IDEAS home Printed from https://ideas.repec.org/a/spr/sankha/v84y2022i2d10.1007_s13171-020-00204-5.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13171-020-00204-5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13171-020-00204-5?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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. 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.
    3. 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.
    4. 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.
    5. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Petzold, Max & Jonsson, Robert, 2003. "Maximum Likelihood Ratio based small-sample tests for random coefficients in linear regression," Working Papers in Economics 102, University of Gothenburg, Department of Economics.
    2. Pan, Yating & Fei, Yu & Ni, Mingming & Nummi, Tapio & Pan, Jianxin, 2022. "Growth curve mixture models with unknown covariance structures," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    3. Siotani, Minoru & Wakaki, Hirofumi, 2006. "Contributions to multivariate analysis by Professor Yasunori Fujikoshi," Journal of Multivariate Analysis, Elsevier, vol. 97(9), pages 1914-1926, October.
    4. Maurizio Lanfranchi & Carlo Giannetto, 2013. "The consumption of wine: a analysis of market conducted in Sicily," Romanian Statistical Review, Romanian Statistical Review, vol. 61(11), pages 21-31, December.
    5. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sankha:v:84:y:2022:i:2:d:10.1007_s13171-020-00204-5. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.