Violating the Assumption of Independence of the Error Components in the Linear Mixed Model for Longitudinal Data

• Activity Number: 156
• Type: Contributed
• Date/Time: Monday, August 7, 2006 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Matthew Gurka*+ and Lloyd Edwards and Keith E. Muller
• Companies: University of Virginia and The University of North Carolina at Chapel Hill and The University of North Carolina at Chapel Hill
• Keywords: variance components ; correlation ; random effects ; model diagnostics ; obesity

Abstract

The linear mixed model is commonly used in the analysis of longitudinal data, where one can simultaneously model the among-unit error (the random effects) and the within-unit error. The effect of violating the normality assumption of these two sources of deviation has been studied. However, the impact of violating the assumption of independence between the random effects and the within-unit error has not received any attention. An examination of data from an intervention trial targeting obesity reveals evidence of a possible violation of the independence assumption. We argue that this violation may occur often in practice, particularly in areas of research like obesity. If the two sources of deviation are dependent, estimation and inference about the variance components of the model, and consequently the random effects estimators, are adversely affected.