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An exact method for the multiple comparison of several polynomial regression models with applications in dose-response study

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  • Sanyu Zhou

    (Shanghai University of Finance and Economics)

Abstract

Research on the multiple comparison during the past 60 years or so has focused mainly on the comparison of several population means. Spurrier (J Am Stat Assoc 94:483–488, 1999) and Liu et al. (J Am Stat Assoc 99:395–403, 2004) considered the multiple comparison of several linear regression lines. They assumed that there was no functional relationship between the predictor variables. For the case of the polynomial regression model, the functional relationship between the predictor variables does exist. This lack of a full utilization of the functional relationship between the predictor variables may have some undesirable consequences. In this article we introduce an exact method for the multiple comparison of several polynomial regression models. This method sufficiently takes advantage of the feature of the polynomial regression model, and therefore, it can quickly and accurately compute the critical constant. This proposed method allows various types of comparisons, including pairwise, many-to-one and successive, and it also allows the predictor variable to be either unconstrained or constrained to a finite interval. The examples from the dose-response study are used to illustrate the method. MATLAB programs have been written for easy implementation of this method.

Suggested Citation

  • Sanyu Zhou, 2018. "An exact method for the multiple comparison of several polynomial regression models with applications in dose-response study," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(3), pages 413-429, July.
    • Handle: RePEc:spr:alstar:v:102:y:2018:i:3:d:10.1007_s10182-017-0313-4
    DOI: 10.1007/s10182-017-0313-4
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    References listed on IDEAS

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    1. Liu W. & Jamshidian M. & Zhang Y., 2004. "Multiple Comparison of Several Linear Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 395-403, January.
    2. Richard Potthoff, 1964. "On the Johnson-Neyman technique and some extensions thereof," Psychometrika, Springer;The Psychometric Society, vol. 29(3), pages 241-256, September.
    3. W. Liu & F. Bretz & A. J. Hayter & H. P. Wynn, 2009. "Assessing Nonsuperiority, Noninferiority, or Equivalence When Comparing Two Regression Models Over a Restricted Covariate Region," Biometrics, The International Biometric Society, vol. 65(4), pages 1279-1287, December.
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