A simultaneous variable selection methodology for linear mixed models |
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Authors: | Juming Pan Junfeng Shang |
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Institution: | 1. Department of Mathematics and Statistics, University of Minnesota, Duluth, USA;2. Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, USA |
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Abstract: | Selecting an appropriate structure for a linear mixed model serves as an appealing problem in a number of applications such as in the modelling of longitudinal or clustered data. In this paper, we propose a variable selection procedure for simultaneously selecting and estimating the fixed and random effects. More specifically, a profile log-likelihood function, along with an adaptive penalty, is utilized for sparse selection. The Newton-Raphson optimization algorithm is performed to complete the parameter estimation. By jointly selecting the fixed and random effects, the proposed approach increases selection accuracy compared with two-stage procedures, and the usage of the profile log-likelihood can improve computational efficiency in one-stage procedures. We prove that the proposed procedure enjoys the model selection consistency. A simulation study and a real data application are conducted for demonstrating the effectiveness of the proposed method. |
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Keywords: | Linear mixed models penalized variable selection profile log-likelihood |
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