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Longitudinal Functional Principal Component Analysis

  • Sonja Greven
  • Ciprian Crainiceanu
  • Brian Caffo
  • Daniel Reich
Conference paper
Part of the Contributions to Statistics book series (CONTRIB.STAT.)

Abstract

We introduce models for the analysis of functional data observed at multiple time points. The model can be viewed as the functional analog of the classical mixed effects model where random effects are replaced by random processes. Computational feasibility is assured by using principal component bases. The methodology is motivated by and applied to a diffusion tensor imaging (DTI) study on multiple sclerosis.

Keywords

Principal Component Analysis Multiple Sclerosis Random Effect Pattern Recognition Stochastic Process 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Greven, S., Crainiceanu, C.M., Caffo, B., Reich, D.: Longitudinal functional principal component analysis. Electron. J. Stat. 4, 1022–1054 (2010)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Brumback, B.A., Rice, J.A.: Smoothing spline models for the analysis of nested and crossed samples of curves. J. Am. Stat. Assoc. 93, 961–976 (1998)MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Di, C.Z., Crainiceanu, C.M., Caffo, B.S., Punjabi, N.M.:Multilevel functional principal component analysis. Ann. Appl. Stat. 3, 458–488 (2008)4. Greven, S., Kneib, T.: On the Behaviour of Marginal and Conditional AIC in Linear Mixed Models. Biometrika 97, 773–789 (2010)Google Scholar
  4. 4.
    Guo, W.: Functional mixed effects models. Biometrics 58: 121-128 (2002)MATHGoogle Scholar
  5. 5.
    Laird, N., Ware, J.H.: Random-effects models for longitudinal data. Biometrics 38, 963–974 (1982)MATHGoogle Scholar
  6. 6.
    Morris, J.S., Carroll, R.J.: Wavelet-based functional mixed models. J. Roy. Stat. Soc. B 68, 179–199 (2006)MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Ramsay, J.O., Silverman, B.W.: Functional data analysis (Second Edition). Springer (2005)Google Scholar
  8. 8.
    Yao, F., M¨uller, H.G., Wang, J.L.: Functional data analysis for sparse longitudinal data. J. Am. Stat. Assoc. 100: 577-590 (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Sonja Greven
    • 1
  • Ciprian Crainiceanu
    • 2
  • Brian Caffo
    • 2
  • Daniel Reich
    • 3
  1. 1.Ludwig-Maximilians-Universität MünchenMunichGermany
  2. 2.Johns Hopkins UniversityBaltimoreUSA
  3. 3.National Institutes of HealthBethesdaUSA

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