Fixed and Random Effects Selection in Mixed Effects Models

Authors

  • Joseph G. Ibrahim,

    Corresponding author
    1. Department of Biostatistics, University of North Carolina, McGavran Greenberg Hall, CB#7420, Chapel Hill, North Carolina 27599-7420, U.S.A.
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  • Hongtu Zhu,

    1. Department of Biostatistics, University of North Carolina, McGavran Greenberg Hall, CB#7420, Chapel Hill, North Carolina 27599-7420, U.S.A.
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  • Ramon I. Garcia,

    1. Department of Biostatistics, University of North Carolina, McGavran Greenberg Hall, CB#7420, Chapel Hill, North Carolina 27599-7420, U.S.A.
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  • Ruixin Guo

    1. Department of Biostatistics, University of North Carolina, McGavran Greenberg Hall, CB#7420, Chapel Hill, North Carolina 27599-7420, U.S.A.
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email: ibrahim@bios.unc.edu

Abstract

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 Association103, 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.

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