A Simple and Efficient Reparameterization for Mixed-Effects Models

• Activity Number: 354
• Type: Contributed
• Date/Time: Tuesday, August 2, 2011 : 10:30 AM to 12:20 PM
• Sponsor: International Chinese Statistical Association
• Author(s): Guangxiang Zhang*+ and John J. Chen
• Companies: The State University of New York at Stony Brook and Stony Brook University
• Keywords: Mixed-effects or multilevel models ; Convergence rate ; Collinearity between random-effects ; Centering ; Optimal linear transformation ; Random slope

Abstract

Linear mixed-effects model has been widely used in hierarchical and longitudinal data analyses. In practice, the fitting algorithm can fail to converge due to boundary issues of the estimated random-effects covariance matrix G. Current available algorithms are not computationally optimal because the condition number of G is unnecessarily increased when the random-effects correlation estimate is not zero. The traditional mean centering technique may even increase the random-effects correlation. To improve the convergence of data with such boundary issue, we propose an adaptive fitting (AF) algorithm using an optimal linear transformation of the random-effects design matrix. The AF algorithm can be easily implemented with standard software and be applied to other mixed-effects models. Simulations show that AF significantly improves the convergence rate, and reduces the condition number and non-positive definite rate of the estimated G, especially under small sample size, relative large noise and high correlation settings. One real life data for Insulin-like Growth Factor (IGF) protein is used to illustrate the application of this algorithm implemented with software package R (nlme).