2013
DOI: 10.1080/10618600.2012.681219
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Fixed and Random Effects Selection by REML and Pathwise Coordinate Optimization

Abstract: We propose a two-stage model selection procedure for the linear mixed-effects models. The procedure consists of two steps: First, penalized restricted log-likelihood is used to select the random effects, and this is done by adopting a Newton-type algorithm. Next, the penalized log-likelihood is used to select the fixed effects via pathwise coordinate optimization to improve the computation efficiency. We prove that our procedure has the oracle properties. Both simulation studies and a real data example are car… Show more

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Cited by 36 publications
(37 citation statements)
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“…A key feature of IC(λ), which sets it apart from standard information criteria used for tuning parameter selection in other penalties for mixed models (e.g., Ibrahim et al, 2011;Lin et al, 2013), is its use of different model complexity penalties. Specifically, a BIC-type penalty of 'log(n)' is used for the fixed effects, and an AIC-type penalty of '2' is used for the random effects.…”
Section: Tuning Parameter Selectionmentioning
confidence: 99%
See 1 more Smart Citation
“…A key feature of IC(λ), which sets it apart from standard information criteria used for tuning parameter selection in other penalties for mixed models (e.g., Ibrahim et al, 2011;Lin et al, 2013), is its use of different model complexity penalties. Specifically, a BIC-type penalty of 'log(n)' is used for the fixed effects, and an AIC-type penalty of '2' is used for the random effects.…”
Section: Tuning Parameter Selectionmentioning
confidence: 99%
“…One appealing approach is to use penalized likelihood methods, although their application to mixed models has only recently been explored. For LMMs, Bondell et al (2010) proposed adaptive lasso penalties for selecting the fixed and random effects, while Peng and Lu (2012) and Lin et al (2013) proposed two-stage methods that separate out the fixed and random effect selection. For GLMMs, Ibrahim et al (2011) proposed a modified version of the penalty in Bondell et al (2010), and employed a Monte Carlo EM algorithm for estimation.…”
Section: Introductionmentioning
confidence: 99%
“…To optimize Equation , the NR algorithm whose convergence rate is quadratic with good initial values can also be used. Motivated by the idea used in References , and , we propose to locally approximate the penalized log‐likelihood function as, lp(ϕ)l(ϕ(0))+l(ϕ(0))T(ϕϕ(0))+12(ϕϕ(0))Tl(ϕ(0))(ϕϕ(0))λrRωr|ϕr|. …”
Section: Methodsmentioning
confidence: 99%
“…The maximization algorithms for linear mixed models are usually based on two basic approaches: the EM and Newton-Raphson (NR) method. 41,42 While the above EM algorithm can be used to estimate parameters, it can be computationally intensive when dealing with high-dimensional data, especially when the tuning parameter also needs to be selected. To optimize Equation (6), the NR algorithm whose convergence rate is quadratic with good initial values can also be used.…”
Section: Approximate Penalized Maximum Likelihood Estimatormentioning
confidence: 99%
“…Chen and Dunson (2003) have considered Bayesian variable selection for the random effects in linear mixed-effect models and Pu and Niu (2006) have extended the general information criterion to choose the fixed effects under similar set-up. Bondell, Krishna and Ghosh (2010), Ibrahim et al (2011) and Lin , Pang and Jiang (2013) considered the simultaneous selection of fixed and random effects through different approaches which are applicable mainly to situations where there are many random effect variables along with the large pool of fixed effect variables. However, as mentioned above, in most applications in medical and clinical biology, the number of random effects is generally small and can be considered prefixed, and we are mainly interested in selecting the fixed effects from a large pool of possible candidates.…”
Section: Introductionmentioning
confidence: 99%