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Informative Estimation and Selection of Correlation Structure for Longitudinal Data

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  • Jianhui Zhou
  • Annie Qu

Abstract

Identifying an informative correlation structure is important in improving estimation efficiency for longitudinal data. We approximate the empirical estimator of the correlation matrix by groups of known basis matrices that represent different correlation structures, and transform the correlation structure selection problem to a covariate selection problem. To address both the complexity and the informativeness of the correlation matrix, we minimize an objective function that consists of two parts: the difference between the empirical information and a model approximation of the correlation matrix, and a penalty that penalizes models with too many basis matrices. The unique feature of the proposed estimation and selection of correlation structure is that it does not require the specification of the likelihood function, and therefore it is applicable for discrete longitudinal data. We carry out the proposed method through a groupwise penalty strategy, which is able to identify more complex structures. The proposed method possesses the oracle property and selects the true correlation structure consistently. In addition, the estimator of the correlation parameters follows a normal distribution asymptotically. Simulation studies and a data example confirm that the proposed method works effectively in estimating and selecting the true structure in finite samples, and it enables improvement in estimation efficiency by selecting the true structures.

Suggested Citation

  • Jianhui Zhou & Annie Qu, 2012. "Informative Estimation and Selection of Correlation Structure for Longitudinal Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 701-710, June.
  • Handle: RePEc:taf:jnlasa:v:107:y:2012:i:498:p:701-710
    DOI: 10.1080/01621459.2012.682534
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    File URL: http://hdl.handle.net/10.1080/01621459.2012.682534
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    Cited by:

    1. Liu, Shu & You, Jinhong & Lian, Heng, 2017. "Estimation and model identification of longitudinal data time-varying nonparametric models," Journal of Multivariate Analysis, Elsevier, vol. 156(C), pages 116-136.
    2. Xu, Jianwen & Wang, You-Gan, 2014. "Intra-cluster correlation structure in longitudinal data analysis: Selection criteria and misspecification tests," Computational Statistics & Data Analysis, Elsevier, vol. 80(C), pages 70-77.
    3. Wang, Xianlong & Qu, Annie, 2014. "Efficient classification for longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 78(C), pages 119-134.
    4. Cho, Hyunkeun & Kim, Seonjin & Kim, Mi-Ok, 2017. "Multiple quantile regression analysis of longitudinal data: Heteroscedasticity and efficient estimation," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 334-343.
    5. Kohli, Priya & Garcia, Tanya P. & Pourahmadi, Mohsen, 2016. "Modeling the Cholesky factors of covariance matrices of multivariate longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 87-100.
    6. Cho, Hyunkeun, 2016. "The analysis of multivariate longitudinal data using multivariate marginal models," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 481-491.
    7. repec:bla:scjsta:v:44:y:2017:i:4:p:932-950 is not listed on IDEAS

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