Data Transformations in Linear Mixed-Effects Models for Longitudinal Data

• Activity Number: 216
• Type: Contributed
• Date/Time: Tuesday, August 5, 2003 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): Matthew James Gurka*+ and Lloyd J. Edwards and Keith E. Muller
• Companies: University of North Carolina, Chapel Hill and University of North Carolina, Chapel Hill and University of North Carolina, Chapel Hill
• Keywords: repeated measurements ; linear mixed-effects model ; transformations ; normal distribution

Abstract

The general linear mixed model provides a powerful tool for representing continuous repeated measurements. Meeting the assumption of Gaussian distribution often requires transforming the response variable. The work of Box and Cox, among others, has led to the development of systematic methods for models with i.i.d. errors, based on comparing models with distinct transformations. Relatively little work has been done to extend the approach to repeated measures of any kind. We briefly review all such work as it relates to the linear mixed model and the special case of the multivariate linear model. We also review systems of multivariate distributions in order to recommend flexible but analytically well-behaved choices. This leads naturally to strategies for extending the Box-Cox approach to classes of longitudinal data important in biomedical research. Simulation studies allow assessing the proposals.