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Simultaneous confidence bands for all contrasts of three or more simple linear regression models over an interval

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  • Jamshidian, Mortaza
  • Liu, Wei
  • Bretz, Frank
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    Abstract

    Simultaneous confidence intervals are used in Scheffé (1953) to assess any contrasts of several normal means. In this paper, the problem of assessing any contrasts of several simple linear regression models by using simultaneous confidence bands is considered. Using numerical integration, Spurrier (1999) constructed exact simultaneous confidence bands for all the contrasts of several regression lines over the whole range (-[infinity],[infinity]) of the explanatory variable when the design matrices of the regression lines are all equal. In this paper, a simulation-based method is proposed to construct simultaneous confidence bands for all the contrasts of the regression lines when the explanatory variable is restricted to an interval and the design matrices of the regression lines may be different. The critical value calculated by this method can be as close to the exact critical value as required if the number of replications in the simulation is chosen sufficiently large. The methodology is illustrated with a real problem in which sizes of the left atrium of infants in three diagnostic groups (severely impaired, mildly impaired and normal) are compared.

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    File URL: http://www.sciencedirect.com/science/article/B6V8V-4Y7P4FW-1/2/baea109fc5e96c0fb8c71d993fdc92a6
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    Bibliographic Info

    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 54 (2010)
    Issue (Month): 6 (June)
    Pages: 1475-1483

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    Handle: RePEc:eee:csdana:v:54:y:2010:i:6:p:1475-1483

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    Web page: http://www.elsevier.com/locate/csda

    Related research

    Keywords: Comparing groups Comparison of regression lines Simultaneous inferences Size of atrium in infants Statistical simulation;

    References

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    1. Wei Liu & Shan Lin & Walter W. Piegorsch, 2008. "Construction of Exact Simultaneous Confidence Bands for a Simple Linear Regression Model," International Statistical Review, International Statistical Institute, vol. 76(1), pages 39-57, 04.
    2. Walter W. Piegorsch & R. Webster West & Wei Pan & Ralph L. Kodell, 2005. "Low dose risk estimation via simultaneous statistical inferences," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(1), pages 245-258.
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