Fixed and Random Effects Selection by REML and Pathwise Coordinate Optimization

Lin, Bingqing; Pang, Zhen; Jiang, Jiming

doi:10.1080/10618600.2012.681219

Cited by 35 publications

(37 citation statements)

References 42 publications

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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%

“…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%

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Joint Selection in Mixed Models using Regularized PQL

Hui

Müller

Welsh

2017

Journal of the American Statistical Association

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The application of generalized linear mixed models present some major challenges for both estimation, due to the intractable marginal likelihood, and model selection, as we usually want to jointly select over both fixed and random effects. We propose to overcome these challenges by combining penalized quasi-likelihood (PQL) estimation with sparsity inducing penalties on the fixed and random coefficients. The resulting approach, referred to as regularized PQL, is a computationally efficient method for performing joint selection in mixed models. A key aspect of regularized PQL involves the use of a group based penalty for the random effects: sparsity is induced such

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Section: Tuning Parameter Selectionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Joint Selection in Mixed Models using Regularized PQL

Hui

Müller

Welsh

2017

Journal of the American Statistical Association

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“…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,

l_{p} (ϕ) \approx l (ϕ^{(0)}) + l^{'} {(ϕ^{(0)})}^{T} (ϕ - ϕ^{(0)}) + \frac{1}{2} {(ϕ - ϕ^{(0)})}^{T} l^{''} (ϕ^{(0)}) (ϕ - ϕ^{(0)}) - λ \sum_{r}^{R} ω_{r} | ϕ_{r} | .

…”

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%

Multikernel linear mixed model with adaptive lasso for complex phenotype prediction

Wen

2020

Statistics in Medicine

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Linear mixed models (LMMs) and their extensions have been widely used for high‐dimensional genomic data analyses. While LMMs hold great promise for risk prediction research, the high dimensionality of the data and different effect sizes of genomic regions bring great analytical and computational challenges. In this work, we present a multikernel linear mixed model with adaptive lasso (KLMM‐AL) to predict phenotypes using high‐dimensional genomic data. We develop two algorithms for estimating parameters from our model and also establish the asymptotic properties of LMM with adaptive lasso when only one dependent observation is available. The proposed KLMM‐AL can account for heterogeneous effect sizes from different genomic regions, capture both additive and nonadditive genetic effects, and adaptively and efficiently select predictive genomic regions and their corresponding effects. Through simulation studies, we demonstrate that KLMM‐AL outperforms most of existing methods. Moreover, KLMM‐AL achieves high sensitivity and specificity of selecting predictive genomic regions. KLMM‐AL is further illustrated by an application to the sequencing dataset obtained from the Alzheimer's disease neuroimaging initiative.

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“…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%

Non-concave penalization in linear mixed-effect models and regularized selection of fixed effects

Ghosh

Thoresen

2017

AStA Adv Stat Anal

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Mixed-effect models are very popular for analyzing data with a hierarchical structure, e.g. repeated observations within subjects in a longitudinal design, patients nested within centers in a multicenter design. However, recently, due to the medical advances, the number of fixed effect covariates collected from each patient can be quite large, e.g. data on gene expressions of each patient, and all of these variables are not necessarily important for the outcome. So, it is very important to choose the relevant covariates correctly for obtaining the optimal inference for the overall study. On the other hand, the relevant random effects will often be low-dimensional and pre-specified. In this paper, we consider regularized selection of important fixed effect variables in linear mixed-effects models along with maximum penalized likelihood estimation of both fixed and random effect parameters based on general non-concave penalties. Asymptotic and variable selection consistency with oracle properties are proved for low-dimensional cases as well as for high-dimensionality of non-polynomial order of sample size (number of parameters is much larger than sample size). We also provide a suitable computationally efficient algorithm for implementation. Additionally, all the theoretical results are proved for a general non-convex optimization problem that applies to several important situations well beyond the mixed model set-up (like finite mixture of regressions etc.) illustrating the huge range of applicability of our proposal.

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Fixed and Random Effects Selection by REML and Pathwise Coordinate Optimization

Cited by 35 publications

References 42 publications

Joint Selection in Mixed Models using Regularized PQL

Joint Selection in Mixed Models using Regularized PQL

Multikernel linear mixed model with adaptive lasso for complex phenotype prediction

Non-concave penalization in linear mixed-effect models and regularized selection of fixed effects

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