Variable Selection in Joint Mean and Dispersion Models via Double Penalized Likelihood

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    Abstract

    In this paper, we propose to jointly model the conditional mean and variance components associated with the response in multilevel data. We set a generalized linear mixed model (GLMM) for the mean and a generalized linear model (GLM) for the variance components. The variable selection method of our choice is the smoothly clipped absolute deviation (SCAD) penalty, a penalized likelihood variable selection procedure, which shrinks the coefficients of redundant variables to 0 while simultaneously estimating the coefficients of the remaining important covariates. To assess the performance of the proposed procedures, we carry out real data analysis as well as extensive simulation studies, and compare to a similar process which excludes variable selection. We conclude that our method outperforms a simple joint meanvariance modelling approach, in both identifying the important components in the joint models and also producing more efficient estimation.
    Original languageEnglish
    Pages (from-to)276-304
    Number of pages28
    JournalSankhya. Series B: applied and interdisciplinary statistics
    Volume76
    Issue number2
    DOIs
    Publication statusPublished - Nov 2014

    Keywords

    • Generalized linear mixed models, hierarchical data, h-likelihood, modelling of mean and covariance structures, smoothly clippedabsolute deviation penalty

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