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Operability Region Equivalence: Simultaneous Confidence Bands for the Equivalence of Two Regression Models over Restricted Regions
Author(s) -
Liu Wei,
Hayter Anthony J.,
Wynn Henry P.
Publication year - 2007
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.200610322
Subject(s) - equivalence (formal languages) , covariate , mathematics , confidence interval , statistics , null hypothesis , regression , homogeneity (statistics) , linear regression , regression analysis , regression diagnostic , polynomial regression , discrete mathematics
In many scientific problems the purpose of comparing two linear regression models is to demonstrate that they have only negligible differences and so can be regarded as being practically equivalent. The frequently used statistical approach of testing the homogeneity null hypothesis of the two models by using a partial F test is not appropriate for this purpose. In this paper, a simultaneous confidence band is proposed which provides an upper bound on the largest possible difference between the two models, in units of the standard error of the observations, over a given region of the covariates. This is demonstrated to be a more practical method for assessing the equivalence of the two regression models. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)