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Joint modelling of paired sparse functional data using principal components


  • Lan Zhou
  • Jianhua Z. Huang
  • Raymond J. Carroll


We propose a modelling framework to study the relationship between two paired longitudinally observed variables. The data for each variable are viewed as smooth curves measured at discrete time-points plus random errors. While the curves for each variable are summarized using a few important principal components, the association of the two longitudinal variables is modelled through the association of the principal component scores. We use penalized splines to model the mean curves and the principal component curves, and cast the proposed model into a mixed-effects model framework for model fitting, prediction and inference. The proposed method can be applied in the difficult case in which the measurement times are irregular and sparse and may differ widely across individuals. Use of functional principal components enhances model interpretation and improves statistical and numerical stability of the parameter estimates. Copyright 2008, Oxford University Press.

Suggested Citation

  • 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.
  • Handle: RePEc:oup:biomet:v:95:y:2008:i:3:p:601-619

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    Cited by:

    1. Shin, Hyejin & Lee, Seokho, 2015. "Canonical correlation analysis for irregularly and sparsely observed functional data," Journal of Multivariate Analysis, Elsevier, vol. 134(C), pages 1-18.
    2. repec:spr:metrik:v:81:y:2018:i:1:d:10.1007_s00184-017-0634-z is not listed on IDEAS
    3. Wei, Jiawei & Zhou, Lan, 2010. "Model selection using modified AIC and BIC in joint modeling of paired functional data," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1918-1924, December.
    4. 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.
    5. Gertheiss, Jan & Goldsmith, Jeff & Staicu, Ana-Maria, 2017. "A note on modeling sparse exponential-family functional response curves," Computational Statistics & Data Analysis, Elsevier, vol. 105(C), pages 46-52.
    6. Hans-Georg Müller & Wenjing Yang, 2010. "Dynamic relations for sparsely sampled Gaussian processes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(1), pages 1-29, May.
    7. Lijie Gu & Li Wang & Wolfgang Härdle & Lijian Yang, 2014. "A simultaneous confidence corridor for varying coefficient regression with sparse functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(4), pages 806-843, December.
    8. Mengmeng Guo & Lhan Zhou & Jianhua Z. Huang & Wolfgang Karl Härdle, 2013. "Functional Data Analysis of Generalized Quantile Regressions," SFB 649 Discussion Papers SFB649DP2013-001, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.

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