Double Penalized Quantile Regression for the Linear Mixed Effects Model

Li, Hanfang; Liu, Yuan; Luo, Youxi

doi:10.1007/s11424-020-9065-4

Cited by 7 publications

(7 citation statements)

References 22 publications

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“…It is important to identify the significant factor effects when seeking to build a dependable model, especially when the quantity of factor effects is larger than the quantity of treatment combinations. The LASSO dimension reduction method can identify the significant variables by adding a convex penalty term, 50 which has been proven to be effective in improving both the prediction accuracy and model interpretability as it combines the good characteristics from the ridge regression and subset selections 51,52 . However, the LASSO has been found to have several limitations in practice because all these features enforce sparsity and perform feature selection—that is, when the sample size is less than the feature size, some critical features may be excluded from the model.…”

Section: Methods: Proposed Dual‐response Surface Methods Frameworkmentioning

confidence: 99%

“…The LASSO dimension reduction method can identify the significant variables by adding a convex penalty term, 50 which has been proven to be effective in improving both the prediction accuracy and model interpretability as it combines the good characteristics from the ridge regression and subset selections. 51,52 However, the LASSO has been found to have several limitations in practice because all these features enforce sparsity and perform feature selection-that is, when the sample size is less than the feature size, some critical features may be excluded from the model. Although it is possible to relax the strength of the penalty, this could lead to the inclusion of irrelevant variables in the model.…”

Section: Significant Factor Effects Identificationmentioning

confidence: 99%

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Framework for robust parameter design and optimization of reliability characteristics

Zhao

et al. 2022

Quality & Reliability Eng

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To achieve better product quality, the dual‐response surface has been widely used to simultaneously achieve targets for the mean and reduced variance. The general assumption is that the experimental data are normally distributed without censoring. However, reliability data are usually non‐normally distributed and censored. Consequently, the classical dual‐response surface method may not be suitable for handling reliability data. This study proposed a dual‐response surface method based on robust parameter design (RPD) for reliability data. First, a percentile lifetime and an interquartile range (IQR) were used for the location and dispersion effects, respectively. A two‐stage method was then developed to identify the effects of significant factors. During the first stage, the Boruta algorithm was employed for factor effect selection, and during the second stage, the least absolute shrinkage and selection operator (LASSO) dimension reduction method was used to determine the final significant factor effects. Finally, a modified standard particle swarm optimization (SPSO) algorithm was adopted to determine the optimal solution. The proposed method was demonstrated using an industrial thermostat experiment. Compared with other methods, the proposed method performed better over various warranty periods, particularly for the 10th percentile.

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Section: Methods: Proposed Dual‐response Surface Methods Frameworkmentioning

confidence: 99%

Section: Significant Factor Effects Identificationmentioning

confidence: 99%

Framework for robust parameter design and optimization of reliability characteristics

Zhao

et al. 2022

Quality & Reliability Eng

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“…Li (2020) [9] proposed a double penalized quantile regression estimation for the LME model that finds αi ∈ R l and β ∈ R h , i = 1, . .…”

Section: Double Penalized Expectile Regressionmentioning

confidence: 99%

“…where the so-called check function of under θth level quantile regression is denoted by γ θ (k) = k(θ − I(k < 0)). Equation ( 7) can simultaneously perform a variable selection operation and estimate the mixed expectile functions of the response variable, as stated in Li (2020) [9].…”

Section: Double Penalized Expectile Regressionmentioning

confidence: 99%

“…For different types of data, Peng (2021) [8] illustrated the practical utility of quantile regression in actual survival data analysis through two cases. Li (2020) [9] constructed a double penalized quantile regression method, and used the Lasso algorithm to solve the parameters. It proved that the estimated accuracy of the double penalized quantile regression is better than the other quantile regression.…”

Section: Introductionmentioning

confidence: 99%

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Double Penalized Expectile Regression for Linear Mixed Effects Model

et al. 2022

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This paper constructs the double penalized expectile regression for linear mixed effects model, which can estimate coefficient and choose variable for random and fixed effects simultaneously. The method based on the linear mixed effects model by cojoining double penalized expectile regression. For this model, this paper proposes the iterative Lasso expectile regression algorithm to solve the parameter for this mode, and the Schwarz Information Criterion (SIC) and Generalized Approximate Cross-Validation Criterion (GACV) are used to choose the penalty parameters. Additionally, it establishes the asymptotic normality of the expectile regression coefficient estimators that are suggested. Though simulation studies, we examine the effects of coefficient estimation and the variable selection at varying expectile levels under various conditions, including different signal-to-noise ratios, random effects, and the sparsity of the model. In this work, founding that the proposed method is robust to various error distributions at every expectile levels, and is superior to the double penalized quantile regression method in the robustness of excluding inactive variables. The suggested method may still accurately exclude inactive variables and select important variables with a high probability for high-dimensional data. The usefulness of doubly penalized expectile regression in applications is illustrated through a case study using CD4 cell real data.

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