Inference on Random Effect Variances with Application to the Assessment of Nonlinearity

• Activity Number: 447
• Type: Contributed
• Date/Time: Wednesday, August 6, 2008 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Sonja Greven*+ and Ciprian M. Crainiceanu and Fabian Scheipl and Helmut Küchenhoff and Annette Peters
• Companies: Johns Hopkins University and Johns Hopkins University and Ludwig-Maximilians-University Munich and Ludwig-Maximilians-University Munich and Helmholtz Zentrum München
• Keywords: Mixed Model ; Random Effect ; Penalized Splines ; Nonparametric Regression ; Non-standard problem

Abstract

Linear mixed models (LMMs) are a powerful inferential tool. One application are mixed model penalized splines used for nonparametric regression. We are interested in inference on random effect variances. An important special case is testing for polynomial regression against a smooth alternative. Our motivating application is the assessment of nonlinearity for air pollution dose-response functions. Testing for a zero variance is nonstandard due to the tested parameter on the boundary of the parameter space. Furthermore, observations are generally not independent in LMMs. We compare several tests in extensive simulations. We find that our fast finite sample approximation based on the restricted likelihood ratio test statistic outperforms all other tests considered. The class of models covered includes models with moderate numbers of clusters, unbalanced designs, or nonparametric smoothing.