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Robust estimation procedures and visual display techniques for a two-way classification model

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Abstract

An important problem in statistics is to study the effect of one or two factors on a dependent variable. This type of problem can be formulated as a regression problem (by using dummy (0,1) variables to represent the levels of factors) and the standard least squares (LS) analysis is well-known. The least absolute value (LAV) analysis is less well known, but certainly is becoming more widely used, especially in exploratory data analysis.The purpose of this report is to present a didactic treatment of visual display methods useful in exploratory data analysis. These visual display techniques (stem- and- leaf, box- and- whisker, and two-way plots) are presented for both the least squares and the least absolute value analyses of a two-way classification model.

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References

  • Andrews, D. F. (1974). A robust method for multiple linear regression.Technometrics 16: 523–531.

    Google Scholar 

  • Andrews, D. F., Bickel, P. J., Hampel, F. R., Huber, P. J., Rogers, W. H. and Tukey, J. W. (1972).Robust Estimates of Location. New Jersey: Princeton University Press.

    Google Scholar 

  • Armstrong, R. D. and Frome, E. L. (1976). A comparison of two algorithms for absolute deviation curve fitting.Journal American Statistical Association 71(354): 328–330.

    Google Scholar 

  • Armstrong, R. D. and Frome, E. L. (1979). Least absolute value estimators for one-way and two-way tables.Naval Research Logistics Quarterly 26(1): 79–96.

    Google Scholar 

  • Armstrong, R. D., Frome, E. L., and Sklar, M G, (1980). Linear programming in exploratory data analysis.Journal of Educational Statistics 5: 293–307.

    Google Scholar 

  • Armstrong, R. D. and Hultz, J. D. (1976). An algorithm for restricted discrete approximation problem in the L1 norm.SIAM Journal on Numerical Analysis 14: 328–330.

    Google Scholar 

  • Barrodale, I. and Roberts, F. D. K. (1977). An improved algorithm for discrete L1 linear approximation.SIAM Journal of Numerical Analysis 10: 839–848.

    Google Scholar 

  • Barrodale, I. and Young, A. (1966). Algorithms for best L1 and L linear approximation on a Set.Numerical Mathematics 8: 295–306.

    Google Scholar 

  • Becker, R. A., Chamber, J. M., and Wilks, A. R. (1988). The new S language. Pacific Grove, CA: Wadsworth & Brooks/Cole.

    Google Scholar 

  • Charnes, A. and Cooper, W. W. (1961).Management Models and Industrial Applications of Linear Programming, Vols I and II, New York: John Wiley and Sons, Inc.

    Google Scholar 

  • Cook, R. D. and Weisberg, S. (1982). Criticism and influence analysis in regression.Sociological Methodology: 313–361.

  • CorelDraw!, Corel Systems Corporation, 1600 Carling Ave., Ottawa, Ontario K1Z 8r7.

  • Dietz, T., Frey, R. S., and Kalof, L. (1987). Estimation with cross-national data: robust and nonparametric methods.American Sociological Review 52(3): 380–391.

    Google Scholar 

  • Daniel, C. (1978). Patterns in Residuals in the Two-Way Layout.Technometrics 20: 385–395.

    Google Scholar 

  • Dutter, R. (1976). Computer linear robust curve fitting program LINWDR. Research Report 10. Fachgruppe für Statistik, ETH, Zurich.

    Google Scholar 

  • Gentle, J. E. (1977). Least absolute values estimation: an introduction.Commun. Statist. — Simul. Computa. B6(4): 313–328.

    Google Scholar 

  • Gentleman, J. F. and Wilk, M. B. (1975). Detecting outliers in a two-way table: statistical behavior of residuals.Technometrics 17: 1–14.

    Google Scholar 

  • Goodman, L. A. (1972). A modified multiple regression approach to the analysis of dichotomous variables.American Sociological Review 37: 28–46.

    Google Scholar 

  • Hampel, F. R. (1971). A general qualitative definition of robustness.Annals of Mathematical Statistics 42: 1887–1896.

    Google Scholar 

  • Hartwig, F. and Dearing, B. E. Exploratory Data Analysis,Sage Series: Quantitative Applications in the Social Sciences No. 07-016.

  • Hogg, R. V. (1974). Adaptive robust procedures; a partial review and some suggestions for future applications and theory.Journal of the American Statistical Association 69.

  • Hoaglin, D. C., Mosteller, F., and Tukey, J. W. (1983).Understanding Robust and Exploratory Data Analysis, Wiley, New York.

    Google Scholar 

  • Hoaglin, D. C., Mosteller, F., and Tukey, J. W. (1985).Exploring Data Tables, Trends, and Shapes. New York: John Wiley & Sons, Inc.

    Google Scholar 

  • Huber, P. J. (1972). Robust statistics: a review.The Annals of Mathematical Statistics 43: 1041–1067.

    Google Scholar 

  • John, J. A. and Draper, N. R. (1978). On Testing for Two Outliers or One Outlier in Two-Way Tables.Technometrics 20: 69–78.

    Google Scholar 

  • Leroy, A. and Rousseeuw, P. J. (1984). PROGRES: A program for robust regression. Technical Report 201. Free University, Brussels, Belgium.

    Google Scholar 

  • Marazzi, A. (1980). Robust linear regression programs in ROBETH. ROBETH document no. 2, Research Report 23. Fachgruppe für Statistik, ETH, Zurich.

    Google Scholar 

  • McNeill, J. J. and Tukey, J. W. (1975). Higher-order diagnosis of two-way tables, illustrated on two sets of demographic empirical distributions.Biometrics: 129–132.

  • Minitab for Windows, Release 9, Minitab, Inc., 3081 Enterprise Dr., State College, PA, 16801–3008.

  • Mosteller, F. and Tukey, J. (1977).Data Analysis and Regression,. Reading, Massachusetts: Addison-Wesley, 1977.

    Google Scholar 

  • PC-ISP, Artemis Systems, 125 Berry Corner Lane, Carlisle, MA 01741.

  • Peters, S. C., Samarov, A., and Welsch, R. E. (1982). Computational procedures for bounded-influence and robust regression (TROLL: BIF and BIFMOD). Technical Report 30. Center for Computational Research in Economics and Management Science, MIT, Cambridge, Mass, 1982.

    Google Scholar 

  • Searle, S. R. (1971).Linear Models. New York: Wiley and Sons.

    Google Scholar 

  • Sklar, M. G. and Armstrong, R. D. (1982). Least absolute value and Chebychev estimation utilizing least squares results.Mathematical Programming 24: 346–352.

    Google Scholar 

  • SAS Institute, Inc., P.O. Box 8000, Cary, NC, 27511.

  • SPSS, Inc., Suite 3000, 444 North Michigan Ave., Chicago, IL, 70711.

  • Tukey, J. W. (1977).Exploratory Data Analysis. Reading, Massachusetts: Addison-Wesley.

    Google Scholar 

  • Wu, L. L. (1985). Robust M-estimation of location and regression.Sociological Methodology: 316–388.

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Sklar, M.G., Armstrong, R.D. Robust estimation procedures and visual display techniques for a two-way classification model. Qual Quant 28, 283–304 (1994). https://doi.org/10.1007/BF01098945

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