Simultaneous confidence bands for all contrasts of three or more simple linear regression models over an interval
Simultaneous confidence bands for all contrasts of three or more simple linear regression models over an interval
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 (??,?) 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
comparing groups, comparison of regression lines, simultaneous inferences, size of atrium in infants, statistical simulation
1475-1483
Jamshidian, Mortaza
7603871f-ac81-48e5-9c95-743cf0334557
Liu, Wei
b64150aa-d935-4209-804d-24c1b97e024a
Bretz, Frank
aa8a675f-f53f-4c50-8931-8e9b7febd9f0
June 2010
Jamshidian, Mortaza
7603871f-ac81-48e5-9c95-743cf0334557
Liu, Wei
b64150aa-d935-4209-804d-24c1b97e024a
Bretz, Frank
aa8a675f-f53f-4c50-8931-8e9b7febd9f0
Jamshidian, Mortaza, Liu, Wei and Bretz, Frank
(2010)
Simultaneous confidence bands for all contrasts of three or more simple linear regression models over an interval.
Computational Statistics and Data Analysis, 54 (6), .
(doi:10.1016/j.csda.2010.01.022).
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 (??,?) 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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Published date: June 2010
Keywords:
comparing groups, comparison of regression lines, simultaneous inferences, size of atrium in infants, statistical simulation
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Statistics
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Local EPrints ID: 176555
URI: http://eprints.soton.ac.uk/id/eprint/176555
ISSN: 0167-9473
PURE UUID: 639b4659-516a-4a9a-96f5-85fbfe735916
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Date deposited: 09 Mar 2011 09:01
Last modified: 15 Mar 2024 02:43
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Author:
Mortaza Jamshidian
Author:
Frank Bretz
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