Asymptotic Properties of an R2 Statistic for Fixed Effects in the Linear

• Activity Number: 659
• Type: Contributed
• Date/Time: Thursday, August 4, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Jeanine Matuszewski*+ and Lloyd J. Edwards
• Companies: The University of North Carolina at Chapel Hill and The University of North Carolina at Chapel Hill
• Keywords: Linear Mixed Model ; R Squared Statistic

Abstract

The R2 statistic has become a widely used tool when analyzing data in the linear univariate setting. There are many R2 statistics for the linear mixed model but their properties are not well established. There is a recently proposed statistic for fixed effects, R2Beta based on the Wald F test in the linear mixed model that has several desirable features. The statistic has a semi-partial form and a correspondence to the Hotelling-Lawley trace multivariate measure of association. In this paper, the focus is on the asymptotic properties of R2Beta. A simulation study is used to illustrate the impact of covariance structure misspecification, varying the denominator degrees of freedom method and estimation techniques. Covariance structure misspecification and denominator degrees of freedom methods substantially impact the asymptotic behavior of while the estimation technique does not.