Fixed and Random Effects Selection in Mixed Effects Models
Version of Record online: 21 JUL 2010
© 2010, The International Biometric Society
Volume 67, Issue 2, pages 495–503, June 2011
How to Cite
Ibrahim, J. G., Zhu, H., Garcia, R. I. and Guo, R. (2011), Fixed and Random Effects Selection in Mixed Effects Models. Biometrics, 67: 495–503. doi: 10.1111/j.1541-0420.2010.01463.x
- Issue online: 20 JUN 2011
- Version of Record online: 21 JUL 2010
- Received July 2009. Revised April 2010. Accepted May 2010.
- Cholesky decomposition;
- EM algorithm;
- ICQ criterion;
- Mixed effects selection;
- Penalized likelihood;
Summary We consider selecting both fixed and random effects in a general class of mixed effects models using maximum penalized likelihood (MPL) estimation along with the smoothly clipped absolute deviation (SCAD) and adaptive least absolute shrinkage and selection operator (ALASSO) penalty functions. The MPL estimates are shown to possess consistency and sparsity properties and asymptotic normality. A model selection criterion, called the ICQ statistic, is proposed for selecting the penalty parameters (Ibrahim, Zhu, and Tang, 2008, Journal of the American Statistical Association 103, 1648–1658). The variable selection procedure based on ICQ is shown to consistently select important fixed and random effects. The methodology is very general and can be applied to numerous situations involving random effects, including generalized linear mixed models. Simulation studies and a real data set from a Yale infant growth study are used to illustrate the proposed methodology.