Identifying Unusual Observations in Ridge Regression Linear Model Using Box-Cox Power Transformation Technique

Aboobacker Jahufer

Department of Mathematical Sciences, Faculty of Applied Sciences, South Eastern University of Sri Lanka, Sammanthurai, Sri Lanka.

DOI: 10.4236/ojs.2014.41003                

Abstract

The use of [1] Box-Cox power transformation in regression analysis is now common; in the last two decades there has been emphasis on diagnostics methods for Box-Cox power transformation, much of which has involved deletion of influential data cases. The pioneer work of [2] studied local influence on constant variance perturbation in the Box-Cox unbiased regression linear mode. Tsai and Wu [3] analyzed local influence method of [2] to assess the effect of the case-weights perturbation on the transformation-power estimator in the Box-Cox unbiased regression linear model. Many authors noted that the influential observations on the biased estimators are different from the unbiased estimators. In this paper I describe a diagnostic method for assessing the local influence on the constant variance perturbation on the transformation in the Box-Cox biased ridge regression linear model. Two real macroeconomic data sets are used to illustrate the methodologies.

Keywords

Box-Cox Transformation; Ridge Regression; Constant Variance Perturbation; Local Influence; Influential Observations

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	G. E. P. Box and D. R. Cox, “An Analysis of Transformation (with Discussion),” Journal of the Royal Statistical Society, Series-B, Vol. 26, 1964, pp. 211-252.
[2]	A. J. Lawrance, “Regression Transformation Diagnostics Using Local Influence,” Journal of the American Statistical Association, Vol. 83, No. 404, 1988, pp. 1067-1072. http://dx.doi.org/10.1080/01621459.1988.10478702
[3]	C. L. Tsai and X. Wu, “Transformation Model Diagnostics,” Technometrics, Vol. 34, No. 2, 1992, pp. 197-202. http://dx.doi.org/10.1080/00401706.1992.10484908
[4]	A. C. Atkinson, “Plots, Transformations and Regression,” Oxford University Press, Oxford, 1985.
[5]	R. D. Cook and P. C. Wang, “Transformations and Influential cases in Regression,” Technometrics, Vol. 25, No. 4, 1983, pp. 337-343. http://dx.doi.org/10.1080/00401706.1983.10487896
[6]	D. V. Hinkley and S. Wang, “More about Transformations and Influential Cases in Regression,” Technometrics, Vol. 30, No. 4, 1988, pp. 435-440. http://dx.doi.org/10.1080/00401706.1988.10488439
[7]	R. D. Cook, “Assessment of Local Influence,” Journal of Royal Statistical Association, Series-B, Vol. 48, 1986, pp. 133-169.
[8]	C. L. Tsai and X. Wu, “Diagnostics in Transformation and Weighted Regression,” Technometrics, Vol. 32, No. 3, 1990, pp. 315-322. http://dx.doi.org/10.1080/00401706.1990.10484684
[9]	D. A. Belsley, E. Kuh and R. E. Welsch, “Regression Diagnostics: Identifying Influential Data and Sources of Collinearity,” Wiley, New York, 1980. http://dx.doi.org/10.1002/0471725153
[10]	A. E. Hoerl and R. W. Kennard, “Ridge Regression: Biased Estimation for Non-Orthogonal Problems,” Technometrics, Vol. 12, No. 1, 1970, pp. 55-67. http://dx.doi.org/10.1080/00401706.1970.10488634
[11]	A. E. Hoerl and R. W. Kennard, “Ridge Regression: Application to Non-Orthogonal Problems,” Technometrics, Vol. 12, No. 1, 1970, pp. 69-82. http://dx.doi.org/10.1080/00401706.1970.10488635
[12]	H. Sun, “Macroeconomic Impact of Direct Foreign Investment in China 1979-1996,” Blackwell Publishers Ltd., 1988.
[13]	J. W. Longley, “An Appraisal of Least Squares Programs for Electronic Computer from the Point of View of the User,” Journal of American Statistical Association, Vol. 62, No. 319, 1967, pp. 819-841. http://dx.doi.org/10.1080/01621459.1967.10500896
[14]	E. Walker and J. B. Birch, “Influence Measures in Ridge Regression,” Technometrics, Vol. 30, No. 2, 1988, pp. 221-227. http://dx.doi.org/10.1080/00401706.1988.10488370
[15]	R. D. Cook, “Detection of Influential Observations in Linear Regression,” Technometrics, Vol. 19, No. 1, 1977, pp. 15-18. http://dx.doi.org/10.2307/1268249
[16]	L. Shi and X. Wang, “Local Influence in Ridge Regression,” Computational Statistics & Data Analysis, Vol. 31, No. 3, 1999, pp. 341-353. http://dx.doi.org/10.1016/S0167-9473(99)00019-5
[17]	A. Jahufer and J. Chen, “Assessing Global Influential Observations in Modified Ridge Regression,” Statistics and Probability Letters, Vol. 79, No. 4, 2009, pp. 513-518. http://dx.doi.org/10.1016/j.spl.2008.09.019
[18]	A. Jahufer and J. Chen, “Identifying Local Influential Observations in Liu Estimator,” Journal of Metrika, Vol. 75, No. 3, 2012, pp. 425-438. http://dx.doi.org/10.1007/s00184-010-0334-4
[19]	A. Jahufer and J. Chen, “Measuring Local Influential Observations in Modified Ridge Regression,” Journal of Data Science, Vol. 9, No. 3, 2011, pp. 359-372.
[20]	A. Jahufer, “Detecting Global Influential Observations in Liu Regression Model,” Open Journal of Statistics, Vol. 3, No. 1, 2013, pp. 5-11. http://dx.doi.org/10.4236/ojs.2013.31002
[21]	A. Jahufer and J. Chen, “Identifying Local Influence in Modified Ridge Regression Using Cook’s Method,” Sri Lankan Journal of Applied Statistics, Vol. 9, 2008, pp. 93-108.
[22]	J. Chen and A. Jahufer, “Assessment of Anomalous Observations in Liu Estimator,” Journal of Management, Vol. 5, 2009, 41-49.