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Regularized reduced rank growth curve models

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  • Takane, Yoshio
  • Jung, Kwanghee
  • Hwang, Heungsun

Abstract

The growth curve model (GCM), also known as GMANOVA, is a useful technique for investigating patterns of change in repeated measurement data over time and examining the effects of predictor variables on temporal trajectories. The reduced rank feature had been introduced previously to GCM for capturing redundant information in the criterion variables in a parsimonious way. In this paper, a ridge type of regularization was incorporated to obtain better estimates of parameters. Separate ridge parameters were allowed in column and row regressions, and the generalized singular value decomposition (GSVD) was applied for rank reduction. It was shown that the regularized estimates of parameters could be obtained in closed form for fixed values of ridge parameters. Permutation tests were used to identify the best dimensionality in the solution, and the K-fold cross validation method was used to choose optimal values of the ridge parameters. A bootstrap method was used to assess the reliability of parameter estimates. The proposed model was further extended to a mixture of GMANOVA and MANOVA. Illustrative examples were given to demonstrate the usefulness of the proposed method.

Suggested Citation

  • Takane, Yoshio & Jung, Kwanghee & Hwang, Heungsun, 2011. "Regularized reduced rank growth curve models," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 1041-1052, February.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:2:p:1041-1052
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    References listed on IDEAS

    as
    1. Yoshio Takane & Sunho Jung, 2008. "Regularized Partial and/or Constrained Redundancy Analysis," Psychometrika, Springer;The Psychometric Society, vol. 73(4), pages 671-690, December.
    2. Yoshio Takane & Heungsun Hwang & Hervé Abdi, 2008. "Regularized Multiple-Set Canonical Correlation Analysis," Psychometrika, Springer;The Psychometric Society, vol. 73(4), pages 753-775, December.
    3. Yoshio Takane & Tadashi Shibayama, 1991. "Principal component analysis with external information on both subjects and variables," Psychometrika, Springer;The Psychometric Society, vol. 56(1), pages 97-120, March.
    4. Arnold Wollenberg, 1977. "Redundancy analysis an alternative for canonical correlation analysis," Psychometrika, Springer;The Psychometric Society, vol. 42(2), pages 207-219, June.
    5. J. Douglas Carroll & Sandra Pruzansky & Joseph Kruskal, 1980. "Candelinc: A general approach to multidimensional analysis of many-way arrays with linear constraints on parameters," Psychometrika, Springer;The Psychometric Society, vol. 45(1), pages 3-24, March.
    6. Yoshio Takane & Henk Kiers & Jan Leeuw, 1995. "Component analysis with different sets of constraints on different dimensions," Psychometrika, Springer;The Psychometric Society, vol. 60(2), pages 259-280, June.
    7. Takane, Yoshio & Hwang, Heungsun, 2007. "Regularized linear and kernel redundancy analysis," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 394-405, September.
    8. Takane, Yoshio & Jung, Sunho, 2009. "Regularized nonsymmetric correspondence analysis," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 3159-3170, June.
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