Effective simultaneous confidence bands for repeated measurements in linear mixed-effect models

Abstract

Linear mixed-effect (LME) models have been extensively accepted to analyse repeated measurements due to their flexibility and ability to handle subject-specific matters. The inclusion of random effects has resulted in much benefit with respect to estimation, but it is complicated to measure their impact on hypothesis testing. While the same complication is present in the construction of simultaneous confidence bands (SCBs), degrees of freedom (df) for SCBs have rarely been discussed unlike those for test statistics. This motivates us to propose the adoption of approximate df to construct SCBs in LME models. Simulation studies were performed to compare the performances of different calculations for the df. The results of simulations demonstrate the efficacy of the use of approximate df. In addition, our proposal allows line-segment SCBs developed under covariance models to function with LME models. Applications with real longitudinal datasets present consistent results with the simulation study.

Keywords:

• Kenward–Roger degree of freedom
• linear mixed-effect models
• line-segment simultaneous confidence bands
• Satterthwaite degree of freedom
• Scheffé method
• Tube method