Simultaneous confidence tubes for comparing several multivariate linear regression models

• Published in: Biometrical journal Vol. 64; no. 2; pp. 290 - 300
• Main Authors: Peng, Jianan, Liu, Wei, Bretz, Frank, Hayter, A. J.
• Format: Journal Article
• Language: English
• Published: Germany Wiley - VCH Verlag GmbH & Co. KGaA 01-02-2022
• Subjects: Confidence Intervals; Linear Models; Models, Statistical; multiple comparisons; Multivariate Analysis; multivariate linear regression; Regression analysis; Regression models; simultaneous confidence bands; simultaneous inference; statistical simulation; Tubes; simultaneous confidence bands; statistical simulation; simultaneous inference; multiple comparisons; multivariate linear regression
• ISSN: 0323-3847; 1521-4036
• DOI: 10.1002/bimj.202000148

Much of the research on multiple comparison and simultaneous inference in the past 60 years or so has been for the comparisons of several population means. Spurrier seems to have been the first to investigate multiple comparisons of several simple linear regression lines using simultaneous confidence bands. In this paper, we extend the work of Liu et al. for finite comparisons of several univariate linear regression models using simultaneous confidence bands to finite comparisons of several multivariate linear regression models using simultaneous confidence tubes. We show how simultaneous confidence tubes can be constructed to allow more informative inferences for the comparison of several multivariate linear regression models than the current approach of hypotheses testing. The methods are illustrated with examples.