Shrinkage estimation in linear mixed models for longitudinal data

Hossain, Shakhawat; Thomson, T.; Ahmed, Ejaz

doi:10.1007/s00184-018-0656-1

Cited by 8 publications

(7 citation statements)

References 26 publications

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“…They showed, in few, that the choice of the shrinkage parameter should guarantee the well known oracle properties in the resulting estimator: The penalized likelihood estimator is root-n consistent if λ n → 0, a set of estimated parameters is set to 0 and the remaining estimators converge asymptotically to a normal distribution when √ nλ n → ∞. Hossain et al (2018) show that under certain regularity conditions and for fixed alternatives B H a = δ = 0, as n increases, the estimatorsβ PT (see in Eq. 35),β P SE (see in Eq.…”

Section: Two-stage Shrinkage Methodsmentioning

confidence: 99%

“…When the ridge parameter increases, the number of individuals and the number of units are quite small and the correlation between explanatory variables is not high, the CRC p outperforms the CC p . Focusing on the shrinkage selection procedures, Hossain et al (2018) compare the performances, in terms of mean squared prediction errors, reached by their PT and PSE estimators against the unrestricted MLE, the restricted MLE, the LASSO and ALASSO methods. They show that their methodology, as the sample size increases and the number of active covariates decreases, brings to better performance than the other estimators except the restricted MLE.…”

Section: Review Of Simulationsmentioning

confidence: 99%

“…To enrich this review, we give a brief look at the real examples described in some of the listed papers. Ahn et al (2012), and Hossain et al (2018) describe the Amsterdam Growth and Health Study, widely used in literature. The Amsterdam Growth and Health Study Data were collected to explore the relationship between lifestyle and health in adolescence and young adulthood.…”

Section: Review Of Real Examplesmentioning

confidence: 99%

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Model selection in linear mixed-effect models

Buscemi

Plaia

2019

AStA Adv Stat Anal

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Linear mixed-effects models are a class of models widely used for analyzing different types of data: longitudinal, clustered and panel data. Many fields, in which a statistical methodology is required, involve the employment of linear mixed models, such as biology, chemistry, medicine, finance and so forth. One of the most important processes, in a statistical analysis, is given by model selection. Hence, since there are a large number of linear mixed model selection procedures available in the literature, a pressing issue is how to identify the best approach to adopt in a specific case. We outline mainly all approaches focusing on the part of the model subject to selection (fixed and/or random), the dimensionality of models and the structure of variance and covariance matrices, and also, wherever possible, the existence of an implemented application of the methodologies set out. Keywords Linear mixed model • Mixed model selection • AIC • BIC • MCP • LASSO • Shrinkage methods • MDL

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Section: Two-stage Shrinkage Methodsmentioning

confidence: 99%

Section: Review Of Simulationsmentioning

confidence: 99%

Section: Review Of Real Examplesmentioning

confidence: 99%

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Model selection in linear mixed-effect models

Buscemi

Plaia

2019

AStA Adv Stat Anal

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“…The main idea behind the estimators that we are about to propose in this section is that the restricted ridge estimators of the previous section can be improved in terms of efficiency by using shrinkage estimation techniques (Mandal et al (2019), Lisawadi et al (2020), Hossain et al (2018), andAhmed (2012)). We will call this class of estimators as ridge-type shrinkage estimators.…”

Section: The Proposed Estimatorsmentioning

confidence: 99%

Ridge-Type Shrinkage Estimators in Low and High Dimensional Beta Regression Model with Application in Econometrics and Medicine

Ahmed¹,

Belaghi²,

Asar³

et al. 2021

Preprint

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Beta regression (BR) model is useful in the analysis of bounded continuous outcomes such as proportions. It is well-known that for any regression model, the presence of multicollinearity leads to poor performance of the maximum likelihood (ML) estimators. The ridge-type estimators have been proposed to alleviate the adverse effects of the multicollinearity. Furthermore, when some predictors have insignificant or weak effects on the outcomes, it is desired to recover as much information as possible from these predictors instead of discarding them all together. In this paper, we proposed ridge-type shrinkage estimators for the low and high dimensional BR model, which address the above two issues simultaneously. We compute the biases and variances of the proposed estimators in closed forms and use Monte Carlo simulations to evaluate their performances. The results show that, both in low and high dimensional data, the performance of the proposed estimators are superior to ridge estimators that discard weak or insignificant predictors. We conclude this paper by applying the proposed methods for two real data from econometric and medicine.

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“…Thus, the main purpose of the longitudinal studies is to estimate the effects of the various parameters and determine their significance while the dependence estimate is treated as secondary. In this context, FitzMaurice and Laird [11] and Sutradhar et al [12] have proposed various likelihood-based and pseudo-likelihood-based estimation procedures to estimate the regression effects but the efficiency of the estimators in these approaches may be questionable, in particular, under multi-collinearity among the predictor variables as considered by Eliot et al [13], Hossain et al [14] and Saleh et al [15].…”

Section: Introductionmentioning

confidence: 99%

Improved mixed model for longitudinal data analysis using shrinkage method

et al. 2018

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The problem of multicollinearity among predictor variables is a frequent issue in longitudinal data analysis. In this context, this paper proposes a mixed ridge regression model via shrinkage methods to analyze such data. Furthermore, in view of obtaining more efficient estimators, we propose preliminary and Stein-type estimators using prior information for fixedeffects parameters. The model parameters are estimated via the EM algorithm. A simulation study is also presented to assess the performance of the estimators under different estimation methods. An application to the HIV data is also illustrated.

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Shrinkage estimation in linear mixed models for longitudinal data

Cited by 8 publications

References 26 publications

Model selection in linear mixed-effect models

Model selection in linear mixed-effect models

Ridge-Type Shrinkage Estimators in Low and High Dimensional Beta Regression Model with Application in Econometrics and Medicine

Improved mixed model for longitudinal data analysis using shrinkage method

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