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Growth Curve Model with Bilinear Random Coefficients

Author

Listed:
  • Shinpei Imori

    (Hiroshima University)

  • Dietrich Rosen

    (Swedish University of Agricultural Sciences
    Linköping University)

  • Ryoya Oda

    (Hiroshima University)

Abstract

In the present paper, we derive a new multivariate model to fit correlated data, representing a general model class. Our model is an extension of the Growth Curve model (also called generalized multivariate analysis of variance model) by additionally assuming randomness of regression coefficients like in linear mixed models. Each random coefficient has a linear or a bilinear form with respect to explanatory variables. In our model, the covariance matrices of the random coefficients is allowed to be singular. This yields flexible covariance structures of response data but the parameter space includes a boundary, and thus maximum likelihood estimators (MLEs) of the unknown parameters have more complicated forms than the ordinary Growth Curve model. We derive the MLEs in the proposed model by solving an optimization problem, and derive sufficient conditions for consistency of the MLEs. Through simulation studies, we confirmed performance of the MLEs when the sample size and the size of the response variable are large.

Suggested Citation

  • Shinpei Imori & Dietrich Rosen & Ryoya Oda, 2022. "Growth Curve Model with Bilinear Random Coefficients," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 477-508, August.
    • Handle: RePEc:spr:sankha:v:84:y:2022:i:2:d:10.1007_s13171-020-00204-5
    DOI: 10.1007/s13171-020-00204-5
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    References listed on IDEAS

    as
    1. Filipiak, Katarzyna & Klein, Daniel, 2017. "Estimation of parameters under a generalized growth curve model," Journal of Multivariate Analysis, Elsevier, vol. 158(C), pages 73-86.
    2. Imori, Shinpei & Rosen, Dietrich von, 2015. "Covariance components selection in high-dimensional growth curve model with random coefficients," Journal of Multivariate Analysis, Elsevier, vol. 136(C), pages 86-94.
    3. Ip, Wai-Cheung & Wu, Mi-Xia & Wang, Song-Gui & Wong, Heung, 2007. "Estimation for parameters of interest in random effects growth curve models," Journal of Multivariate Analysis, Elsevier, vol. 98(2), pages 317-327, February.
    4. Zaixing Li, 2015. "Testing for Random Effects in Growth Curve Models," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(3), pages 564-572, February.
    5. Fujikoshi, Yasunori & von Rosen, Dietrich, 2000. "LR Tests for Random-Coefficient Covariance Structures in an Extended Growth Curve Model," Journal of Multivariate Analysis, Elsevier, vol. 75(2), pages 245-268, November.
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