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Modeling and Prediction of Multiple Correlated Functional Outcomes

Author

Listed:
  • Jiguo Cao

    (Simon Fraser University)

  • Kunlaya Soiaporn

    (Capital One)

  • Raymond J. Carroll

    (Texas A&M University
    University of Technology Sydney)

  • David Ruppert

    (Cornell University)

Abstract

We propose a copula-based approach for analyzing functional data with correlated multiple functional outcomes exhibiting heterogeneous shape characteristics. To accommodate the possibly large number of parameters due to having several functional outcomes, parameter estimation is performed in two steps: first, the parameters for the marginal distributions are estimated using the skew t family, and then the dependence structure both within and across outcomes is estimated using a Gaussian copula. We develop an estimation algorithm for the dependence parameters based on the Karhunen–Loève expansion and an EM algorithm that significantly reduces the dimension of the problem and is computationally efficient. We also demonstrate prediction of an unknown outcome when the other outcomes are known. We apply our methodology to diffusion tensor imaging data for multiple sclerosis (MS) patients with three outcomes and identify differences in both the marginal distributions and the dependence structure between the MS and control groups. Our proposed methodology is quite general and can be applied to other functional data with multiple outcomes in biology and other fields. Supplementary materials accompanying this paper appear online.

Suggested Citation

  • Jiguo Cao & Kunlaya Soiaporn & Raymond J. Carroll & David Ruppert, 2019. "Modeling and Prediction of Multiple Correlated Functional Outcomes," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 24(1), pages 112-129, March.
    • Handle: RePEc:spr:jagbes:v:24:y:2019:i:1:d:10.1007_s13253-018-00344-0
    DOI: 10.1007/s13253-018-00344-0
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    References listed on IDEAS

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    1. Haocheng Li & John Staudenmayer & Raymond J. Carroll, 2014. "Hierarchical functional data with mixed continuous and binary measurements," Biometrics, The International Biometric Society, vol. 70(4), pages 802-811, December.
    2. Ana-Maria Staicu & Ciprian M. Crainiceanu & Daniel S. Reich & David Ruppert, 2012. "Modeling Functional Data with Spatially Heterogeneous Shape Characteristics," Biometrics, The International Biometric Society, vol. 68(2), pages 331-343, June.
    3. Dubin, Joel A. & Muller, Hans-Georg, 2005. "Dynamical Correlation for Multivariate Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 872-881, September.
    4. Jiguo Cao & Liangliang Wang & Zhongwen Huang & Junyi Gai & Rongling Wu, 2017. "Functional Mapping of Multiple Dynamic Traits," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 22(1), pages 60-75, March.
    5. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389, May.
    6. Lan Zhou & Jianhua Z. Huang & Raymond J. Carroll, 2008. "Joint modelling of paired sparse functional data using principal components," Biometrika, Biometrika Trust, vol. 95(3), pages 601-619.
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