Simulation-Based Simultaneous Confidence Bands for All Contrasts of Three or More Simple Linear Regression Models Over an Interval

• Activity Number: 36
• Type: Contributed
• Date/Time: Sunday, August 2, 2009 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Computing
• Author(s): Mortaza Jamshidian*+ and Wei Liu and Frank Bertz
• Companies: California State University, Fullerton and University of Southampton and Novartis Pharma AG
• Keywords: Comparing groups ; Comparison of regression lines ; Simultaneous inference ; Statistical simulation

Abstract

Simultaneous confidence intervals are used in Scheffe (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. Spurrier (1999) constructed exact simultaneous confidence bands for all the contrasts of several regression lines 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 may be restricted to an interval and the design matrices of the regression lines may be different. 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.