Monte Carlo evidence.Journal of Econometrics 21, 1: 133–54.
Griffith, D. A. 1980. Toward a theory of spatial statistics.Geographical Analysisi 12, 4: 325–39.
Haining, R. 1978a. Estimating spatial interaction models.Environment and Planning A 10, 3: 305–20.
Haining, Robert. 1978b.Specification and estimation problems in models of spatial dependence. Evanston, Ill.: Northwestern University, Studies in Geography no. 24.
Hausman, J. A. 1978. Specification tests in econometrics.Econometrica 46, 6: 1251–71.
Hepple, Leslie W. 1976. A maximum likelihood model for econometric estimation with spatial series. InTheory and practice in regional science, London papers in regional science 6, ed. I. Masser, pp. 90–104. London: Pion.
Hepple, Leslie W. 1979. Bayesian analysis of the linear model with spatial dependence. InExploratory and explanatory statistical analysis of spatial data, eds. C. Bartels and R. Ketellapper, pp. 179–99. Boston, Mass.: Martinus Nijhoff, Boston.
Hooper, Peter M. and Hewings, Geoffrey J. D. 1981. Some properties of space-time processes.Geographical Analysis 13, 3: 203–23.
Hordijk, L. 1974. Spatial correlation in the disturbances of a linear interregional model.Regional Science and Urban Economics 4, 3: 117–40.
Hordijk, L. 1979. Problems in estimating econometric relations in space.Papers Regional Science Association 42: 99–115.
Jackson, O. A. Y. 1968. Some results on tests of separate families of hypotheses.Biometrika 55, 2: 355–63.
Kooijman, S. 1976. Some remarks on the statistical analysis of grids, especially with respect to ecology.Annals of Systems Research 5: 113–32.
MacKinnon, James G., White, Halbert and Davidson, Russell. 1983. Tests for model specification in the presence of alternative hypotheses: some further results.Journal of Econometrics 21, 1: 53–70.
Muth, Richard F. 1969.Cities and housing. Chicago: The University of Chicago Press.
Ord, Keith. 1975. Estimation methods for models of spatial interaction.Journal of the American Statistical Association 70: 120–26.
Paelinck, Jean H. P. 1982. Operational spatial analysis.Papers, Regional Science Association 50: 1–7.
Paelinck, Jean H. P. and Klaassen, Leo H. 1979.Spatial econometrics. Farnborough, U.K.: Saxon House.
Pereira, Basilio de B. 1977a. A note on the consistency and on the finite sample comparisons of some tests of separate families of hypotheses.Biometrika 64, 1: 109–13.
Pereira, Basilio de B. 1977b. Discriminating among separate models: a bibliography.International Statistical Review 45: 163–72.
Pereira, Basilio de B. 1978a. Empirical comparisons of some tests of separate families of hypotheses.Metrika 25, 4: 219–34.
Pereira, Basilio de B. 1978b. Tests and efficiencies of separate regression models.Biometrika 65, 2: 319–27.
Pesaran, M. H. 1974. On the general problem of model selection.Review of Economic Studies 41, 2: 153–71.
Pesaran, M. H. 1982a. On the comprehensive method of testing non-nested regression models.Journal of Econometrics 18, 2: 263–74.
Pesaran, M. H. 1982b. Comparison of local power of alternative tests of non-nested regression models.Econometrica 50, 5: 1287–1305.
Pesaran, M. H. and Deaton, A. S. 1978. Testing non-nested nonlinear regression models.Econometrica 46, 3: 677–94.
Quandt, Richard E. 1974. A comparison of methods for testing non-nested hypotheses.The Review of Economics and Statistics 56: 92–99.
Ramsey, James B. 1974. Classical model selection through specification tests. InFrontiers in Econometrics, ed. P. Zarembka, pp. 13–47. New York: Academic Press.
Sargan, J. D. 1958. The estimation of economic relationships using instrumental variables.Econometrica 26, 3: 393–415.
Sawa, Takamitsu. 1978. Information criteria for discriminating among alternative regression models.Econometrica 46, 6: 1273–91.
Stetzer, F. 1982. Specifying weights in spatial forecasting models: the results of some experiments.Environment and Planning A 14, 5: 571–84.
Theil, Henri. 1961.Economic forecasts and policy. Amsterdam: North-Holland.
Walker, A. M. 1967. Some tests of separate families of hypotheses in time series analysis.Biometrika 54, 1/2: 39–68.
White, Halbert. 1980. A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity.Econometrica 48, 4: 817–38.
White, Halbert. 1981. Consequences and detection of misspecified nonlinear regression models.Journal of the American Statistical Association 76: 419–33.
White, Halbert. 1982. Regularity conditions for Cox's test of non-nested hypotheses.Journal of Econometrics 19, 2/3: 301–18.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Anselin, L. Specification tests on the structure of interaction in spatial econometric models. Papers of the Regional Science Association 54, 165–182 (1984). https://doi.org/10.1007/BF01940131
Issue Date:
DOI: https://doi.org/10.1007/BF01940131