The Growth Curve Model and Reduced-Rank Regression Methods

  • Gregory C. Reinsel
  • Raja P. Velu
Part of the Lecture Notes in Statistics book series (LNS, volume 136)


One additional general model class which has aspects of reduced-rank regression, especially in its mathematical structure, is that of the growth curve or generalized multivariate ANOVA (GMANOVA) model. This type of model is often applied in the analysis of longitudinal or repeated measures data arising in biomedical and other areas. For these models, the components yjk of the m-dimensional response vector Yk = (y 1k , ..., y mk )’ usually correspond to responses on a single characteristic of a subject made over m distinct times or occasions, with interest in studying features of the mean response over time, and a sample of T independent subjects is available. Corresponding to each subject is an n-dimensional set of time-invariant explanatory variables X k , which may include factors for treatment assignments held fixed over all occasions. In addition, it may be postulated that the pattern of mean response over time for any subject can be represented by some parametric function, e.g., polynomial function, of time whose coefficients are specified to be linear functions of the time-invariant explanatory variables X k .


Growth Curve Growth Curve Model Conditional Model Error Covariance Matrix Blood Sugar Concentration 
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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Gregory C. Reinsel
    • 1
  • Raja P. Velu
    • 2
  1. 1.Department of StatisticsUniversity of Wisconsin, MadisonMadisonUSA
  2. 2.School of ManagementSyracuse UniversitySyracuseUSA

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