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Variable Selection in Linear Mixed Models Using an Extended Class of Penalties
Author(s) -
Taylor Julian D.,
Verbyla Arūnas P.,
Cavanagh Colin,
Newberry Marcus
Publication year - 2012
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/j.1467-842x.2012.00687.x
Subject(s) - mathematics , estimator , covariate , generalized linear mixed model , mixed model , selection (genetic algorithm) , variable (mathematics) , feature selection , class (philosophy) , linear model , statistics , model selection , set (abstract data type) , mathematical optimization , computer science , artificial intelligence , mathematical analysis , programming language
Summary There is an emerging need to advance linear mixed model technology to include variable selection methods that can simultaneously choose and estimate important effects from a potentially large number of covariates. However, the complex nature of variable selection has made it difficult for it to be incorporated into mixed models. In this paper we extend the well known class ofL rpenalties and show that they can be integrated succinctly into a linear mixed model setting. Under mild conditions, the estimator obtained from this mixed model penalised likelihood is shown to be consistent and asymptotically normally distributed. A simulation study reveals that the extended family of penalties achieves varying degrees of estimator shrinkage depending on the value of one of its parameters. The simulation study also shows there is a link between the number of false positives detected and the number of true coefficients when using the same penalty. This new mixed model variable selection (MMVS) technology was applied to a complex wheat quality data set to determine significant quantitative trait loci (QTL).