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A Bayesian regression model for multivariate functional data

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  • Rosen, Ori
  • Thompson, Wesley K.

Abstract

In this paper we present a model for the analysis of multivariate functional data with unequally spaced observation times that may differ among subjects. Our method is formulated as a Bayesian mixed-effects model in which the fixed part corresponds to the mean functions, and the random part corresponds to individual deviations from these mean functions. Covariates can be incorporated into both the fixed and the random effects. The random error term of the model is assumed to follow a multivariate Ornstein-Uhlenbeck process. For each of the response variables, both the mean and the subject-specific deviations are estimated via low-rank cubic splines using radial basis functions. Inference is performed via Markov chain Monte Carlo methods.

Suggested Citation

  • Rosen, Ori & Thompson, Wesley K., 2009. "A Bayesian regression model for multivariate functional data," Computational Statistics & Data Analysis, Elsevier, vol. 53(11), pages 3773-3786, September.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:11:p:3773-3786
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    References listed on IDEAS

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    1. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, October.
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    7. Wesley K. Thompson & Ori Rosen, 2008. "A Bayesian Model for Sparse Functional Data," Biometrics, The International Biometric Society, vol. 64(1), pages 54-63, March.
    8. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, October.
    9. M. Kessler & A. Rahbek, 2004. "Identification and Inference for Multivariate Cointegrated and Ergodic Gaussian Diffusions," Statistical Inference for Stochastic Processes, Springer, vol. 7(2), pages 137-151, May.
    10. Smith M. & Kohn R., 2002. "Parsimonious Covariance Matrix Estimation for Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1141-1153, December.
    11. Veerabhadran Baladandayuthapani & Bani K. Mallick & Mee Young Hong & Joanne R. Lupton & Nancy D. Turner & Raymond J. Carroll, 2008. "Bayesian Hierarchical Spatially Correlated Functional Data Analysis with Application to Colon Carcinogenesis," Biometrics, The International Biometric Society, vol. 64(1), pages 64-73, March.
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    Cited by:

    1. Martínez-Camblor, Pablo & Corral, Norberto, 2011. "Repeated measures analysis for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3244-3256, December.
    2. Trung Dung Tran & Emmanuel Lesaffre & Geert Verbeke & Joke Duyck, 2021. "Latent Ornstein‐Uhlenbeck models for Bayesian analysis of multivariate longitudinal categorical responses," Biometrics, The International Biometric Society, vol. 77(2), pages 689-701, June.

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