Longitudinal data analysis using sufficient dimension reduction method

Li, Lexin; Yin, Xiangrong

doi:10.1016/j.csda.2009.04.018

Cited by 16 publications

(18 citation statements)

References 24 publications

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“…We can study the proposed methods in this paper to consider the estimation in the divergent parameters (Wu and Li, 2014;Zhu et al, 2006) and variable selection problems (Chen et al, 2010). One can also use the proposed methods in this paper to consider the measurement errors data (Li and Yin, 2007), longitudinal data (Bi and Qu, 2015;Li and Yin, 2009), missing data (Ding and Wang, 2011;Guo et al, 2014) in a future work. The research for this topic is ongoing.…”

Section: Discussion and Further Researchmentioning

confidence: 99%

Dimension reduction based on conditional multiple index density function

Zhang¹,

He²,

Lü³

et al. 2018

Braz. J. Probab. Stat.

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In this paper, a dimension reduction method is proposed by using the first derivative of the conditional density function of response given predictors. To estimate the central subspace, we propose a direct methodology by taking expectation of the product of predictor and kernel function about response, which helps to capture the directions in the conditional density function. The consistency and asymptotic normality of the proposed estimation methodology are investigated. Furthermore, we conduct some simulations to evaluate the performance of our proposed method and compare with existing methods, and a real data set is analyzed for illustration.

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Section: Discussion and Further Researchmentioning

confidence: 99%

Dimension reduction based on conditional multiple index density function

Zhang¹,

He²,

Lü³

et al. 2018

Braz. J. Probab. Stat.

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“…Li and Yin , who applied the dimension reduction method of Li et al . to settings where both the outcome and the predictors are measured repeatedly over time, first introduced SDR into the analysis of longitudinal data.…”

Section: Discussionmentioning

confidence: 99%

Sufficient dimension reduction for longitudinally measured predictors

Pfeiffer

Forzani

Bura

2011

Statistics in Medicine

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We propose a method to combine several predictors (markers) that are measured repeatedly over time into a composite marker score without assuming a model and only requiring a mild condition on the predictor distribution. Assuming that the first and second moments of the predictors can be decomposed into a time and a marker component via a Kronecker product structure, that accommodates the longitudinal nature of the predictors, we develop first moment sufficient dimension reduction techniques to replace the original markers with linear transformations that contain sufficient information for the regression of the predictors on the outcome. These linear combinations can then be combined into a score that has better predictive performance than the score built under a general model that ignores the longitudinal structure of the data. Our methods can be applied to either continuous or categorical outcome measures. In simulations we focus on binary outcomes and show that our method outperforms existing alternatives using the AUC, the area under the receiver-operator characteristics (ROC) curve, as a summary measure of the discriminatory ability of a single continuous diagnostic marker for binary disease outcomes.

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“…Li and Yin (2009) first considered sufficient dimension reduction for the analysis of longitudinal data. They treated time as a discrete random variable.…”

Section: Introductionmentioning

confidence: 99%

Sufficient Dimension Folding for Regression Mean Function

Xue¹,

Yin²

2014

Journal of Computational and Graphical Statistics

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In this article, we consider sufficient dimension folding for the regression mean function when predictors are matrix-or array-valued. We propose a new concept named central mean dimension folding subspace and its two local estimation methods: folded outer product of gradients estimation (folded-OPG) and folded minimum average variance estimation (folded-MAVE). We establish the asymptotic properties for folded-MAVE. A modified BIC criterion is used to determine the dimensions of the central mean dimension folding subspace. We evaluate the performances of the two local estimation methods by simulated examples and demonstrate the efficacy of folded-MAVE in finite samples. And in particular, we apply our methods to analyze a longitudinal study of primary biliary cirrhosis. Supplementary materials for this article are available online.

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Longitudinal data analysis using sufficient dimension reduction method

Cited by 16 publications

References 24 publications

Dimension reduction based on conditional multiple index density function

Dimension reduction based on conditional multiple index density function

Sufficient dimension reduction for longitudinally measured predictors

Sufficient Dimension Folding for Regression Mean Function

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