Quality & Quantity

, Volume 45, Issue 2, pp 403–423 | Cite as

The raise method. An alternative procedure to estimate the parameters in presence of collinearity

  • Catalina Garcia Garcia
  • José García Pérez
  • José Soto Liria
Article

Abstract

Recently, Feng-Jeng (Qual Quant 42:417–426, 2008) has proposed the nested estimation procedure as another alternative from the practical point of view of the problem of multicollinearity. Although the nested estimation procedure can promise to avoid multicollinearity, it can also avoid important information by eliminating variables. We are presenting another alternative called the raise method, which keeps all the information which could be highly recommended in some cases. We apply our proposal to a known example and compare the results with the nested estimation procedure, the ridge regression and the principal components.

Keywords

Multicollinearity Nested estimate procedure Raise method 

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References

  1. Basilensky A.: Factor analysis regression. Can. J. Stat. 9, 109–117 (1981)CrossRefGoogle Scholar
  2. Basilensky A.: Statistical Factor Analysis and Related Methods. Wiley, New York (1994)CrossRefGoogle Scholar
  3. Belsey D.A., Kuh E., Welsch R.E.: Regression Diagnostics: Identifying Influencial Data and Sources of Collinearity. Wiley, United States of America (1980)CrossRefGoogle Scholar
  4. Brown W.G., Beattie B.R.: Improving estimates of economics parameters by use ridge regression with production function applications. Am. J. Agric. Econ. 57(1), 21–32 (1975)CrossRefGoogle Scholar
  5. Casella G.: Condition numbers and minimax ridge regression estimators. J. Am. Stat. Assoc. 80(391), 753–758 (1985)CrossRefGoogle Scholar
  6. Chan N.N.: On an unbaised predictor in factor analysis. Biometrika 64, 642–644 (1977)CrossRefGoogle Scholar
  7. Farrar D.E., Glaubert R.R.: Multicollinearity in regression analysis. The problem revisited. Rev. Econ. Stat. 49, 92–107 (1967)CrossRefGoogle Scholar
  8. Feng-Jeng L.: Solving multicollinearity in the process of fitting regression model using the nested estimate procedure. Qual. Quant. 42, 417–426 (2008)CrossRefGoogle Scholar
  9. Fourgeaud C., Gourieux C., Pradel J.: Some theorical results for generalized ridge regression estimators. J. Econom. 25(2), 191–203 (1984)CrossRefGoogle Scholar
  10. Garcia, J., Andujar, A., Soto, J.: Acerca de la detección de la colinealidad en modelos de regresión lineal. XIII Reunión Asepelt España, Burgos (1999)Google Scholar
  11. Garcia Ferrer A.: El problema de la multicolinealidad en los modelos de regresión lineales: Algunas soluciones posibles. Revista Española de Economía 77, 120–139 (1977)Google Scholar
  12. Greene W.: Econometric Analysis. Prentice Hall, New Jersey (2003)Google Scholar
  13. Hemmerle W.J.: An explicit solution for generalized ridge regression. Technometrics 17, 309–314 (1975)CrossRefGoogle Scholar
  14. Hocking R.R., Speed F.M., Lynn M.J.: A class of biased estimators in linear regression. Technometrics 18, 425–438 (1976)CrossRefGoogle Scholar
  15. Hoerl A.E., Kennard R.W.: Ridge regression: biased estimation for nonorthogonal problems. Technometrics 12, 55–67 (1970a)CrossRefGoogle Scholar
  16. Hoerl A.E., Kennard R.W.: Ridge regression: applications to nonorthogonal problems. Technometrics 12, 69–82 (1970b)CrossRefGoogle Scholar
  17. Hoerl A.E., Kennard R.W., Baldwin K.F.: Ridge regression. Some simulations. Commun. Stat. 4(2), 105–123 (1975)CrossRefGoogle Scholar
  18. Isogawa Y., Okamato M.: Lineal prediction in the factor analysis model. Biometrika 67, 482–484 (1980)CrossRefGoogle Scholar
  19. Johnston J.: Métodos de Econometría. Vicens-Vives, Barcelona (1989)Google Scholar
  20. Kendall M.G.: A Course in Multivariate Analysis. Griffin, London (1957)Google Scholar
  21. Lauridsen J., Mur J.: Multicollinearity in cross sectional regressions. J. Geogr. Syst. 8, 317–333 (2006)CrossRefGoogle Scholar
  22. Lawley D.N., Maxwel A.E.: Regression and factor analysis. Biometrika 60, 331–338 (1973)Google Scholar
  23. Marquardt D.W.: Generalized inverses, ridge regression, biased lineal estimation and nonlinear estimation. Technometrics 12(3), 590–612 (1970)CrossRefGoogle Scholar
  24. Massy W.F.: Principal components regression in exploratory statistical research. J. Am. Stat. Assoc. 60, 234–256 (1965)CrossRefGoogle Scholar
  25. McDonald G.G., Galarneau D.I.: A Monte Carlo evaluation of some ridge-type estimator. J. Am. Stat. Assoc. 70(350), 407–416 (1975)CrossRefGoogle Scholar
  26. Polverini F.: Multicollinerita e stimatori “ridge” del modello classico di regressione lineare. Giornali degi Ecoomisti e Annali di Economia 37(1–2), 89–112 (1978)Google Scholar
  27. Rao C.R.: A note on a generalized inverse of a matrix with applications to problems in mathematical statistics. J. R. Stat. Soc. B24, 152–158 (1962)Google Scholar
  28. Rawlings J.O.: Applied Regression Analysis: A Research Tool. Cole Statistics and Probability Series. The Wadsworth and Brooks, California (1988)Google Scholar
  29. Scott J.: Factor analysis and regression. Econometrica 34, 552–562 (1966)CrossRefGoogle Scholar
  30. Scott J.: Factor analysis and regression revisited. Econometrica 37, 719 (1969)CrossRefGoogle Scholar
  31. Silvey S.D.: Multicollinearity and imprecise estimation. J. Stat. Soc. 31(B), 539–552 (1969)Google Scholar
  32. Stein, C.: Inadmissibility of the usual estimator for mean of multivariate normal distribution. In: Neyman, J. (ed.) Proceedings of the Third Berkley Symposium on Mathematical and Statistics Probability, vol. 1, pp. 197–206 (1956)Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  • Catalina Garcia Garcia
    • 1
  • José García Pérez
    • 2
  • José Soto Liria
    • 2
  1. 1.Quantitative Methods, Granada UniversityGranadaSpain
  2. 2.Applied Economy, Almeria UniversityAlmeriaSpain

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