Premium
Fixed and Random Effects Selection in Mixed Effects Models
Author(s) -
Ibrahim Joseph G.,
Zhu Hongtu,
Garcia Ramon I.,
Guo Ruixin
Publication year - 2011
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.1541-0420.2010.01463.x
Subject(s) - random effects model , mathematics , consistency (knowledge bases) , selection (genetic algorithm) , mixed model , statistic , feature selection , model selection , scad , asymptotic distribution , statistics , penalty method , generalized linear mixed model , computer science , mathematical optimization , estimator , artificial intelligence , medicine , psychology , meta analysis , psychiatry , myocardial infarction , geometry
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 IC Q 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 IC Q 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.