Simultaneous fixed and random effects selection in finite mixture of linear mixed‐effects models

Du, Yeting; Khalili, Abbas; Nešlehová, Johanna; Steele, Russell

doi:10.1002/cjs.11192

Cited by 14 publications

(11 citation statements)

References 31 publications

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“…For instance, the mixing proportions varying as function of (sufficient fixed effect) predictors is similar to that of a mixture of experts model (Jordan & Jacobs 1994;Nguyen & Chamroukhi 2018), although in our approach these predictors do not also affect the mixture component densities. Furthermore, (1) could be considered a special case of a finite mixture of linear mixed effects models (Du et al 2013), where the random effects (and error variance) are common across mixture components, and the fixed effects only enter into the mixing proportions. Perhaps more importantly, and as we shall see in Section 3, the proposed approach means we can leverage the wide array of methods that have been developed for estimation and inference of finite mixture models, and employ them instead for the purposes of SDR.…”

Section: Comparison To Multiple-index and Other Finite Mixture Modelsmentioning

confidence: 99%

Sufficient dimension reduction for clustered data via finite mixture modelling

Hui

Nghiem

2022

Aus NZ J of Statistics

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Summary Sufficient dimension reduction (SDR) is an attractive approach to regression modelling. However, despite its rich literature and growing popularity in application, surprisingly little research has been done on how to perform SDR for clustered data, for example as is commonly arises in longitudinal studies. Indeed, current popular SDR methods have been mostly based on a marginal estimating equation approach. In this article, we propose a new approach to SDR for clustered data based on a combination of finite mixture modelling and mixed effects regression. Finite mixture models offer a flexible means of estimating the fixed effects central subspace, based on slicing the space up and probabilistically clustering observations to each slice (mixture component). Dimension reduction is achieved by having the mixing proportions vary only through the sufficient fixed effect predictors. We then incorporate random effects as a natural means of accounting for correlations within clusters. We employ a Monte Carlo expectation–maximisation algorithm to estimate the model parameters and fixed effects central subspace, and discuss methods for associated uncertainty quantification and prediction. Simulation studies demonstrate that our approach performs strongly against both estimating equation methods for estimating the fixed effects central subspace, and SDR methods which do not account for within‐cluster correlation. Finally, we apply the proposed approach to a data set on air pollutant monitoring across 13 stations in the Eastern United States.

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Section: Comparison To Multiple-index and Other Finite Mixture Modelsmentioning

confidence: 99%

Sufficient dimension reduction for clustered data via finite mixture modelling

Hui

Nghiem

2022

Aus NZ J of Statistics

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“…Pointed out by one reviewer, there is one paper by Du et al. (2013) worked on a mixture of LMM with variable selection that can handle high‐dimensional covariates. However, there are some limitations: (1) The selection of random effects in Du et al.…”

Section: Introductionmentioning

confidence: 99%

“…However, there are some limitations: (1) The selection of random effects in Du et al. (2013)'s paper is through the penalization of the diagonal elements of the random effects. If the diagonal element is estimated to be zero, then all the corresponding off‐diagonal elements are assumed to be zero.…”

Section: Introductionmentioning

confidence: 99%

Model-Based Clustering of High-Dimensional Longitudinal Data via Regularization

Yang

2022

Biometrics

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We propose a model‐based clustering method for high‐dimensional longitudinal data via regularization in this paper. This study was motivated by the Trial of Activity in Adolescent Girls (TAAG), which aimed to examine multilevel factors related to the change of physical activity by following up a cohort of 783 girls over 10 years from adolescence to early adulthood. Our goal is to identify the intrinsic grouping of subjects with similar patterns of physical activity trajectories and the most relevant predictors within each group. The previous analyses conducted clustering and variable selection in two steps, while our new method can perform the tasks simultaneously. Within each cluster, a linear mixed‐effects model (LMM) is fitted with a doubly penalized likelihood to induce sparsity for parameter estimation and effect selection. The large‐sample joint properties are established, allowing the dimensions of both fixed and random effects to increase at an exponential rate of the sample size, with a general class of penalty functions. Assuming subjects are drawn from a Gaussian mixture distribution, model effects and cluster labels are estimated via a coordinate descent algorithm nested inside the Expectation‐Maximization (EM) algorithm. Bayesian Information Criterion (BIC) is used to determine the optimal number of clusters and the values of tuning parameters. Our numerical studies show that the new method has satisfactory performance and is able to accommodate complex data with multilevel and/or longitudinal effects.

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“…Yang (2012) proposed Bayesian variable selection for logistic mixed model with nonparametric random effects. Du et al (2013) considered the fixed and random effects selection in finite mixture of linear mixed-effects models. Lin et al (2013) proposed a two-stage model selection procedure for the linear mixed-effects models.…”

Section: Introductionmentioning

confidence: 99%

Doubly regularized estimation and selection in linear mixed-effects models for high-dimensional longitudinal data

Wang

Song

et al. 2018

Statistics and Its Interface

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The linear mixed-effects model (LMM) is widely used in the analysis of clustered or longitudinal data. This paper aims to address analytic challenges arising from estimation and selection in the application of the LMM to high-dimensional longitudinal data. We develop a doubly regularized approach in the LMM to simultaneously select fixed and random effects. On the theoretical front, we establish large sample properties for the proposed method under the high-dimensional setting, allowing both numbers of fixed effects and random effects to be much larger than the sample size. We present new regularity conditions for the diverging rates, under which the proposed method achieves both estimation and selection consistency. In addition, we propose a new algorithm that solves the related optimization problem effectively so that its computational cost is comparable with that of the Newton-Raphson algorithm for maximum likelihood estimator in the LMM. Through simulation studies we assess performances of the proposed regularized LMM in both aspects of variable selection and estimation. We also illustrate the proposed method by two data analysis examples.

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Simultaneous fixed and random effects selection in finite mixture of linear mixed‐effects models

Cited by 14 publications

References 31 publications

Sufficient dimension reduction for clustered data via finite mixture modelling

Sufficient dimension reduction for clustered data via finite mixture modelling

Model-Based Clustering of High-Dimensional Longitudinal Data via Regularization

Doubly regularized estimation and selection in linear mixed-effects models for high-dimensional longitudinal data

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