The Growth Curve Model and Reduced-Rank Regression Methods

Abstract

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 .