Statistics and Data Science Seminar
Prof. Sijian Wang
University of Wisconsin - Madison
Regularized REML for Estimation and Selection of Fixed and Random Effects in Linear Mixed-Effects Models
Abstract: The linear mixed effects model (LMM) is widely used in the analysis of clustered or longitudinal data. In the practice of LMM, inference on the structure of random effects component is of great importance not only to yield proper interpretation of subject-specific effects but also to draw valid statistical conclusions. This task of inference becomes significantly challenging when a large number of fixed effects and random effects are involved in the analysis. The difficulty of variable selection arises from the need of simultaneously regularizing both mean model and covariance structures, with possible parameter constraints between the two. In this paper, we propose a novel method of regularized restricted maximum likelihood to select fixed and random effects simultaneously in the LMM. The Cholesky decomposition is invoked to ensure the positive-definiteness of the selected covariance matrix of random effects, and selected random effects are invariant with respect to the ordering of predictors appearing in the model. We develop a new algorithm that solves the related optimization problem effectively, in which the computational load turns out to be comparable with that of the Newton-Raphson algorithm for MLE or REML in the LMM. We also investigate large sample properties for the proposed estimation, including the oracle property. Both simulation studies and data analysis are included for illustration. This is a joint work with Peter XK Song and Ji Zhu.
Wednesday April 7, 2010 at 3:00 PM in SEO 636